Introduction to MATLAB® · The first lesson of Introduction to MATLAB® provides an overview of the MATLAB® programming environment, performing mathematical calculations in the

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Developed by:

Aaron J. Brumbaugh

[email protected]

Summer 2018

Introduction to MATLAB®

Instructional Unit

Title 2 Distribution A.

TABLE OF CONTENTS

Table of Contents................................................................................................................................................... 2

1. Mathematics and Variables in Matlab ® (Part 1) ............................................................................................ 6

1.1. Introduction ................................................................................................................................................... 6

1.2. Materials ........................................................................................................................................................ 6

1.3. Overview of Plan ............................................................................................................................................ 6

1.3.1. Learning Target – MATLAB.1 .................................................................................................................. 6




1.4. Guided Notes ................................................................................................................................................. 8

1.5. Assessment – Practice Problems .................................................................................................................. 12

1.6. Answer Keys ................................................................................................................................................. 14

1.6.1. Guided Notes ........................................................................................................................................ 14

1.6.2. Practice Problems ................................................................................................................................. 17

1.7. Resources ..................................................................................................................................................... 21

2. Mathematics and Variables in Matlab ® (Part 2) .......................................................................................... 22

2.1. Introduction ................................................................................................................................................. 22

2.2. Materials ...................................................................................................................................................... 22

2.3. Overview of Plan .......................................................................................................................................... 22

2.3.1. Learning Target – MATLAB.5 ................................................................................................................ 22

2.4. Guided Notes ............................................................................................................................................... 23


2.6. Answer Keys ................................................................................................................................................. 28

2.6.1. Guided Notes ........................................................................................................................................ 28


2.7. Resources ..................................................................................................................................................... 32

3. Creating Scripts in MATLAB® ........................................................................................................................ 33

3.1. Introduction ................................................................................................................................................. 33

3.2. Materials ...................................................................................................................................................... 33

3.3. Overview of Plan .......................................................................................................................................... 33




3.4. Guided Notes ............................................................................................................................................... 34


3.6. Answer Keys ................................................................................................................................................. 39


3.6.1. Guided Notes ........................................................................................................................................ 40


3.7. Resources ..................................................................................................................................................... 46

4. Comments and Formatting Strings ............................................................................................................... 47

4.1. Introduction ................................................................................................................................................. 47

4.2. Materials ...................................................................................................................................................... 47

4.3. Overview of Plan .......................................................................................................................................... 47

4.3.1. Learning TargeT – MATLAB.9 ............................................................................................................... 47

4.3.2. Learning Target – MATLAB.10 .............................................................................................................. 48

4.4. Guided Notes ............................................................................................................................................... 48


4.6. Answer Keys ................................................................................................................................................. 55

4.6.1. Guided Notes ........................................................................................................................................ 55


4.7. Resources ..................................................................................................................................................... 63

5. Matrices and Matrix Operations .................................................................................................................. 64

5.1. Introduction ................................................................................................................................................. 64

5.2. Materials ...................................................................................................................................................... 64

5.3. Overview of Plan .......................................................................................................................................... 64





5.4. Guided Notes ............................................................................................................................................... 66


5.6. Answer Keys ................................................................................................................................................. 71

5.6.1. Guided Notes ........................................................................................................................................ 71


5.7. Resources ..................................................................................................................................................... 78

6. Graphing in MATLAB® .................................................................................................................................. 79

6.1. Introduction ................................................................................................................................................. 79

6.2. Materials ...................................................................................................................................................... 79

6.3. Overview of Plan .......................................................................................................................................... 79




6.4. Guided Notes ............................................................................................................................................... 81



6.6. Answer Keys ................................................................................................................................................. 86

6.6.1. Guided Notes ........................................................................................................................................ 86


6.7. Resources ..................................................................................................................................................... 93

7. Conditional Statements in MATLAB® ........................................................................................................... 94

7.1. Introduction ................................................................................................................................................. 94

7.2. Materials ...................................................................................................................................................... 94

7.3. Overview of Plan .......................................................................................................................................... 94




7.4. Guided Notes ............................................................................................................................................... 96

7.5. Assessment – Practice Problems ................................................................................................................ 103

7.6. Answer Keys ............................................................................................................................................... 105

7.6.1. Guided Notes ...................................................................................................................................... 105

7.6.2. Practice Problems ............................................................................................................................... 113

7.7. Resources ................................................................................................................................................... 116

8. Introduction to Loops: For Loops ............................................................................................................... 117

8.1. Introduction ............................................................................................................................................... 117

8.2. Materials .................................................................................................................................................... 117

8.3. Overview of Plan ........................................................................................................................................ 117

8.3.1. Learning Target – MATLAB.21 ............................................................................................................ 117


8.4. Guided Notes ............................................................................................................................................. 118


8.6. Answer Keys ............................................................................................................................................... 126

8.6.1. Guided Notes ...................................................................................................................................... 126


8.7. Resources ................................................................................................................................................... 136

9. Introduction to Loops: While Loops ........................................................................................................... 137

9.1. Introduction ............................................................................................................................................... 137

9.2. Materials .................................................................................................................................................... 137

9.3. Overview of Plan ........................................................................................................................................ 137



9.4. Guided Notes ............................................................................................................................................. 138


9.6. Answer Keys ............................................................................................................................................... 145


9.6.1. Guided Notes ...................................................................................................................................... 145


9.7. Resources ................................................................................................................................................... 154

9.8. Image Credits ............................................................................................................................................. 154


1. MATHEMATICS AND VARIABLES IN MATLAB ® (PART 1)

Primary Resource (if applicable): https://www.mathworks.com/help/matlab/

1.1. INTRODUCTION

The first lesson of Introduction to MATLAB® provides an overview of the MATLAB®

programming environment, performing mathematical calculations in the command window,

and working with variables.

1.2. MATERIALS

Each student will need:

PC/Mac with MATLAB® installed

Copy of Introduction to MATLAB® - Mathematics and Variables in MATLAB® (Part 1)

guided notes (these may be printed or shared digitally):

https://padlet.com/abrumbaugh/introMatlab

The teacher will need:

PC/MAC with MATLAB® installed

Ceiling projector or method for displaying their computer screen for students to see


answer key

1.3. OVERVIEW OF PLAN

This lesson can be taught via direct instruction or student-paced learning through online videos

located at https://padlet.com/abrumbaugh/introMatlab.

1.3.1. LEARNING TARGET – MATLAB.1

Be able to describe MATLAB® and its general capabilities.

Students should understand that MATLAB® is a computational programming language that is

used in the fields of science, engineering, and many others for a variety of reasons. The

software allows users to perform a wide variety of calculations from simple to complex and has

a strong, yet natural, programming environment that allows users to automate their work.

MATLAB® is very beneficial as it can quickly calculate a series of computations on a large set of

https://www.mathworks.com/help/matlab/




data, create easy-to-read dynamic models, and run complex simulations that help users better

understand the real world phenomena that they are studying.


Be able to identify the different parts of the MATLAB® window and explain what they do.

Students should have a general understanding of the MATLAB® window that is displayed on the

screen when they run the program. This is very important as some of the materials for this unit

will refer to specific parts of the window such as the editor or command window.

The current folder section displays any MATLAB® files that are in the working directory. The

working directory is initially set up to the MATLAB® folder when the software is installed on the

computer, however it can be changed at any time. Any files saved outside of the working

directory will not be found by MATLAB® and thus inaccessible. It is recommended that students

save or move their work to the working directory of MATLAB®.

The command window is a space where students can type individual commands to see what

they do. It is ideal for testing out a specific line of code to see what it does or single line

calculations. The command window is also where the output of any script/program created in

the editor will display.

The editor is where scripts (i.e., programs) are created. If a problem requires multiple

calculations or commands to be done in succession, the editor is the space to be working in. It is

also important to note that work in the editor can be saved as an .m file (MATLAB®’s file type)

and used again later, whereas work in the command window cannot be saved. The editor will

run any lines of code written in the space from the top down, one line at a time until it reaches

the end of the script.

The workspace is an area of the MATLAB® window that displays any variables that have been

created by the command window or editor. Along with the variable names, students will be

able to see the current value of each variable as well as the type of each variable (e.g., double,

logical).


Be able to perform basic mathematical operations in MATLAB®.

Throughout this course, students will use a variety of mathematical operations in MATLAB®

ranging from basic (e.g., addition, subtraction) to more advanced (e.g., modular arithmetic,

trigonometry). In this first lesson, students need to become familiar with performing addition,


subtraction, multiplication, and division, as they are the backbone to many of the problems that

appear throughout this unit. Furthermore, students will need to understand and be able to

follow many of the calculations in this lesson and throughout the unit.

It is important to note that one issue that may arise with this learning target is with regards to

multiplication. MATLAB® does not execute “implied” multiplication such as 2(3). Typing such

an expression into the command window would result in a syntax error. Students will need to

explicitly type an asterisk (*) to tell MATLAB® to multiply the two numbers (e.g., 2 ∗ 3).


Be able to declare and use variables in MATLAB®.

Like most programming languages, MATLAB® uses variables in its programming features.

Students should understand that variables are used to store data that is either user defined or

generated within a program. The values stored in a variable can be recalled and used later in a

program.

It is important that students understand how to declare a variable, that is, how to assign a

specific value or expression to a variable. When declaring a variable, the variable’s name should

come first followed by an equal sign followed by the value or expression that the variable

should be equal to (i.e., variable name = value/expression). The variable can have any name;

however, the name must begin with a letter (e.g., num is a valid name, 2num is NOT a valid

name). Students also should be aware that variable names are case sensitive, meaning that

num, Num, and NUM are three different variables. A variable’s value is not permanent and can

be overwritten or changed throughout a program if necessary.

Once defined, variables can be used in calculations in place of their numeric counterpart. For

instance, if num = 12,345,678, and we wanted to find a number double in value, we could type

num * 2 as opposed to 12,345,678 * 2.

1.4. GUIDED NOTES


Mathematics and Variables in MATLAB® (Part 1)

Name:___________________________ Date:_____________ Period:__________

Learning Targets:


Figure 1: MATLAB Window. The MathWorks©, Inc.: MATLAB® version R2018a. Screenshot by author.

MATLAB.1 – Be able to describe MATLAB® and its general capabilities.

MATLAB.2 – Be able to identify the different parts of the MATLAB® window and explain what

they do.

MATLAB.3 – Be able to perform basic mathematical operations in MATLAB®.

MATLAB.4 – Be able to declare and use variables in MATLAB®.

What is MATLAB®? (MATLAB.1)

MATLAB® (short for Matrix Laboratory) is a mathematical software package that is primarily

used for numerical ___________________ and data _________________________, along with

various _______________________ capabilities.

The MATLAB® Window (MATLAB.2)

MATLAB® Basics (MATLAB.3)

MATLAB® can be used to perform various mathematical computations just like a calculator.

Here are some of the more commonly used mathematical operations (Table 1):

Current Folder – Editor –

Command Window –

Workspace –


Operation Symbol

Addition +

Subtraction -

Multiplication *

Division /

Exponent/Power ^ Table 1: MATLAB Math Operations

Example 1 (MATLAB.3)

Use MATLAB® to calculate each of the following. Be sure to use order of operations.

A) 3(9 − 2)3 − 1234 B) 1804

4+ 80(7 − 10) C)

12+5(11+3)5

6(2−6)2

What are Variables in MATLAB®? (MATLAB.4)

A variable in MATLAB® (and other programming languages) is a letter or word used to

______________ data.

Declaring a variable means to assign a specific ______________________________ to a

variable.

Syntax: variableName = value/expression

Examples: 𝑥 = 5 𝑛𝑢𝑚𝑏𝑒𝑟 = 3 ∗ 𝑥 − 2

NOTE: Variable names must begin with a letter, and the variable name must be typed on the

left side of the “=” sign.



A) Create a variable named y that has a value of 10.

B) Create a variable named dog that has a value of -3.

C) Create a variable named spam that has a value of 7.5.

D) Use parts A – C to determine the value of 3𝑦 − (𝑠𝑝𝑎𝑚

𝑑𝑜𝑔) + 9. Store your answer as value.


Examine the following code. Determine the final value of x.

𝑥 = 4

𝑦 = 2 ∗ 𝑥

𝑥 = 9 ∗ 𝑦

𝑥 = 𝑦

𝑦 = 𝑥/2

𝑧 = 𝑥 + 𝑦

Cleaning up the Command Window

The following commands can be typed within the Command Window:

clc – Clears all text in the Command Window

clear – Erases all variables currently being used in the workspace

clear variableName – Erases a specific variable currently being used in the workspace

; – Suppresses the output in MATLAB®


1.5. ASSESSMENT – PRACTICE PROBLEMS

Students should be able to complete the practice problems below to demonstrate their

understanding. Encourage students to refer to their notes, research online, or work together to

overcome any issues they may encounter. It is recommended that students receive a digital

version of these problems so that they can copy and paste their answers straight from

MATLAB®.

Practice Problems:

1) Use MATLAB® to perform each calculation. Be sure to use proper syntax and order of

operations.

A) 11(12 − 7)2 − 2(4) B) (21

7) (8) +

(2−5)2

9 C)

12(8−9)3+21

(−3−8)2

2) Write down the code that gives the variable Spam the value of 14.

3) If a = 15, b = -6, and c = 21, what is the value of 𝑎−𝑏

𝑐+ 3𝑐 − 𝑎𝑏2?

4) Examine the following code and determine the value of cat at the end.

𝑝𝑖𝑔 = 7

𝑑𝑜𝑔 = −5

𝑐𝑎𝑡 = 3

𝑝𝑖𝑔 = 𝑑𝑜𝑔 + 𝑐𝑎𝑡

𝑑𝑜𝑔 = 3 ∗ 𝑐𝑎𝑡 − 4 ∗ 𝑑𝑜𝑔

𝑐𝑎𝑡 = 3 + 𝑐𝑎𝑡 − 𝑑𝑜𝑔 ∗ 𝑝𝑖𝑔


52 feet

120 feet

5) Use MATLAB® to calculate the volume of a cylinder that has a radius of 5 cm and a height of

24 cm. Be sure to write your code in the space below along with your answer.

NOTE: The formula for volume of a cylinder is 𝑉 = 𝜋𝑟2ℎ and to type 𝜋 into MATLAB® use the

keyword pi.

6) A person wants to do some landscaping in their backyard. They would like to fence in the

backyard as well as plant a new type of grass. An outline of the space is shown below. The

backyard is a rectangle and the fence will be installed along the border of the backyard.

The fence to be used costs $79.20 for an 8-foot long panel and must be purchased in whole

panels (cannot buy part of a panel). The grass seed is $13.39 for a 3-pound bag, and will cover

an area of about 1500 square feet.

Use MATLAB® and the above information to determine the total cost of landscaping the

backyard.

Break the Problem Down:

A) How much fence will be needed? Create a variable to store this information. Write your

code in the space below.


B) How much grass seen will be needed? Create a variable to store this information. Write

your code in the space below. (HINT: How do you find the area of the shape?)

C) Use the information you found and the variables you created in A and B to determine

the total cost of the landscaping project.

1.6. ANSWER KEYS

1.6.1. GUIDED NOTES



Name:___________________________ Date:_____________ Period:__________

Learning Targets:

MATLAB.1 – Be able to describe MATLAB and its general capabilities.

MATLAB.2 – Be able to identify the different parts of the MATLAB window and explain what

they do.

MATLAB.3 – Be able to perform basic mathematical operations in MATLAB.

MATLAB.4 – Be able to declare and use variables in MATLAB.

What is MATLAB? (MATLAB.1)

MATLAB (short for Matrix Laboratory) is a mathematical software package that is primarily used

for numerical COMPUTATION and data ANALYSIS along with various PROGRAMMING

capabilities.


Figure 1: MATLAB Window. The MathWorks©, Inc.: MATLAB® version R2018a. Screenshot by author.

The MATLAB Window (MATLAB.2)

MATLAB Basics (MATLAB.3)

MATLAB can be used to perform various mathematical computations just like a calculator. Here

are some of the more commonly used mathematical operations (Table 1):

Operation Symbol

Addition +

Subtraction -

Multiplication *

Division /

Exponent/Power ^ Table 1: MATLAB Math Operations


Use MATLAB to calculate each of the following. Be sure to use order of operations.

Current Folder –

SHOWS ALL

MATLAB FILES

CREATED IN

THE

WORKING

DIRECTORY

Editor –

SPACE USED TO WRITE

SCRIPTS/PROGRAMS

Command Window –

SPACE USED TO TEST COMMANDS

(EXECUTES ONE LINE AT A TIME).

OUTPUT OF A PROGRAM ALSO IS

DISPLAYED HERE.

Workspace –

SHOWS ALL

VARIABLES

CURRENTLY

IN USE

ALONG

WITH THEIR

VALUES


A) 3(9 − 2)3 − 1234 B) 1804

4+ 80(7 − 10) C)

12+5(11+3)5

6(2−6)2

What are Variables in MATLAB? (MATLAB.4)

A variable in MATLAB (and other programming languages) is a letter or word used to STORE

data.

Declaring a variable means to assign a specific VALUE OR EXPRESSION to a variable.

Syntax: variableName = value/expression

Examples: 𝑥 = 5 𝑛𝑢𝑚𝑏𝑒𝑟 = 3 ∗ 𝑥 − 2

NOTE: Variable names must begin with a letter, and the variable name must be typed on the

left side of the “=” sign.


A) Create a variable named y that has a value of 10.

y = 10

B) Create a variable named dog that has a value of -3.

dog = -3

C) Create a variable named spam that has a value of 7.5.

spam = 7.5

D) Use parts A – C to determine the value of 3𝑦 − (𝑠𝑝𝑎𝑚

𝑑𝑜𝑔) + 9. Store your answer as value.

value = 41.5



Examine the following code. Determine the final value of x.

𝑥 = 4

𝑦 = 2 ∗ 𝑥

𝑥 = 9 ∗ 𝑦

𝑥 = 𝑦

𝑦 = 𝑥/2

𝑧 = 𝑥 + 𝑦

Cleaning up the Command Window

The following commands can be typed within the Command Window:

clc – Clears all text in the Command Window

clear – Erases all variables currently being used in the workspace

clear variableName – Erases specific variable currently being used in the workspace

; – Suppresses the output in MATLAB

1.6.2. PRACTICE PROBLEMS

Practice Problems:

1) Use MATLAB to perform each calculation. Be sure to use proper syntax and order of

operations.

A) 11(12 − 7)2 − 2(4) B) (21

7) (8) +

(2−5)2

9 C)

12(8−9)3+21

(−3−8)2

x y z

4 - -

4 8 -

72 8 -

8 8 -

8 4 -

8 4 12


2) Write down the code that gives the variable Spam the value of 14.

3) If a = 15, b = -6, and c = 21, what is the value of 𝑎−𝑏

𝑐+ 3𝑐 − 𝑎𝑏2?

4) Examine the following code and determine the value of cat at the end.

𝑝𝑖𝑔 = 7

𝑑𝑜𝑔 = −5

𝑐𝑎𝑡 = 3

𝑝𝑖𝑔 = 𝑑𝑜𝑔 + 𝑐𝑎𝑡

𝑑𝑜𝑔 = 3 ∗ 𝑐𝑎𝑡 − 4 ∗ 𝑑𝑜𝑔

𝑐𝑎𝑡 = 3 + 𝑐𝑎𝑡 − 𝑑𝑜𝑔 ∗ 𝑝𝑖𝑔

pig dog cat

7 - -

7 -5 -

7 -5 3

7 29 3

7 29 -197


52 feet

120 feet

5) Use MATLAB to calculate the volume of a cylinder that has a radius of 5 cm and a height of

24 cm. Be sure to write your code in the space below, along with your answer.

NOTE: The formula for volume of a cylinder is 𝑉 = 𝜋𝑟2ℎ and to type 𝜋 into MATLAB use the

keyword pi.

or

6) A person wants to do some landscaping in their backyard. They would like to fence in the

backyard as well as plant a new type of grass. An outline of the space is shown below. The

backyard is a rectangle and the fence will be installed along the border of the backyard.

The fence to be used costs $79.20 for an 8-foot long panel and must be purchased in whole

panels (cannot buy part of a panel). The grass seed is $13.39 for a 3-pound bag, and will cover

an area of about 1500 square foot.

Use MATLAB and the above information to determine the total cost of landscaping the

backyard.

Break the Problem Down:


A) How much fence will be needed? Create a variable to store this information. Write your

code in the space below.

First, students should find the perimeter of the yard by adding up all the side lengths.

This will give students the total number of feet of fence needed (344 feet), but since we

can only buy the fence in 8-ft panels, students will need to divide the perimeter by 8.

Students should find that 43 panels will need to be purchased.

B) How much grass seen will be needed? Create a variable to store this information. Write

your code in the space below. (HINT: How do you find the area of the shape?)

For this question, students will have to find the area of the backyard using the formula

𝐴𝑟𝑒𝑎 = 𝑙𝑒𝑛𝑔𝑡ℎ ∗ 𝑤𝑖𝑑𝑡ℎ, where the length is 120 feet and the width is 52 feet. Once

students have the area, they need to divide it by the number of square feet a bag of

grass seed will cover. This results in 4.16 bags needed; however, since we cannot

purchase part of a bag, 5 bags will be necessary to cover the backyard.

C) Use the information you found and the variables you created in A and B to determine

the total cost of the landscaping project.

The total cost for landscaping will be 3.4752e+03 which is scientific notation for: $3472.50

(The actual cost is $3472.55, but gets truncated due to MATLAB’s formatting)


NOTE: If students do some research, they should be able to find a way to have the answer

display in a different notation. One way is to type the words format long g into the command

window and press enter. This will re-format all answers in the command window until the

format is changed or MATLAB is closed.

1.7. RESOURCES

1. The MathWorks©, Inc./MATLAB® Official Support Page:




2. MATHEMATICS AND VARIABLES IN MATLAB ® (PART 2)

2.1. INTRODUCTION

In this lesson, students will work with trigonometry and coordinate geometry. Specifically,

students will learn how to use sine, cosine, tangent, and square roots in MATLAB®.

2.2. MATERIALS




guided notes (these may be printed or shared digitally):




Ceiling projector or method of displaying their computer screen for students to see


answer key





Be able to perform advanced mathematical calculations with MATLAB®.

By the end of this lesson, students should feel comfortable entering more advanced commands

for more complicated calculations in MATLAB®. Students should also be aware that there are

many more computations that MATLAB® can perform. A large list of these different options is

located at https://www.mathworks.com/help/symbolic/mathematical-functions.html.

With this lesson focusing heavily on trigonometry, have students pay close attention to the

units used for angle measurements in these problems. A problem with angle measurements in

degrees will have a different syntax than a problem with angle measurements in radians.



https://www.mathworks.com/help/symbolic/mathematical-functions.html


Furthermore, make sure students are using parentheses wisely and following order of

operations.

2.4. GUIDED NOTES



Name:___________________________ Date:_____________ Period:__________

Learning Targets:

MATLAB.5 – Be able to perform advanced mathematical calculations with MATLAB®.

Advanced Mathematics in MATLAB® (MATLAB.5)

MATLAB® can perform more than just basic mathematical operations (e.g., addition,

subtraction). MATLAB® has access to many different mathematical functions that can be used

in a variety of situations. For a list of these functions, see

https://www.mathworks.com/help/symbolic/mathematical-functions.html.

Right Triangle Trigonometry Review

Trigonometry is a branch of mathematics that studies the sides and angles of a triangle and the

relationships between them. Recall from math class, for any right triangle (i.e., a triangle that

contains a 90° angle), the following ratios are true.

Sine: Cosine: Tangent:

sin(𝜃) = cos(𝜃) = tan(𝜃) =

To remember the trigonometric ratios:

Hypotenuse

θ

Opposite

Adjacent



sin(𝐴) = sin(𝐵) =

cos(𝐴) = cos(𝐵) =

tan(𝐴) = tan(𝐵) =

Syntax for Trigonometric Functions in MATLAB®

Trigonometric Function Angle Measured in DEGREES

Angle Measured in RADIANS

Sine sind(angle_measure) sin(angle_measure)

Cosine cosd(angle_measure) cos(angle_measure)

Tangent tand(angle_measure) tan(angle_measure) Figure 2: Trigonometric Functions in MATLAB®

NOTE: Be sure to identify whether a given problem measures angles in degrees or radians, as

the syntax for each trigonometric ratio changes.


Use MATLAB® to find the missing side lengths of the triangle. Be sure to write the code you

used to find your answers.

20°

30 ft

x

y

a

c

B

A C b



Use MATLAB® to solve the following:

From a point on the ground 47 feet from the foot of a tree, the angle of elevation of the

top of the tree is 35°. Find the height of the tree and write the code you used to find

your answer.



To take the square root of a number in MATLAB®, use the command sqrt(number). Use the

Pythagorean Theorem (𝑎2 + 𝑏2 = 𝑐2) to determine the missing side length of each triangle in

MATLAB®.

A) B)

6 cm

10 cm

x

25 cm

21 cm

x




The distance formula can be used to find the distance between two points on a coordinate

plane. The distance formula is 𝑑 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2. Use this formula to find the

distance between the given points.

A) (2, 3) (−3, 10) B) (−7.5, 10) (11,−22)






MATLAB®.

Practice Problems:

1) Use MATLAB® to find the missing side lengths of the triangle. Be sure to write the code you


x

55°

12 m y


2) Use MATLAB® to solve the following:

You are watching an airplane. The angle of elevation of the airplane is about 23°. If the

airplane’s altitude (height) is 2500 meters, how far away are you from the airplane?

3) Use MATLAB® to find the missing side length of each triangle.

A) B)

4) Use MATLAB® to find the distance between each pair of points.

A) (−12, 16) (7, 18) B) (12.8, 9) (−5,−7.2)

5 ft

12 ft

x 38 ft

x

17 ft


2.6. ANSWER KEYS

2.6.1. GUIDED NOTES



Name:___________________________ Date:_____________ Period:__________

Learning Targets:

MATLAB.5 – Be able to perform advanced mathematical calculations with MATLAB®.

Advanced Mathematics in MATLAB® (MATLAB.5)

MATLAB® can perform more than just basic mathematical operations (e.g., addition,

subtraction). MATLAB® has access to many different mathematical functions that can be used

in a variety of situations. For a list of these functions, see

https://www.mathworks.com/help/symbolic/mathematical-functions.html.

Right Triangle Trigonometry Review

Trigonometry is a branch of mathematics that studies the sides and angles of a triangle and the

relationships between them. Recall from math class, for any right triangle (i.e., a triangle that

contains a 90° angle), the following ratios are true.

Sine: Cosine: Tangent:

sin(𝜃) = 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒

𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 cos(𝜃) =

𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡

𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 tan(𝜃) =

𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒

𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡

To remember the trigonometric ratios: 𝑆𝑂𝐻 − 𝐶𝐴𝐻 − 𝑇𝑂𝐴

sin(𝐴) =𝑎

𝑐 sin(𝐵) =

𝑏

𝑐

cos(𝐴) = 𝑏

𝑐 cos(𝐵) =

𝑎

𝑐

tan(𝐴) =𝑎

𝑏 tan(𝐵) =

𝑏

𝑎

Hypotenuse

θ

Opposite

Adjacent

a

c

B

A C b



Syntax for Trigonometric Functions in MATLAB®

Trigonometric Function Angle Measured in DEGREES

Angle Measured in RADIANS

Sine sind(angle_measure) sin(angle_measure)

Cosine cosd(angle_measure) cos(angle_measure)

Tangent tand(angle_measure) tan(angle_measure) Figure 2: Trigonometric Functions in MATLAB®

NOTE: Be sure to identify whether a given problem measures angles in degrees or radians, as

the syntax for each trigonometric ratio changes.


Use MATLAB® to find the missing side lengths of the triangle. Be sure to write the code you




From a point on the ground 47 feet from the foot of a tree, the angle of elevation of the top of

the tree is 35°. Find the height of the tree and write the code you used to find your answer.

20°

30 ft

x

y




To take the square root of a number in MATLAB, use the command sqrt(number). Use the

Pythagorean Theorem (𝑎2 + 𝑏2 = 𝑐2) to determine the missing side length of each triangle in

MATLAB®.

A) B)



The distance formula can be used to find the distance between two points on a coordinate

plane. The distance formula is 𝑑 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2. Use this formula to find the

distance between the given points.

A) (2, 3) (−3, 10) B) (−7.5, 10) (11,−22)

6 cm

10 cm

x

25 cm

21 cm

x



Practice Problems:

1) Use MATLAB® to find the missing side lengths of the triangle. Be sure to write the code you


2) Use MATLAB® to solve the following:

You are watching an airplane. The angle of elevation of the airplane is about 23°. If the

airplane’s altitude (height) is 2500 meters, how far away are you from the airplane?

3) Use MATLAB® to find the missing side length of each triangle.

A) B)

x

55°

12 m y

5 ft

12 ft

x 38 ft

x

17 ft


4) Use MATLAB® to find the distance between each pair of points.

A) (−12, 16) (7, 18) B) (12.8, 9) (−5,−7.2)

2.7. RESOURCES



2. MATLAB® Mathematical Functions:




3. CREATING SCRIPTS IN MATLAB®

3.1. INTRODUCTION

In this lesson students will learn how to work with the editor in MATLAB® to create scripts, use

scripts to solve a variety of mathematical problems, and learn how to use the input function.

3.2. MATERIALS



Copy of Introduction to MATLAB® - Creating Scripts in MATLAB® guided notes (these

may be printed or shared digitally): https://padlet.com/abrumbaugh/introMatlab



Ceiling projector or way to display their computer screen for students to see

Copy of Introduction to MATLAB® - Creating Scripts in MATLAB® answer key





Be able to explain what a script is in MATLAB®

A script is MATLAB®’s version of a program. Students should understand that scripts are a series

of lines of code that are entered into the editor window. These lines of code will run in order

from top to bottom once the Run button, represented by the green arrow, is pressed. Scripts

are very useful for automating several calculations or commands at one time.


Be able to create scripts that model and solve simple mathematical problems.

Building on the work completed in the first two lessons, students will apply their ability to do

mathematics in MATLAB® with scripting. Students will utilize the MATLAB® editor to create

scripts that take a set of variables and perform various calculations with them. Students should




see how creating a script for a set of problems is more efficient than repeatedly using the

command window for each individual problem.


Be able to use the input function within scripts in MATLAB®

This is the first non-mathematical function that students will learn how to use in MATLAB®. The

input function has the ability to take a value that has been entered by a user running the

program and store it within a specified variable. The input function also allows programmers to

display a prompt that informs the user as to what information they should type in. Encourage

students to write clear and concise prompts when using the input function.

The input function allows users to type in numbers/scalars, matrices and arrays, as well as

strings. Depending on the type of information that is to be entered, the input function syntax

will change slightly. If the program is expecting a numeric answer, whether it is a single number

(scalar) or matrix (a rectangular array of numbers), the syntax will be variableName =

input(‘Prompt’). If the program is expecting a string, such as a person’s name, the syntax will be

variableName = input(‘Prompt’,’s’).

3.4. GUIDED NOTES


Creating Scripts in MATLAB®

Name:___________________________ Date:_____________ Period:__________

Learning Targets:

MATLAB.6 – Be able to explain what a script is in MATLAB®.

MATLAB.7 – Be able to create scripts that model and solve simple mathematical problems.

MATLAB.8 – Be able to use the input function within scripts in MATLAB®.

Scripts in MATLAB® (MATLAB.6)

In MATLAB®, a script is a sequence of __________ that executes one line at a time from the top

down.


Figure 2: New Script Button. The MathWorks©,Inc.: MATLAB© R2018a. Screenshot by author.

Figure 3: Run Button. The MathWorks©,Inc.: MATLAB© R2018a. Screenshot by author.

Scripts are useful in MATLAB® as they can _________________ many tasks such as

mathematical calculations.

Scripts are created in the ___________________ window and are saved as the ____________

file type.

Automating Calculations Using Scripts (MATLAB.7)

To create a new script in MATLAB®, click the New Script button

(see Figure 2)

on the HOME tab. This will open up the Editor window where the

code will be typed.

You might notice that pressing Enter after typing a

line of code in the Editor window does not run any

code, and instead, moves the cursor down to the

next line of the Editor window. This is because the

Editor will run all of the code only when the Run

button (see Figure 3) is selected from the EDITOR

tab.


A) Create a script that takes two variable values, a and b, and finds the difference of the two

numbers. Write the lines of code in the space below.

B) Create a script that calculates the area of a triangle. Write the lines of code in the space

below.


C) Create a script that finds the hypotenuse of a right triangle using the Pythagorean Theorem

(𝑎2 + 𝑏2 = 𝑐2). Write the lines of code in the space below.

Data Types

MATLAB®, as well as other programming languages, uses two primary types of data: numeric

and string. There are many different types of numeric data (e.g., integer, float), and they are

composed of numbers. The string data type is a value that is a letter, character, or combination

of letters and characters. It is important to have a basic understanding and awareness of data

types as many of the built-in functions of MATLAB® require a specific data type.

Input Function

The input function is a built-in function of MATLAB® that allows a program to get information

from a user (e.g., measurements, name). Depending on the data type that is to be entered (i.e.,

numeric or string), the syntax for input varies (Table 2):

Numeric Input String Input

Syntax variableName = input(‘Prompt’) variableName = input(‘Prompt’,’s’)

Example length = input(‘What is the length?’) name = input(‘What is your name?’,’s’)

Table 2: Input Syntax

*NOTE: For both input types, the prompt (i.e., the words that will be displayed) must be in

single quotes.


A) Create a script that has the user enter the radius and height of a cylinder, and then uses

those values to calculate the volume of the cylinder.


B) Use your script to find the volume of a cylinder with radius 10 cm and height 25 cm.


A) Create a script that calculates a user’s gross pay (i.e., amount made before taxes are taken

out) based on their hourly wage, number of hours they worked, and any tips/commission they

may have made during the week.

B) Use your script to find the gross pay of someone who makes $6.75 per hour, worked for 35

hours, and made $257.50 in tips.






MATLAB®.

Practice Problems:

1) The area of a trapezoid is found by taking ½ the sum of the two bases multiplied by the

height of the trapezoid, or 𝐴 =1

2(𝑏1 + 𝑏2)ℎ.

Base 1 (𝑏1)

Base 2 (𝑏2)

Height


A) Create a script in MATLAB® that will calculate the area of a trapezoid. Write your script

in the space below.

B) Use your script to find the areas of the following trapezoids.

Area:_______________ Area:_______________

2) Radio antennas are supported by long cables to keep them from toppling. Write a script that

takes the angle the cable makes with the ground and the distance of the cable attachment from

the base of the tower and finds the height of the tower AND length of the cable. (HINT: You will

need to use trigonometry.)

Script:

Check your script with the following test cases:

A) 25 feet, 30 degrees

8 m

15 m

10 m

221 ft

445 ft

250 ft


B) 100 feet, 60 degrees

3) Banks offer savings, checking, and investment plans that gain compound interest. To

determine the amount of money in one of these accounts, the formula, 𝐴 = 𝑃 (1 +𝑟

𝑛)𝑛𝑡

, can

be used. In this formula, 𝐴 is the amount of money in the account, 𝑃 is the principal/starting

amount of money in the account, 𝑟 is the interest rate as a decimal (e.g., 3% = 0.03, 2.5% =

0.025, 15.3% = 0.153), 𝑛 is the number of compounding periods in one year, and 𝑡 is the time in

years.

Create a script that will calculate the value of 𝐴 given 𝑃, 𝑟, 𝑛, and 𝑡. Use the script to complete

the table below.

Script:

Starting Amount

(P)

Rate

(r)

# of Compounds per Year

(n)

Time

(t)

Final Amount

(A)

$1,000 5% 4 10 years

$5,000 3.4% 12 15 years

$12,550 4.35% 26 25 years

3.6. ANSWER KEYS


Figure 2: New Script Button. . The MathWorks©,Inc.: MATLAB© R2018a. Screenshot by author.

Figure 3: Run Button. The MathWorks©,Inc.: MATLAB© R2018a. Screenshot by author.

3.6.1. GUIDED NOTES


Creating Scripts in MATLAB®

Name:___________________________ Date:_____________ Period:__________

Learning Targets:

MATLAB.6 – Be able to explain what a script is in MATLAB®.

MATLAB.7 – Be able to create scripts that model and solve simple mathematical problems.

MATLAB.8 – Be able to use the input function within scripts in MATLAB®.

Scripts in MATLAB® (MATLAB.6)

In MATLAB®, a script is a sequence of CODE that executes one line at a time from the top down.

Scripts are useful in MATLAB® as they can AUTOMATE many tasks such as mathematical

calculations.

Scripts are created in the EDITOR window and are saved as the .M file type.

Automating Calculations Using Scripts (MATLAB.7)

To create a new script in MATLAB®, click the New Script button

(see Figure 2)

on the HOME tab. This will open up the Editor window where the

code will be typed.

You might notice that pressing Enter after typing a

line of code in the Editor window does not run any

code, and instead, moves the cursor down to the

next line of the Editor window. This is because the

Editor will run all of the code only when the Run

button (see Figure 3) is selected from the EDITOR


tab.


A) Create a script that takes two variable values, a and b, and finds the difference of the two

numbers. Write the lines of code in the space below.

B) Create a script that calculates the area of a triangle. Write the lines of code in the space

below.

C) Create a script that finds the hypotenuse of a right triangle using the Pythagorean Theorem

(𝑎2 + 𝑏2 = 𝑐2). Write the lines of code in the space below.

Data Types

MATLAB®, as well as other programming languages, uses two primary types of data: numeric

and string. There are many different types of numeric data (e.g., integer, float), and they are

composed of numbers. The string data type is a value that is a letter, character, or combination

of letters and characters. It is important to have a basic understanding and awareness of data

types as many of the built-in functions of MATLAB® require a specific data type.


Input Function

The input function is a built-in function of MATLAB® that allows a program to get information

from a user (e.g., measurements, name). Depending on the data type that is to be entered (i.e.,

numeric or string), the syntax for input varies (Table 2):

Numeric Input String Input

Syntax variableName = input(‘Prompt’) variableName = input(‘Prompt’,’s’)

Example length = input(‘What is the length?’) name = input(‘What is your name?’,’s’)

Table 2: Input Syntax

*NOTE: For both input types, the prompt (i.e., the words that will be displayed) must be in

single quotes.


A) Create a script that has the user enter the radius and height of a cylinder, and then uses

those values to calculate the volume of the cylinder.

B) Use your script to find the volume of a cylinder with radius 10 cm and height 25 cm.



A) Create a script that calculates a user’s gross pay (i.e., amount made before taxes are taken

out) based on their hourly wage, number of hours they worked, and any tips/commission they

may have made during the week.

B) Use your script to find the gross pay of someone who makes $6.75 per hour, worked for 35

hours, and made $257.50 in tips.


Practice Problems:

1) The area of a trapezoid is found by taking ½ the sum of the two bases multiplied by the

height of the trapezoid, or 𝐴 =1

2(𝑏1 + 𝑏2)ℎ.

A) Create a script in MATLAB® that will calculate the area of a trapezoid. Write your script

in the space below.

B) Use your script to find the areas of the following trapezoids.

Area: 15 𝑚2 Area: 83250 𝑓𝑡2

Base 1 (𝑏1)

Base 2 (𝑏2)

Height

8 m

15 m

10 m

221 ft

445 ft

250 ft


2) Radio antennas are supported by long cables to keep them from toppling. Write a script that

takes the angle the cable makes with the ground and the distance of the cable attachment from

the base of the tower and finds the height of the tower AND length of the cable. (HINT: You will

need to use trigonometry.)

Script:

Check your script with the following test cases:

A) 25 feet, 30 degrees

B) 100 feet, 60 degrees


3) Banks offer savings, checking, and investment plans that gain compound interest. To

determine the amount of money in one of these accounts, the formula, 𝐴 = 𝑃 (1 +𝑟

𝑛)𝑛𝑡

, can

be used. In this formula, 𝐴 is the amount of money in the account, 𝑃 is the principal/starting

amount of money in the account, 𝑟 is the interest rate as a decimal (e.g., 3% = 0.03, 2.5% =

0.025, 15.3% = 0.153), 𝑛 is the number of compounding periods in one year, and 𝑡 is the time in

years.

Create a script that will calculate the value of 𝐴 given 𝑃, 𝑟, 𝑛, and 𝑡. Use the script to complete

the table below.

Script:

Starting Amount

(P)

Rate

(r)

# of Compounds per Year

(n)

Time

(t)

Final Amount

(A)

$1,000 5% 4 10 years $1,643.62

$5,000 3.4% 12 15 years $8,320.45

$12,550 4.35% 26 25 years $37,200.12


3.7. RESOURCES



2. MATLAB® Onramp Tutorial: https://matlabacademy.mathworks.com/


https://matlabacademy.mathworks.com/


4. COMMENTS AND FORMATTING STRINGS

4.1. INTRODUCTION

In this lesson, students will learn about the importance of comments within code and how

comments can be created in MATLAB®. Students will also learn how to format the output of a

script using the fprintf function and new line switch.

4.2. MATERIALS



Copy of Introduction to MATLAB® - Comments and Formatting Strings guided notes

(these may be printed or shared digitally): https://padlet.com/abrumbaugh/introMatlab




Copy of Introduction to MATLAB® - Comments and Formatting Strings answer key





Be able to use comments to annotate code within a program/script.

One important feature of MATLAB® and many other programming languages is the ability to

add comments to code. Comments allow programmers to annotate their code making it more

readable by others who may not be familiar with the programming language. Comments can be

used as a resource to the programmer as they may need to look back at a program they created

earlier to review/re-learn how they completed a certain task. Comments can act as pseudocode

that explains the intention of how certain parts of a program are supposed to work. Students

should begin developing good programming habits throughout this unit, and leaving comments

in code is one them.




The percent sign (%) is used to leave a comment in MATLAB®. When MATLAB® encounters a %,

it interprets the symbol and all characters immediately following it as a comment. The

computer does not run this code, but rather skips over it. MATLAB® color codes comments in a

green font.


Be able to use the fprintf function to format outputs that contain strings.

To make the output of a script easier to read and/or understand, students can utilize the fprintf

function. This function allows students to incorporate a string (e.g., sentence, word) with a

numeric output. For instance, a student may write a program that calculates the distance

between two objects. Typically, MATLAB® will display a single number as the output; however,

with the fprintf function, students will be able to add a unit to this answer (e.g., 5 feet) or place

the answer in a sentence (e.g., “The distance between the two poles is 5 feet.”) This formatting

option is beneficial as it clearly states what the output represents and can make it much easier

for non-programmers to use and interpret the work done by the script.

The syntax for the fprintf function may be intimidating for some students. The syntax is as

follows:

fprintf(‘Text to be displayed %specifier.’, variableName)

The function works similarly to the input function covered in the previous lesson. After the

keyword fprintf, students will type a sentence or word within single quotes between the

parentheses. To insert a variable’s value/output in the sentence, a specifier must be typed

where the value is supposed to appear within the sentence. Students can then type a comma

after the single quotes and type the name of the variable(s) that should be inserted into the

sentence. It is possible for students to use multiple specifiers in a sentence as long as the

number of variables is equal to the number of specifiers.

There are several specifier types, but each begin with the percent sign (%). Students should

take care when determining the specifier type to use (e.g., “Should the answer have a decimal?

Does the answer contain letters or only numbers?”). A table of specifier types is listed in the

guided notes.

4.4. GUIDED NOTES


Comments and Formatting Strings


Figure 4: Comments. The MathWorks©,Inc.: MATLAB© R2018a. Screenshot by author.

Name:___________________________ Date:_____________ Period:__________

Learning Targets:

MATLAB.9 – Be able to use comments to annotate code within a program/script.

MATLAB.10 – Be able to use the fprintf function to format outputs that contain strings.

Making Comments within a Program (MATLAB.9)

Most programming languages have a feature that allows users to create comments within their

code. The computer skips over lines that are comments and does not read/run them.

Comments can be created by placing a __________________ anywhere in a program file (e.g.,

on its own line, at the end of a line.) The green text in Figure 6 are comments.

Example

It is good practice to add comments that describe the code you have written. Here are some

reasons why comments are beneficial when programming:

Helps __________________________________ understand what a program does or is

supposed to do

Can act as a ________________________ for a programmer

Can be used as a form of _________________________ which explains what a program

does in coding language

Can be used to document _____________________ that were used when creating the

program



Figure 5: Formatting with fprintf. The MathWorks©,Inc.: MATLAB© R2018a. Screenshot by author.

Use MATLAB® to create a script that calculates the area of a circle after the user gives a radius

for the circle. Create at least two comments throughout the code explaining what it does, and

use the script to answer the two test cases.

Script with Comments:

Test Cases: A) radius = 12 inches area = B) radius = 20𝜋 cm area =

Formatting Strings (MATLAB.10)

In MATLAB®, we can format our outputs (i.e., what is printed to the screen) in a way that is

more meaningful and easier to understand. One way to do this is to use the fprintf( ) function

(see Figure 7). This function will allow us to take an answer we get from a calculation and

display it within a sentence.

This function contains several fields that can be filled in, but we will focus only on a few of

these fields for now. The simplified syntax is:

Syntax: fprintf(‘Text to be displayed %specifier’, variableName)

Example:

NOTE: The “%” is NOT treated as a comment when used within the fprintf( ) function. Instead, it

is used to tell MATLAB® where you would like a variable value to be placed (i.e., the specifier).


In this example, %.2f is a specifier/place holder for the variable pay. The .2 tells MATLAB® to

round the value to two decimal places, and the f tells MATLAB® that the value should be of type

float (i.e., a number that contains decimals.)

Here is a list (Table 3) of commonly used formatting specifiers for the fprintf( ) function:

Specifier Description

%s Prints a string

%c Prints a single character

%d Prints an integer (no decimal)

%f Prints a floating point number (decimal) Table 3: Specifiers for fprintf

NOTE: You can place a period/decimal point and value between the % and f to specify the

number of decimal points a float should contain when being formatted with fprintf( ).

Example 2 (MATLAB.9, 10)

Pizza Shack is offering a special price on their pizzas for their 25-year anniversary. A customer

can get any large two-topping pizza for $6.99 and any large specialty pizza for $9.99. Pizza

Shack will also deliver your order to you for $1.50.

Use MATLAB® to create a script that allows a customer to specify the number of each type of

pizza they would like, calculates their total, and then applies a 7.5% tax and delivery fee. The

script should then only display the total amount that the customer owes for their order in a

well-formatted sentence.

Test your script by calculating the total cost of an order for 3 two-topping pizzas and 2 specialty

pizzas.


Figure 6: NO New Line Switch. The MathWorks©,Inc.: MATLAB© R2018a. Screenshot

by author.

Figure 9: New Line Switch. The MathWorks©,Inc.: MATLAB© R2018a.

Screenshot by author.

Figure 10: Multiple New Line Switches. The MathWorks©,Inc.: MATLAB© R2018a. Screenshot

by author.

Figure 11: NO New Line Switch with Input Function. The MathWorks©,Inc.: MATLAB© R2018a. Screenshot by

author.

Figure 12: New Line Switch with Input Function. The MathWorks©,Inc.: MATLAB© R2018a. Screenshot by

author.

New Line Switch

The new line switch is another way that we can format our output. The new line switch will

display text or input field on the next line. This can be useful in making scripts/programs more

user-friendly and easier to read.

Syntax: fprintf(‘Text to be displayed \n’) input(‘Text to be displayed \n’)

Note: \n will only be interpreted as a new line switch when it is a part of fprintf( ), input( ), or

other MATLAB® functions.

Examples:

Example 3

Create a script in MATLAB® utilizing the new line switch command to write each word of the

sentence, “The quick brown fox jumps over the lazy dog.” on its own line.

Script:







MATLAB®.

Practice Problems:

From this lesson forward, all scripts/programs should contain some comments that annotate

what it should do when executed.

1) Use MATLAB® to create a script that calculates the gross pay of an individual after they have

typed in their hourly wage, number of hours worked, and tips/commission made during the

week. Then calculate the individual’s net pay (i.e., gross income minus taxes) by removing 15%

of their gross income for taxes.

The program should only display the amount that was withheld for taxes and the individual’s

net pay in well-formatted sentences (e.g., “A total of $150 was withheld for taxes.” “Your net

pay is $850.”)

Script:

Use your script to calculate the following test cases:

A) Darryl makes $15.75 each hour as a sales associate at a major appliance store. Last week, he

worked 37 hours and made $288 in commission.

Taxes:_______________________ Net Pay:_______________________


B) Ramya earns $6.89 each hour as a waitress. Last week, she worked for 40 hours and made

$521.27 in tips.

Taxes:_______________________ Net Pay:_______________________

C) Ja’son earns $14.35 per hour as an automotive sales representative. Last week, he worked 30

hours and made $537.50 in commission.

Taxes:_______________________ Net Pay:_______________________

2) For a projectile fired across a flat plane (i.e., two dimensional), the equations of motion that

can be used to find the time the projectile is in the air and the distance it has traveled are:

𝑡𝑖𝑚𝑒 =2∗velocity∗sin(𝑎𝑛𝑔𝑙𝑒)

𝑔 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑡𝑖𝑚𝑒 ∗ 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 ∗ cos (𝑎𝑛𝑔𝑙𝑒).

NOTE: “Velocity” refers to the initial/starting velocity of the projectile, the “angle” is the angle

of launch from the horizontal axis, and “g” is the acceleration due to gravity (in this problem

𝑔 = 9.81 𝑚/𝑠2).

Create a script that takes the initial velocity, and angle of the projectile and returns the travel

time and landing distance in a well-formatted sentence (must be a single sentence that contains

both values).

Script:



A) Velocity = 100 m/s Angle = 30°

Time = _____________ Distance = _______________

B) Velocity = 25 m/s Angle = 10°

Time = _____________ Distance = _______________

C) Velocity = 30 m/s Angle = 70°

Time = _____________ Distance = _______________

3) Create a script in MATLAB® that will recreate the text seen below.

Script:

Learning MATLAB

can

be difficult

but

fun

4.6. ANSWER KEYS

4.6.1. GUIDED NOTES



Figure 6: Comments. The MathWorks©,Inc.: MATLAB© R2018a. Screenshot by author.

Comments and Formatting Strings

Name:___________________________ Date:_____________ Period:__________

Learning Targets:

MATLAB.9 – Be able to use comments to annotate code within a program/script.

MATLAB.10 – Be able to use the fprintf function to format outputs that contain strings.

Making Comments within a Program (MATLAB.9)

Most programming languages have a feature that allows users to create comments within their

code. The computer skips over lines that are comments and does not read/run them.

Comments can be created by placing a ____%____ anywhere in a program file (e.g., on its own

line, at the end of a line.) The green text in Figure 6 are comments.

Example

It is good practice to add comments that describe the code you have written. Here are some

reasons why comments are beneficial when programming:

Helps non-programmers/readers understand what a program does or is supposed to do

Can act as a resource for a programmer

Can be used a form of pseudocode which explains in coding language what a program

does

Can be used to document references that were used when creating the program



Figure 7: Formatting with fprintf. The MathWorks©,Inc.: MATLAB© R2018a. Screenshot by author.

Use MATLAB® to create a script that calculates the area of a circle after the user gives a radius

for the circle. Create at least two comments throughout the code explaining what it does, and

use the script to answer the two test cases.

Script with Comments:

Test Cases:

A) radius = 12 inches area = 452.39 𝑖𝑛2 B) radius = 20𝜋 cm area = 12,402.51 𝑐𝑚2

Formatting Strings (MATLAB.10)

In MATLAB®, we can format our outputs (i.e., what is printed to the screen) in a way that is

more meaningful and easier to understand. One way to do this is to use the fprintf( ) function

(see Figure 7). This function will allow us to take an answer we get from a calculation and

display it within a sentence.

This function has several fields that can be filled in, but we will focus only on a few of these

fields for now. The simplified syntax is:

Syntax: fprintf(‘Text to be displayed %specifier’, variableName)

Example:


NOTE: The “%” is NOT treated as a comment when used within the fprintf( ) function. Instead, it

is used to tell MATLAB® where you would like a variable value to be placed (i.e., the specifier).

In this example, %.2f is a specifier/place holder for the variable pay. The .2 tells MATLAB® to

round the value to two decimal places, and the f tells MATLAB® that the value should be of type

float (i.e., a number that contains decimals.)

Here is a list (Table 3) of commonly used formatting specifiers for the fprintf( ) function:

Specifier Description

%s Prints a string

%c Prints a single character

%d Prints an integer (no decimal)

%f Prints a floating point number (decimal) Table 3: Specifiers for fprintf

NOTE: You can place a period/decimal point and value between the % and f to specify the

number of decimal points a float should contain when being formatted with fprintf( ).


Pizza Shack is offering a special price on their pizzas for their 25-year anniversary. A customer

can get any large two-topping pizza for $6.99 and any large specialty pizza for $9.99. Pizza

Shack will also deliver your order to you for $1.50.

Use MATLAB® to create a script that allows a customer to specify the number of each type of

pizza they would like, calculates their total, and then applies a 7.5% tax and delivery fee. The

script should then only display the total amount that the customer owes for their order in a

well-formatted sentence.


Figure 7: NO New Line Switch. The MathWorks©,Inc.: MATLAB© R2018a. Screenshot

by author. Figure 9: New Line Switch. The

MathWorks©,Inc.: MATLAB© R2018a. Screenshot by author.

Figure 10: Multiple New Line Switches. The MathWorks©,Inc.: MATLAB© R2018a.


Figure 11: NO New Line Switch with Input Function. The MathWorks©,Inc.: MATLAB© R2018a.


Figure 12: New Line Switch with Input Function. The MathWorks©,Inc.: MATLAB© R2018a. Screenshot by

author.

Test your script by calculating the total cost an order for 3 two-topping pizzas and 2 specialty

pizzas.

New Line Switch

The new line switch is another way that we can format our output. The new line switch will

display text or input field on the next line. This can be useful in making scripts/programs more

user friendly and easier to read.

Syntax: fprintf(‘Text to be displayed \n’) input(‘Text to be displayed \n’)

Note: \n will only be interpreted as a new line switch when it is a part of fprintf( ), input( ), or

other MATLAB® functions.

Examples:


Example 3

Create a script in MATLAB® utilizing the new line switch command to write each word of the

sentence, “The quick brown fox jumps over the lazy dog.” on its own line.

Script:


Practice Problems:

From this lesson forward, all scripts/programs should contain some comments that annotate

what it should do when executed.

1) Use MATLAB® to create a script that calculates the gross pay of an individual after they have

typed in their hourly wage, number of hours worked and tips/commission made during the

week. Then calculate the individual’s net pay (i.e., gross income minus taxes) by removing 15%

of their gross income for taxes.

The program should only display the amount that was withheld for taxes and the individual’s

net pay in well-formatted sentences (e.g., “A total of $150 was withheld for taxes.” “Your net

pay is $850.”)

Script:



A) Darryl makes $15.75 each hour as a sales associate at a major appliance store. Last week, he

worked 37 hours and made $288 in commission.

Taxes: $130.61 Net Pay: $740.14

B) Ramya earns $6.89 each hour as a waitress. Last week, she worked for 40 hours and made

$521.27 in tips.

Taxes: $119.53 Net Pay: $677.34

C) Ja’son earns $14.35 per hour as an automotive sales representative. Last week, he worked 30

hours and made $537.50 in commission.

Taxes: $145.20 Net Pay: $822.80

2) For a projectile fired across a flat plane (i.e., two dimensional), the equations of motion that

can be used to find the time the projectile is in the air and the distance it has traveled are:

𝑡𝑖𝑚𝑒 =2∗velocity∗sin(𝑎𝑛𝑔𝑙𝑒)

𝑔 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑡𝑖𝑚𝑒 ∗ 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 ∗ cos (𝑎𝑛𝑔𝑙𝑒).


NOTE: “Velocity” refers to the initial/starting velocity of the projectile, the “angle” is the angle

of launch from the horizontal axis, and “g” is the acceleration due to gravity (in this problem

𝑔 = 9.81 𝑚/𝑠2).

Create a script that takes the initial velocity, and angle of the projectile and returns the travel

time and landing distance in a well-formatted sentence (must be a single sentence that contains

both values).

Script:


A) Velocity = 100 m/s Angle = 30°

Time = 10.19 sec Distance = 882.80 meters

B) Velocity = 25 m/s Angle = 10°



C) Velocity = 30 m/s Angle = 70°


3) Create a script in MATLAB® that will recreate the text seen below.

Script:

Learning MATLAB

can

be difficult

but

fun

4.7. RESOURCES



2. Formatting Strings in MATLAB®:

https://www.mathworks.com/help/matlab/matlab_prog/formatting-strings.html

3. Explanation of fprintf function:

https://www.cs.utah.edu/~germain/PPS/Topics/Matlab/fprintf.html


https://www.mathworks.com/help/matlab/matlab_prog/formatting-strings.html

https://www.cs.utah.edu/~germain/PPS/Topics/Matlab/fprintf.html


5. MATRICES AND MATRIX OPERATIONS

5.1. INTRODUCTION

In this lesson, students will learn about matrices and how they work within MATLAB®. More

specifically, students will learn what a matrix is, how to create matrices with varying dimensions

in MATLAB®, how to perform mathematical operations on sets of data through matrices, and

how to index into a matrix.

5.2. MATERIALS



Copy of Introduction to MATLAB® - Matrices and Matrix Operations guided notes (these





Copy of Introduction to MATLAB® - Matrices and Matrix Operations answer key





Be able to define the term matrix.

It is important that students have a general understanding of a matrix. While many

programming environments work with one value at a time, MATLAB® (short for Matrix

Laboratory) works with matrices and arrays. A matrix (plural: matrices) is a rectangular

arrangement of numeric values, variables, and/or expressions. With MATLAB®’s proficiency

with matrices and arrays it is possible to perform calculations and tasks on large sets of data

very quickly.





Be able to state the dimensions of a given matrix.

Every matrix has a set of dimensions, which describe the size of the matrix. The dimensions of a

matrix can be expressed by stating the number of rows the matrix has by the number of

columns a matrix has. For instance, a matrix with 2 rows and 5 columns has the dimensions 2 x

5 (i.e., 2 by 5). Students need to understand how to find the dimensions of a matrix, as some

matrix operations (e.g., adding and subtracting) are only possible when the dimensions of the

matrices are the same. Students will undoubtedly encounter errors in this lesson and future

lessons due to matrix dimensions that are not compatible, and it is important they understand

why they are occurring.


Be able to perform mathematical operations on matrices and arrays in MATLAB®

After this lesson, students should be able to create matrices in MATLAB® and perform

mathematical operations on and with them when possible. Performing mathematical

operations (e.g., addition, subtraction) on matrices is very similar to performing the same

operations on single numbers in MATLAB®. Students will want to exercise a bit of caution when

performing operations on matrices, however, as many operations require the dimensions of the

matrices involved to have the same dimensions (e.g., addition and subtraction) or matching

column and row (e.g., multiplication).

There is a well-defined algorithm for multiplying two matrices of compatible dimensions.

However, there are times when students will need to multiply corresponding elements of two

matrices, which goes against the steps of the multiplication algorithm, and thus leads to a

different product. Instead, students will have to place a period (.) just before the multiplication

symbol (*). This performs an element-wise operation where each corresponding element of

two matrices is multiplied together to create a new matrix. As students begin multiplying

matrices in MATLAB®, watch for dimension errors that MATLAB® may give, and encourage

students to use element-wise multiplication for problems that require it.


Be able to index into a matrix and array in MATLAB®

In MATLAB® and other programming languages, an index is a number that refers to a specific

location/position in a matrix or array. Matrices and arrays can be indexed into by typing the

matrix name followed by a value or range of values within a set of parentheses. The specific

details on how to do this are in the guided notes below.


Indexing is important, as it will allow students to perform calculations on a specific subset of

elements within a matrix or array. This lesson will cover indexing in various forms, such as

selecting a single element, single row or column, and multiple rows or columns.

5.4. GUIDED NOTES


Matrices and Matrix Operations

Name:____________________________ Date:__________________ Period:__________

Learning Targets:

MATLAB.11 – Be able to define the term matrix.

MATLAB.12 – Be able to state the dimensions of a given matrix.

MATLAB.13 – Be able to perform mathematical operations on matrices and arrays in MATLAB®.

MATLAB.14 – Be able to index into a matrix and array in MATLAB®.

What is a Matrix? (MATLAB.11, 12)

A matrix is a rectangular array of

__________________________________________________________________.

Every matrix has a pair of dimensions. The dimensions of a matrix is given by the number of

__________ by the number of _____________.

Examples: [1 23 4

] [1 0 00 1 00 0 1

] [𝑎 𝑏 𝑐𝑑 𝑒 𝑓] [

4𝑥 + 2𝑦 − 𝑧−6𝑥 + 𝑦3𝑥 + 2𝑧

]

Dimensions: ________ ________ ________ ________

Creating Matrices and Arrays

Just like with regular numbers, we can perform operations on a set of numbers using matrices

and arrays. First though, we need to be able to create a matrix. We can do so by using the

following syntax:


Row Vector (a single row matrix)

Syntax: 𝑚𝑎𝑡𝑟𝑖𝑥𝑁𝑎𝑚𝑒 = [𝑣1 𝑣2 𝑣3 … 𝑣𝑛]

(NOTE: There is one space between each value/element)

Example: 𝑟𝑜𝑤𝑉𝑒𝑐𝑡𝑜𝑟 = [5 2.50 7 10] [5 2.50 7 10]

Matrix with multiple rows

Syntax: 𝑚𝑎𝑡𝑟𝑖𝑥𝑁𝑎𝑚𝑒 = [𝑣1 𝑣2 … 𝑣𝑛; 𝑤1 𝑤2 … 𝑤𝑛; 𝑥1 𝑥2 … 𝑥𝑛]

(NOTE: Use a semi-colon, “;”, to tell MATLAB when to start a new row in a matrix/array)

Example: 𝑐𝑜𝑢𝑛𝑡 = [1 2 3; 4 5 6; 7 8 9] [1 2 34 5 67 8 9

]

Column Vector (a single column matrix)

Syntax: 𝑚𝑎𝑡𝑟𝑖𝑥𝑁𝑎𝑚𝑒 = [𝑣1; 𝑣2; 𝑣3; … ; 𝑣𝑛]

Example: 𝑐𝑜𝑙𝑢𝑚𝑛𝑉𝑒𝑐𝑡𝑜𝑟 = [1; 2; 3; 4] [

1234

]

Operations with Matrices and Arrays

The elements/values within a matrix or array can be combined using mathematical operations

just like regular numbers. This is useful when we want to perform a specific operation(s) on a

large set of data.


Let 𝐴 = [1 05 43 −5

], 𝐵 = [0 1 7], 𝐶 = [10 5 −4−1 0 2

], 𝐷 = [1 00 1

], and 𝐸 = [−9 138 −2

].

Use MATLAB to find each of the following if possible.


A) 𝐷 + 𝐸 B) 5B C) 𝐴𝐶


Below is data on a small portion of sales at a bookstore.

A) Create a matrix in MATLAB named sales that represents the data in the table.

B) Create a new matrix in MATLAB named month that estimates the potential sales for the

bookstore after a month (4 weeks) if each week is the same as the data presented.

Indexing in MATLAB

Weekly Bookstore Revenue (in $)

Fiction Non-Fiction Reference

Monday 2,512 1,333 989

Tuesday 6,387 6,111 1,001

Friday 5,909 6,212 1,205


Indexing is the process of selecting a __________________ of elements/values from a matrix or

array.

Here are some of the ways (Table 4) that we can index into a matrix:

Description Syntax Example

Accessing a single value from a single-row matrix

matrixName(columnNumber) 𝑉 = [7 9 15 −4 1] →

𝑉(1) = 7, 𝑉(3) = 15, 𝑉(5) = 1

Accessing a single value from a matrix

matrixName(rowNumber,columnNumber) 𝑉 = [

1 2 34 5 67 8 9

] →

𝑉(1,1) = 1, 𝑉(2,3) = 6

Accessing an entire row of a matrix

matrixName(rowNumber,:) 𝑉 = [

1 2 34 5 67 8 9

]

𝑉(1, : ) = [1 2 3] 𝑉(3, : ) = [7 8 9]

Accessing an entire column of a matrix

matrixName(:, columnNumber) 𝑉 = [

1 2 34 5 67 8 9

] →

𝑉(: , 2) = [258] 𝑉(: , 3) = [

369]

Accessing a range of values in a matrix

matrixName(rowStart:rowEnd,columnStart:columnEnd)

𝑉 = [1 2 34 5 67 8 9

] →

𝑉(1: 2,2: 3) = [2 35 6

]

Table 4: Methods of Indexing

Example 3


Use the matrices 𝐴 = [4 −7 9

−18 10 0] and 𝐵 = [

13 −4 3 0 1110 13 0 7 −151 6 5 −14 3

] to write code that

selects the given values.

A) element with value of 0 in A B) elements -18, 10, and 0 in A

C) elements 0, 7, and -14 in B D) elements in the first two rows

and first three columns in B






MATLAB®.

Practice Problems:

1) Use matrices below to find each of the following calculations in MATLAB if possible.

𝑥 = [3 −52 7

] 𝑦 = [11 04 −7

] 𝑤 = [3 5

−10 70 1

] 𝑣 = [1 02 43 −7

]

A) 𝑥𝑦 B) 2𝑤 + 4𝑣 C) 𝑥 − 𝑦

2) Use the matrices in 1) to write a single index statement that selects the given values.

A) element 0 in y B) elements 5, 7, 1 in w C) elements 1, 0 in v

D) elements -10, 7, 0, 1 in w E) elements 0, 4, -7 in v F) elements 1, 0, 2, 4

in v


3) The two tables below show two days of software sales by console and genre at a video game

store.

A) Use MATLAB to create two matrices to represent the tables above. Store each table in its

own variable.

B) Use MATLAB to create a matrix that represents the total sales from both days.

C) GameGo has a special sale on Switch games on day 3 (not shown), and found that they sold

25% more copies of every type of Switch game than on day 2. Use indexing and matrix

operations to find a matrix (single column) that represents the total of Switch games of each

type sold on day 3.

5.6. ANSWER KEYS

5.6.1. GUIDED NOTES


GameGo Day 1 Sales

PS4 Xbox

1 Switch

Action 125 118 110

Adventure 110 115 79

Role-Playing

98 32 74

Puzzle 55 49 71

Sports 117 163 65

GameGo Day 2 Sales

PS4 Xbox

1 Switch

Action 120 121 104


Role-Playing

101 30 72

Puzzle 54 51 76

Sports 112 157 52


Matrices and Matrix Operations

Name:____________________________ Date:__________________ Period:__________

Learning Targets:

MATLAB.11 – Be able to define the term matrix.

MATLAB.12 – Be able to state the dimensions of a given matrix.

MATLAB.13 – Be able to perform mathematical operations on matrices and arrays in MATLAB®.

MATLAB.14 – Be able to index into a matrix and array in MATLAB®.

What is a Matrix? (MATLAB.11, 12)

A matrix is a rectangular array of numbers, variables, and expressions.

Every matrix has a pair of dimensions. The dimensions of a matrix is given by the number of

rows by the number of columns.

Examples: [1 23 4

] [1 0 00 1 00 0 1

] [𝑎 𝑏 𝑐𝑑 𝑒 𝑓] [

4𝑥 + 2𝑦 − 𝑧−6𝑥 + 𝑦3𝑥 + 2𝑧

]

Dimensions: 2 x 2 3 x 3 2 x 3 3 x 1

Creating Matrices and Arrays

Just like with regular numbers, we can perform operations on a set of numbers using matrices

and arrays. First though, we need to be able to create a matrix. We can do so by using the

following syntax:

Row Vector (a single row matrix)

Syntax: 𝑚𝑎𝑡𝑟𝑖𝑥𝑁𝑎𝑚𝑒 = [𝑣1 𝑣2 𝑣3 … 𝑣𝑛]

(NOTE: There is one space between each value/element)

Example: 𝑟𝑜𝑤𝑉𝑒𝑐𝑡𝑜𝑟 = [5 2.50 7 10] [5 2.50 7 10]

Matrix with multiple rows


Syntax: 𝑚𝑎𝑡𝑟𝑖𝑥𝑁𝑎𝑚𝑒 = [𝑣1 𝑣2 … 𝑣𝑛; 𝑤1 𝑤2 … 𝑤𝑛; 𝑥1 𝑥2 … 𝑥𝑛]

(NOTE: Use a semi-colon, “;”, to tell MATLAB when to start a new row in a matrix/array)

Example: 𝑐𝑜𝑢𝑛𝑡 = [1 2 3; 4 5 6; 7 8 9] [1 2 34 5 67 8 9

]

Column Vector (a single column matrix)

Syntax: 𝑚𝑎𝑡𝑟𝑖𝑥𝑁𝑎𝑚𝑒 = [𝑣1; 𝑣2; 𝑣3; … ; 𝑣𝑛]

Example: 𝑐𝑜𝑙𝑢𝑚𝑛𝑉𝑒𝑐𝑡𝑜𝑟 = [1; 2; 3; 4] [

1234

]

Operations with Matrices and Arrays

The elements/values within a matrix or array can be combined using mathematical operations

just like regular numbers. This is useful when we want to perform a specific operation(s) on a

large set of data.


Let 𝐴 = [1 05 43 −5

], 𝐵 = [0 1 7], 𝐶 = [10 5 −4−1 0 2

], 𝐷 = [1 00 1

], and 𝐸 = [−9 138 −2

].

Use MATLAB to find each of the following if possible.

A) 𝐷 + 𝐸 B) 5B C) 𝐴𝐶


Below is data on a small portion of sales at a bookstore.


A) Create a matrix in MATLAB named sales that represents the data in the table.

B) Create a new matrix in MATLAB named month that estimates the potential sales for the

bookstore after a month (4 weeks) if each week is the same as the data presented.

Indexing in MATLAB

Indexing is the process of selecting a subset of elements/values from a matrix or array.

Here are some of the ways (Table 4) that we can index into a matrix:

Description Syntax Example

Accessing a single value from a single-row matrix

matrixName(columnNumber) 𝑉 = [7 9 15 −4 1] →

𝑉(1) = 7, 𝑉(3) = 15, 𝑉(5) = 1

Weekly Bookstore Revenue (in $)

Fiction Non-Fiction Reference

Monday 2,512 1,333 989

Tuesday 6,387 6,111 1,001

Friday 5,909 6,212 1,205


Accessing a single value from a matrix

matrixName(rowNumber,columnNumber) 𝑉 = [

1 2 34 5 67 8 9

] →

𝑉(1,1) = 1, 𝑉(2,3) = 6

Accessing an entire row of a matrix

matrixName(rowNumber,:) 𝑉 = [

1 2 34 5 67 8 9

]

𝑉(1, : ) = [1 2 3] 𝑉(3, : ) = [7 8 9]

Accessing an entire column of a matrix

matrixName(:, columnNumber) 𝑉 = [

1 2 34 5 67 8 9

] →

𝑉(: , 2) = [258] 𝑉(: , 3) = [

369]

Accessing a range of values in a matrix

matrixName(rowStart:rowEnd,columnStart:columnEnd)

𝑉 = [1 2 34 5 67 8 9

] →

𝑉(1: 2,2: 3) = [2 35 6

]

Table5: Methods of Indexing

Example 3

Use the matrices 𝐴 = [4 −7 9

−18 10 0] and 𝐵 = [

13 −4 3 0 1110 13 0 7 −151 6 5 −14 3

] to write code that

selects the given values.

A) element with value of 0 in A A(2, 3) B) elements -18, 10, and 0 in A A(2, :)

C) elements 0, 7, and -14 in B B(:, 4) D) elements in the first two rows and first

three columns in B B(1:2, 1:3)



Practice Problems:

1) Use matrices below to find each of the following calculations in MATLAB if possible.

𝑥 = [3 −52 7

] 𝑦 = [11 04 −7

] 𝑤 = [3 5

−10 70 1

] 𝑣 = [1 02 43 −7

]

A) 𝑥𝑦 B) 2𝑤 + 4𝑣 C) 𝑥 − 𝑦

2) Use the matrices in 1) to write a single index statement that selects the given values.

A) element 0 in y B) elements 5, 7, 1 in w C) elements 1, 0 in v

y(1,2) w(:, 2) v(1, :)

D) elements -10, 7, 0, 1 in w E) elements 0, 4, -7 in v F) elements 1, 0, 2, 4

w(2:3, 1:2) or w(2:3, :) v(:, 2) in v

v(1:2, 1:2) or v(1:2, :)

3) The two tables below show two days of software sales by console and genre at a video game

store.

GameGo Day 1 Sales

PS4 Xbox

1 Switch


A) Use MATLAB to create two matrices to represent the tables above. Store each table in its

own variable.

B) Use MATLAB to create a matrix that represents the total sales from both days.

Action 125 118 110


Role-Playing

98 32 74

Puzzle 55 49 71

Sports 117 163 65

GameGo Day 2 Sales

PS4 Xbox

1 Switch

Action 120 121 104


Role-Playing

101 30 72

Puzzle 54 51 76

Sports 112 157 52


C) GameGo has a special sale on Switch games on day 3 (not shown), and found that they sold

25% more copies of every type of Switch game than on day 2. Use indexing and matrix

operations to find a matrix (single column) that represents the total of Switch games of each

type sold on day 3.

Or

5.7. RESOURCES

1. The MathWorks©,Inc./MATLAB® Official Support Page:


2. An Introduction to Solving Engineering Problems with MATLAB® e-book:

https://www.ck12.org/book/Engineering%3A-An-Introduction-to-Solving-Engineering-

Problems-with-Matlab/


https://www.ck12.org/book/Engineering%3A-An-Introduction-to-Solving-Engineering-Problems-with-Matlab/



6. GRAPHING IN MATLAB®

6.1. INTRODUCTION

In this lesson, students will learn to use the graphing capabilities of MATLAB®. Specifically,

students will learn how to plot individual points, mathematical functions, format the

appearance of a graph, and create labels for a graph in MATLAB®.

6.2. MATERIALS



Copy of Introduction to MATLAB® - Graphing in MATLAB® guided notes (these may be

printed or shared digitally): https://padlet.com/abrumbaugh/introMatlab




Copy of Introduction to MATLAB® - Graphing in MATLAB® answer key





Be able to create a graph from data in MATLAB®.

One capability of MATLAB® is its ability to easily and quickly produce graphical displays of data.

Students should have a general understanding of how to utilize the plot command of MATLAB®

to graph a given set of data after this lesson.

The plot command follows the syntax plot(x,y) using the keyword plot followed by two

arguments, x and y. x represents the value(s) of the independent variable that determines the

horizontal direction of the point. y represents the value(s) of the dependent variable and

determines the vertical direction of the point. x and y can be two individual numbers or two

row or column vectors each containing several numbers.





Be able to graph mathematical functions in MATLAB®.

Aside from individual data points, MATLAB® can create graphs for mathematical functions (e.g.,

linear, quadratic, trigonometric) that are defined as variables. One skill that students will need

to learn to graph mathematical functions is to create a set of x-values that the function is

defined for.

Creating a list of x-values involves creating a row vector of values for which a function is defined

for. The method for doing this has a similar syntax to indexing from the previous lesson. The

basic syntax is x = startNumber:incrementValue:endNumber. This command will create a row

vector with the first element equal to startNumber and each successive element equal to the

sum of the incrementValue and previous element. This list of numbers will continue in this

fashion until the endNumber is reached. As an example, the command x = 1:0.5:3 will produce

the following row vector, x = [1 1.5 2 2.5 3]. It no increment value is given (e.g., x = 1:10) the

increment will be set to 1 by default.


Be able to format the display of a graph in MATLAB®

MATLAB® makes it easy to format a graph from changing the color of the graph to the types of

icons used for the points plotted on the graph. Students will want to become familiar with how

to do this feature as they will be graphing multiple sets of data on the same graph. By

formatting each graph it will allow viewers to easily differentiate between the two sets of data

and make conjectures about trends they see in the data.

To format a graph, students will need to enter additional arguments within the plot command

(e.g., plot(x,y, ‘arguments’)). It is important to note that all formatting arguments are placed in

single quotes after the x and y variables. The order that the formatting options are placed

within the single quotes is not important (e.g., ‘- o’ is the same as ‘o –‘).

A partial list, as well as a link to a full list, of formatting options is given in the guided notes

below.

Lastly, students should be able to create labels for the axes of their graphs as well as a title for

the figure. Stress to students that any graph created in MATLAB® should be easy to read, and

that part of that readability comes from having clear labels on their graphs. Creating these in

MATLAB® is relatively easy, following a simple syntax. The syntax for these features is outlined

in the guided notes below.


6.4. GUIDED NOTES


Graphing in MATLAB®

Name:____________________________ Date:__________________ Period:__________

Learning Targets:

MATLAB.15 – Be able to create a graph from data in MATLAB®.

MATLAB.16 – Be able to graph mathematical functions in MATLAB®.

MATLAB.17 – Be able to format the display of a graph in MATLAB®.

Creating a Graph in MATLAB (MATLAB.15)

The most basic way to graph a set of data in MATLAB® is to use the ___________ command.

Syntax: plot(x, y)

NOTE: x represents the values that go on the horizontal (x) axis, y represents the values that go

on the vertical (y) axis


Create a graph in MATLAB® using the following information.

A) 𝑥 = [1 3 4] 𝑦 = [2 5 9] B) 𝐴 =

[ 1 23 45 67 89 10]


Figure 8: Graph Example. The MathWorks©,Inc.: MATLAB© R2018a.


Graphing Mathematical Functions (MATLAB.16)

We can graph more than just individual data points from a matrix in MATLAB®. We can also

graph mathematical functions/equations using MATLAB®.

Example: 𝑦 = 𝑥2

1st – Specify a range of values for x (x = startValue:increment:endValue) 𝑥 = −3: 0.5: 3

2nd – Specify the mathematical function that is used to obtain values for y 𝑦 = 𝑥. ^2

NOTE: We need to put the ‘.’ before ‘^’ in order to avoid an error with matrix dimensions.

The ‘.’ applies the power to each number in x rather than multiplying x by itself.

3rd – Use the plot command to create a graph of the function plot(𝑥, 𝑦)

4th – Graph (Figure 12) will appear in Figure window


Create a graph for each function in MATLAB®.

A) 𝑥 = −2𝜋:𝜋

4: 2𝜋 B) 𝑥 = −5: 0.1: 5

𝑦 = sin (𝑥) 𝑦 = 3𝑥3 − 5𝑥 + 2


Formatting Graphs in MATLAB (MATLAB.17) There are many ways that we can format a graph in MATLAB® such as changing the line type and color. Here is a partial list (

and color. Here is a partial list (

Table 5) of formatting options for graphing in MATLAB®.

(For a full list of options visit https://www.mathworks.com/help/matlab/ref/linespec.html or

search “MATLAB Linespec” online)

Line Style Specifiers Mark/Point Specifiers Color Specifiers

‘-‘ Solid Line (Default) ‘o’ Circle ‘r’ Red

‘- -‘ Dashed Line ‘+’ Plus Sign ‘g’ Green

‘:’ Dotted Line ‘*’ Asterisk ‘b’ Blue

‘d’ No Line

Table 5: Graph Formatting Options

To apply one, or multiple, specifiers to a graph, use the following:

Syntax: plot(x, y, ‘specifier symbol(s)’)

NOTE: All specifiers must come after the y-variable and be between the single quotes since they

are treated by MATLAB® as strings.

Examples:

plot(x, y, ‘- -r’) creates a red dashed line

plot(x, y, ‘-+b’) creates a solid blue line with plus signs as points

plot(x, y, ‘d’) creates diamond-shaped markers with no line

Example 3

https://www.mathworks.com/help/matlab/ref/linespec.html


Figure 9: Labeled Graph

Graph the function 𝑦 = √𝑥 − 5 for 𝑥 = 5: 0.5: 15 with a dotted line, circle markers, on a green

line.

Creating Graph Labels (MATLAB.17)

As we begin to model real-world phenomena with MATLAB®, it is important that we clearly

label our products so that others can clearly understand them. One way we can do this is by

titling the graph and labeling the axes. The syntax for creating graph labels is listed in Table 6. A

fully labeled graph can be seen in Figure 13.

Label Type Syntax Example

Title title(‘Enter Text Here’) title(‘Distance vs. Time Graph’)

x-axis xlabel(‘Enter Text Here’) xlabel(‘Time (seconds)’)

y-axis ylabel(‘Enter Text Here’) ylabel(‘Distance (feet)’) Table 6: Graph Labels







MATLAB®.

Practice Problems

1) Create a graph in MATLAB® using the following information.

A) 𝑥 = [−5 9 3 0] B) 𝑃 =

[ −3 25 92 6

−1 83 0]

𝑦 = [1 3 2 −3]

2) Plot each of the following functions using dashed red lines.

A) 𝑥 = −5: 0.5: 5 B) 𝑥 = −2: 0.1: 2

𝑦 =1

2𝑥 𝑦 = 𝑥5 − 4𝑥3 + 5𝑥 − 1


3) The following data (Table 7) shows the high temperature for a period of days and the

admission sales to a public swimming pool.

Temperature (℉) Admission Sales ($)

72 300

75 328

81 400

83 412

87 600

85 564

90 684

88 644

80 572 Table 7: Admission Sales for Public Swimming Pool

A) Store the data in a matrix called swim.

B) Create a graph of the data with the following specifications:

- Temperature is the x-value

- Admission Sales is the y-value

- Data points are represented by blue circles

- The graph is titled Swimming Pool Revenue

- Both x- and y-axes are labeled with units

6.6. ANSWER KEYS

6.6.1. GUIDED NOTES



Graphing in MATLAB®

Name:____________________________ Date:__________________ Period:__________

Learning Targets:

MATLAB.15 – Be able to create a graph from data in MATLAB®.

MATLAB.16 – Be able to graph mathematical functions in MATLAB®.

MATLAB.17 – Be able to format the display of a graph in MATLAB®.

Creating a Graph in MATLAB (MATLAB.15)

The most basic way to graph a set of data in MATLAB® is to use the plot command.

Syntax: plot(x, y)

NOTE: x represents the values that go on the horizontal (x) axis, y represents the values that go

on the vertical (y) axis


Create a graph in MATLAB® using the following information.

A) 𝑥 = [1 3 4] 𝑦 = [2 5 9] B) 𝐴 =

[ 1 23 45 67 89 10]


Figure 10: Graph Example. The MathWorks©,Inc.: MATLAB© R2018a.


Graphing Mathematical Functions (MATLAB.16)

We can graph more than just individual data points from a matrix in MATLAB®. We can also

graph mathematical functions/equations using MATLAB®.

Example: 𝑦 = 𝑥2

1st – Specify a range of values for x (x = startValue:increment:endValue) 𝑥 = −3: 0.5: 3

2nd – Specify the mathematical function that is used to obtain values for y 𝑦 = 𝑥. ^2

NOTE: We need to put the ‘.’ before ‘^’ in order to avoid an error with matrix dimensions.

The ‘.’ applies the power to each number in x rather than multiplying x by itself.

3rd – Use the plot command to create a graph of the function plot(𝑥, 𝑦)

4th – Graph (Figure 12) will appear in Figure window


Create a graph for each function in MATLAB®.

A) 𝑥 = −2𝜋:𝜋

4: 2𝜋 B) 𝑥 = −5: 0.1: 5


𝑦 = sin (𝑥) 𝑦 = 3𝑥3 − 5𝑥 + 2

Formatting Graphs in MATLAB (MATLAB.17) There are many ways that we can format a graph in MATLAB® such as changing the line type and color. Here is a partial list (

and color. Here is a partial list (

Table 5) of formatting options for graphing in MATLAB®.

(For a full list of options visit https://www.mathworks.com/help/matlab/ref/linespec.html or

search “MATLAB Linespec” online)

Line Style Specifiers Mark/Point Specifiers Color Specifiers

‘-‘ Solid Line (Default) ‘o’ Circle ‘r’ Red

‘- -‘ Dashed Line ‘+’ Plus Sign ‘g’ Green

‘:’ Dotted Line ‘*’ Asterisk ‘b’ Blue

‘d’ No Line

Table 7: Graph Formatting Options

To apply one, or multiple, specifiers to a graph, use the following:

https://www.mathworks.com/help/matlab/ref/linespec.html


Syntax: plot(x, y, ‘specifier symbol(s)’)

NOTE: All specifiers must come after the y-variable and be between the single quotes since they

are treated by MATLAB® as strings.

Examples:

plot(x, y, ‘- -r’) creates a red dashed line

plot(x, y, ‘-+b’) creates a solid blue line with plus signs as points

plot(x, y, ‘d’) creates diamond-shaped markers with no line

Example 3

Graph the function 𝑦 = √𝑥 − 5 for 𝑥 = 5: 0.5: 15 with a dotted line, circle markers, on a green

line.

Creating Graph Labels (MATLAB.17)

As we begin to model real-world phenomena with MATLAB®, it is important that we clearly

label our products so that others can clearly understand them. One way we can do this is by

titling the graph and labeling the axes. The syntax for creating graph labels is listed in Table 6. A

fully labeled graph can be seen in Figure 13.

Label Type Syntax Example

Title title(‘Enter Text Here’) title(‘Distance vs. Time Graph’)


Figure13: Labeled Graph. The MathWorks©,Inc.: MATLAB© R2018a. Screenshot by author.

x-axis xlabel(‘Enter Text Here’) xlabel(‘Time (seconds)’)

y-axis ylabel(‘Enter Text Here’) ylabel(‘Distance (feet)’) Table 8: Graph Labels


Practice Problems

1) Create a graph in MATLAB® using the following information.

A) 𝑥 = [−5 9 3 0] B) 𝑃 =

[ −3 25 92 6

−1 83 0]

𝑦 = [1 3 2 −3]


2) Plot each of the following functions using dashed red lines.

A) 𝑥 = −5: 0.5: 5 B) 𝑥 = −2: 0.1: 2

𝑦 =1

2𝑥 𝑦 = 𝑥5 − 4𝑥3 + 5𝑥 − 1

3) The following data (Table 7) shows the high temperature for a period of days and the

admission sales to a public swimming pool.

Temperature (℉) Admission Sales ($)

72 300

75 328

81 400

83 412

87 600

85 564


90 684

88 644

80 572 Table 9: Admission Sales for Public Swimming Pool

A) Store the data in a matrix called swim.

B) Create a graph of the data with the following specifications:

- Temperature is the x-value

- Admission Sales is the y-value

- Data points are represented by blue circles

- The graph is titled Swimming Pool Revenue

- Both x- and y-axes are labeled with units

6.7. RESOURCES


1. Mathworks®/MATLAB® Official Support Page:





7. CONDITIONAL STATEMENTS IN MATLAB®

7.1. INTRODUCTION

In this lesson, students will begin to create logic within a MATLAB® script using conditional

statements. Students will learn about each of the following: conditional/if statements in

MATLAB®, syntax for a conditional statement, common relational and logical operators, else

and else…if statements, and creating scripts that utilize conditional statements.

7.2. MATERIALS



Copy of Introduction to MATLAB® - Conditional Statements in MATLAB® guided notes





Copy of Introduction to MATLAB® - Conditional Statements in MATLAB® answer key





Be able to describe how a conditional/if statement works in computer programming.

A conditional statement, also commonly referred to as an if statement, is a statement that

allows the computer to make a logical decision. A conditional statement works by presenting

the computer with a logical statement (a statement that is either true or false) as a condition. If







an input makes the condition true, then the computer will perform a specific task. If the input

makes the condition false, then the computer will not perform the task. A detailed flowchart for

a conditional/if statement is given in the guided notes to help students better understand this

logical structure.

It is very important that students understand conceptually how a conditional statement works.

Not only will this knowledge help students in creating conditional statements, but it will also

help them troubleshoot issues that may arise in their programs by stepping through the logical

steps that the conditional statement takes.


Be able to explain the meaning of the major logical operators in computer programming.

Conditional statements require the use of logical operators when setting up the condition to be

checked. For instance, should we check to see when a variable grows larger than a specified

value or should we check to see when a variable is equivalent to a specified value? Each of

these questions requires the use of a different logical operator to check the condition.

There are many different logical and relational operators; however, students will only need to

know some of the more commonly used ones (e.g., inequality symbols, and, or). A table of the

common logical and relational operators is provided for students in the guided notes.

Not only will knowledge of these operators be important for working with conditional

statements but will be used extensively in the next two lessons about loops.


Be able to utilize conditional statements in MATLAB® scripts.

After this lesson, students should become familiar with setting up and using conditional

statements within their scripts. A conditional statement has a multiline syntax that is a bit

different from what students have done up to this point.

To start a conditional statement, the keyword if must be typed followed by a logical statement

(i.e., the condition) that is to be checked by the computer. The next part of the conditional

statement is typed under the logical statement by pressing the Enter key. Here, students will

type the commands they wish the computer to run if an input value makes the condition true.

Lastly, the conditional statement must end with the keyword end to tell the computer that the

conditional statement is done. The general syntax for a conditional statement is shown in the

guided notes.


One thing to note when creating conditional statements in MATLAB® is the indentation that

MATLAB® uses. The list of commands within an if statement is indented 4 spaces to the right of

where the if statement started. While this indentation is not necessary for the program to run

correctly, there are many programming languages where the indentation is crucial. Therefore, it

is considered best practice that any commands within an if statement or loop body are

indented 4 spaces from where the start of the if statement or loop begin.

7.4. GUIDED NOTES

Introduction to MATLAB

Conditional Statements in MATLAB

Name:___________________________ Date:_____________ Period:__________

Learning Targets:

MATLAB.18 – Be able to describe how a conditional/if statement works in computer

programming.

MATLAB.19 – Be able to explain the meaning of the major logical operators in computer

programming.

MATLAB.20 – Be able to utilize conditional statements in MATLAB scripts.

How Do Computers Make Decisions? (MATLAB.18)

There are times when we want a MATLAB script to perform different tasks depending on what

the user types. To accomplish this, we can use a conditional statement.

A conditional statement is a statement of the form _________________________ and allows

the computer to run a specific set of code in response to user input. The flowchart below

(Figure 16) illustrates the steps taken within a conditional/if statement.


Logic of a Conditional Statement (MATLAB.18)

NO

Input

Condition:

Does the input make the

condition true?

YES

Run code under IF BLOCK

Continuation of

Program

Figure 11: Conditional Statement Flowchart. Created by author.


Conditional Statements in MATLAB (MATLAB.18)

The syntax for a conditional statement in MATLAB is the following:

1) if <condition> 1) The <condition> will be a ________________________ that is

either TRUE or FALSE.

2) statement(s) 2) The statements are the commands the MATLAB will run

if the condition is _________.

3) end 3) Every if block must end with the keyword end.

NOTE: Make sure to use proper spacing. Statements after the if statement should be indented 4

spaces and the end keyword should align itself with the if statement.

Relational and Logical Operators in MATLAB (MATLAB.19)

The following symbols (Table 10) can be used to create a logical expression in a conditional

statement.

Symbol Meaning

<

<=

>

>=

==

~=

&& (AND)

|| (OR)


Table 10: Relational and Logical Operators


Determine what will happen in each of the following scripts. In these examples if a condition is

NOT true, nothing will happen.

A)

B)

C)


If…Else and Elseif Statements in MATLAB (MATLAB.18)

We can make conditional statements more versatile by using else or elseif blocks.

The else block of an if…else statement (Figure 17) is a section of code that runs when the

condition is ____________.

An elseif block (Figure ) in an if…else statement allows the script to check multiple

_________________ and execute the first of which is true.

Logic of an If…Else Statement (MATLAB.18)

NO

Input

Condition:


condition true?

YES

Run code under ELSE

BLOCK

Continuation

of Program

Run code under IF

BLOCK

Figure 12: If...Else Statement. Created by author.


Logic of an If…Elseif…Else Statement (MATLAB.18)


Determine the output will be for each of the following scripts.

A) B)

TRUE TRUE TRUE

Continuation of

Program

FALSE

Condition 3

Input

Condition 1

Condition 2

FALSE

FALSE

Perform action/code under

ELSE BLOCK

Run code under IF

BLOCK

Run code under ELSEIF

BLOCK 1 Run code under ELSEIF

BLOCK 2

Figure 13: If...Elseif...Else Statement. Created by author.



Examine the script shown below.

For A – C, determine the output of the script for each of the following inputs:

A) numHours = 3

B) numHours = 15

C) numHours = 40

D) What number would the user have to type into the script to get the message, “How can you

play that many hours?”



A) Create a script that allows the user to type in two numbers. The script should then compare

the two numbers and state the relation between them (“a is larger than b”, “a is equal to b”,

etc.)

B) Create a script that will display the statement, “MATLAB is fun!” when the user types a

number that is less than or equal to 5 or greater than 11.






MATLAB®.

Practice Problems

1) A store that specializes in flooring offers special rates on carpet when purchased in certain

quantities. The table below shows the price for carpet and installation:

Amount (Square Feet) Price (Per Square Foot) Installation Fee (Per Square Foot)

1 – 100 $2.79 $1.75

101 – 200 $2.50 $1.50

201 – 400 $2.19 $1.25

401 – 800 $1.79 $1.00


Create a script that calculates the total cost (including 7.5% for tax) on any amount of carpet

that the user types in. The script should print the final amount in a well-formatted sentence.

The script should also let the user know if they typed in an invalid amount of carpet.

2) Suppose you are a design engineer for a company that manufactures consumer electronic

devices and you are estimating the cost of producing a new product. The product has four

components that are purchased from electronic parts suppliers and assembled in your factory.

You have received cost information from your suppliers for each of the parts; as is typical in the

electronics industry, the cost of a part depends on the number of parts you order from the

supplier.

Your assembly cost for each unit includes the cost of labor and your assembly plant. You have estimated that these costs are C0=$45.00/unit.

The cost of each part depends on the number of parts purchased; we will use the variable n to represent the number of parts, and the variables CA, CB, CC, and CD to represent the unit cost of each type of part. These costs are given in the table below.

Unit Cost of Part A

Unit Cost of Part B

Unit Cost of Part C

Unit Cost of Part D

Number of Parts (n)

CA Number of Parts (n)

CB Number of Parts (n)

CC Number of Parts (n)

CD

1 – 4 $16.00 1 – 9 $24.64 1 – 24 $17.98 1 – 9 $12.50

5 – 24 $14.00 10 – 49 $24.32 25 – 49 $16.78 10 – 99 $10.42

25 – 99 $12.70 50 – 99 $24.07 50 or more $15.78 100 or more $9.62

100 or more

$11.00 100 or more

$23.33

More than 800 $1.50 Free


The unit cost is unit = C0 + CA + CB + CC + CD.

To find the unit cost to build one unit, we look in the above tables with a value of n = 1; the unit cost is $45.00+ $16.00+ $24.64+ $17.98+ $12.50= $116.12 To find the unit cost to build 20 units, we look in the above tables with a value of n = 20 and get $45.00+ $14.00+ $24.32+ $17.98+ $10.42= $109.72 As expected, the unit cost for 20 units is lower than the unit cost for one unit.

Create a script that asks for the total number of parts needed, n, and computes the total unit

cost for the new product. (Morrell & Gjendemsjø, 2012)

Morrell, Darryl, and Anders Gjendemsjø. "An Introduction to Solving Engineering Problems with MATLAB." CK-12, CK-12, 23

Feb. 2012, www.ck12.org/book/Engineering%3A-An-Introduction-to-Solving-Engineering-Problems-with-Matlab/. Accessed 26

June 2018.

7.6. ANSWER KEYS

7.6.1. GUIDED NOTES


Conditional Statements in MATLAB

Name:___________________________ Date:_____________ Period:__________

Learning Targets:

MATLAB.18 – Be able to describe how a conditional/if statement works in computer

programming.


MATLAB.19 – Be able to explain the meaning of the major logical operators in computer

programming.

MATLAB.20 – Be able to utilize conditional statements in MATLAB scripts.

How Do Computers Make Decisions? (MATLAB.18)

There are times when we want a MATLAB script to perform different tasks depending on what

the user types. To accomplish this, we can use a conditional statement.

A conditional statement is a statement of the form if…then… and allows the computer to run a

specific set of code in response to user input. The flowchart below (Figure 16) illustrates the

steps taken within a conditional/if statement.

Logic of a Conditional Statement (MATLAB.18)

NO

Input

Condition:


condition true?

YES

Run code under IF BLOCK

Continuation of

Program

Figure 14: Conditional Statement Flowchart. Created by author.


Conditional Statements in MATLAB (MATLAB.18)

The syntax for a conditional statement in MATLAB is the following:

1) if <condition> 1) The <condition> will be a logical/Boolean expression that is

either TRUE or FALSE.

2) statement(s) 2) The statements are the commands the MATLAB will run

if the condition is TRUE.

3) end 3) Every if block must end with the keyword end.

NOTE: Make sure to use proper spacing. Statements after the if statement should be indented 4

spaces and the end keyword should align itself with the if statement.

Relational and Logical Operators in MATLAB (MATLAB.19)

The following symbols (Table 10) can be used to create a logical expression in a conditional

statement.

Symbol Meaning

< Less than

<= Less than or equal to

> Greater than

>= Greater than or equal to

== Equal to/Same

~= Not equal to

&& (AND) Used to join two or more conditions. Evaluates to TRUE when ALL conditions are true.

|| (OR) Used to join two or more conditions. Evaluates to TRUE when at least one condition is true.

Table 10: Relational and Logical Operators



Determine what will happen in each of the following scripts. In these examples if a condition is

NOT true, nothing will happen.

A)

The script will display “a is less than 5”

B)

The script will calculate 2.5 * 4 since 2.5 > 0, and store the answer in x.

The script will then display “10”.

C)

The script will not do anything since the condition (c < 0) is not true.

If…Else and Elseif Statements in MATLAB (MATLAB.18)

We can make conditional statements more versatile by using else or elseif blocks.

The else block of an if…else statement (Figure 17) is a section of code that runs when the

condition is FALSE.


An elseif block (Figure 18) in an if…else statement allows the script to check multiple conditions

and execute the first of which is true.

Logic of an If…Else Statement (MATLAB.18)

NO

Input

Condition:


condition true?

YES

Run code under ELSE

BLOCK

Continuation

of Program

Run code under IF

BLOCK

Figure 17: If...Else Statement. Created by author.


Logic of an If…Elseif…Else Statement (MATLAB.18)


Determine the output for each of the following scripts.

A)

TRUE TRUE TRUE

Continuation of

Program

FALSE

Condition 3

Input

Condition 1

Condition 2

FALSE

FALSE

Perform action/code under

ELSE BLOCK

Run code under IF

BLOCK

Run code under ELSEIF

BLOCK 1 Run code under ELSEIF

BLOCK 2

Figure 18: If...Elseif...Else Statement. Created by author.


Since myGrade >= 60 is TRUE when myGrade = 67, the output will be, “You are passing the

class.”

B)

The second condition (item >= 10 && item < 15) is the true condition when item = 10.

Therefore, the script will perform the calculation: cost = 2.75 * 10 + 5. The answer 32.50 will be

displayed on the screen.


Examine the script shown below.

For A – C, determine the output of the script for each of the following inputs:

A) numHours = 3

An input of 3 makes the second condition true. The message, “You must be busy with other

things.” will be displayed.


B) numHours = 15

An input of 15 makes the fourth condition true. The message, “You must have a lot of free

time.” will be displayed.

C) numHours = 40

An input of 40 makes the fourth condition true. The message, “You must have a lot of free

time.” will be displayed.

D) What number would the user have to type into the script to get the message, “How can you

play that many hours?”

For this to occur, the first four conditions must be false. The first condition covers an input of 0;

the second condition covers input values larger than 0 but less than or equal to 5; the third

condition covers input values larger than 5 but less than or equal to 10; and the fourth

condition covers all input values larger than 10. The only input values not addressed by the

conditions are the numbers that are less than 0 (i.e., negative numbers.) Any negative input

value will cause all four conditions to fail and the message, “How can you play that many

hours?” to be displayed.


A) Create a script that allows the user to type in two numbers. The script should then compare

the two numbers and state the relation between them (“a is larger than b”, “a is equal to b”,

etc.)

B) Create a script that will display the statement, “MATLAB is fun!” when the user types a

number that is less than or equal to 5 or greater than 11.

NOTE: There are many ways to create this script. This is one way.



Practice Problems

NOTE: There are multiple ways to create the scripts in these problems. One example solution is

provided.

1) A store that specializes in flooring offers special rates on carpet when purchased in certain

quantities. The table below shows the price for carpet and installation:

Create a script that calculates the total cost (including 7.5% for tax) on any amount of carpet

that the user types in. The script should print the final amount in a well-formatted sentence.

The script should also let the user know if they typed in an invalid amount of carpet.

Amount (Square Feet) Price (Per Square Foot) Installation Fee (Per Square Foot)

1 – 100 $2.79 $1.75

101 – 200 $2.50 $1.50

201 – 400 $2.19 $1.25

401 – 800 $1.79 $1.00

More than 800 $1.50 Free


2) Suppose you are a design engineer for a company that manufactures consumer electronic

devices and you are estimating the cost of producing a new product. The product has four

components that are purchased from electronic parts suppliers and assembled in your factory.

You have received cost information from your suppliers for each of the parts; as is typical in the

electronics industry, the cost of a part depends on the number of parts you order from the

supplier.

Your assembly cost for each unit includes the cost of labor and your assembly plant. You have estimated that these costs are C0=$45.00/unit.

The cost of each part depends on the number of parts purchased; we will use the variable n to represent the number of parts, and the variables CA, CB, CC, and CD to represent the unit cost of each type of part. These costs are given in the table below.

Unit Cost of Part A

Unit Cost of Part B

Unit Cost of Part C

Unit Cost of Part D

Number of Parts (n)

CA Number of Parts (n)

CB Number of Parts (n)

CC Number of Parts (n)

CD

1 – 4 $16.00 1 – 9 $24.64 1 – 24 $17.98 1 – 9 $12.50

5 – 24 $14.00 10 – 49 $24.32 25 – 49 $16.78 10 – 99 $10.42

25 – 99 $12.70 50 – 99 $24.07 50 or more $15.78 100 or more $9.62

100 or more

$11.00 100 or more

$23.33

The unit cost is unit = C0 + CA + CB + CC + CD.

To find the unit cost to build one unit, we look in the above tables with a value of n = 1; the unit cost is $45.00+ $16.00+ $24.64+ $17.98+ $12.50= $116.12 To find the unit cost to build 20 units, we look in the above tables with a value of n = 20 and get $45.00+ $14.00+ $24.32+ $17.98+ $10.42= $109.72 As expected, the unit cost for 20 units is lower than the unit cost for one unit.


Create a script that asks for the total number of parts needed, n, and computes the total unit

cost for the new product. (Morrell & Gjendemsjø, 2012)

Morrell, Darryl, and Anders Gjendemsjø. "An Introduction to Solving Engineering Problems with MATLAB." CK-12, CK-12, 23

Feb. 2012, www.ck12.org/book/Engineering%3A-An-Introduction-to-Solving-Engineering-Problems-with-Matlab/. Accessed 26

June 2018.


7.7. RESOURCES










8. INTRODUCTION TO LOOPS: FOR LOOPS

8.1. INTRODUCTION

In this lesson, students will be introduced to looping. Students will learn about the structure of

for loops, how to step through and explain each step of a for loop, as well as how to create for

loops to perform small programming tasks and graphing.

8.2. MATERIALS



Copy of Introduction to MATLAB® - Introduction to Loops: For Loops guided notes (these





Copy of Introduction to MATLAB® - Introduction to Loops: For Loops answer key





Be able to explain how a for loop works in MATLAB® and other programming languages.

For loops are a common structure found in MATLAB® and other programming languages. The

logic behind a for loop is important for students to understand as they are used heavily in

MATLAB® and many other programming languages.

A for loop is a structure within a program that repeats a section of code multiple times. The

number of iterations (i.e., repetitions) is based on the end value of an index variable (i.e.,

counter). After each execution of the code, the index variable increases by 1 until it has reached

its end value. Once the end value is reached, the loop terminates and any code occurring after

the loop will be executed.




Students should be able to analyze a for loop and explain what value(s) it will output. Students

should also be able to explain what the loop does at various points during its execution.


Be able to utilize for loops in MATLAB® scripts.

After this lesson, students should be able to create for loops for a variety of situations from

evaluating a mathematical function, creating a graph, and performing a series of calculations to

solve a problem. It is important to note that for loops can be used in many situations, and that

this lesson covers a very limited number of those situations.

Loops can be difficult for students, especially students with little to no programming

background. This lesson may take a few days for students to complete. As students begin to

create their own for loops, encourage them to step through the code line by line either

mentally or, preferably, on paper. This will not only help with troubleshooting should problems

arise in their code but will also help students process the logical steps that occur during a for

loop.

8.4. GUIDED NOTES


Introduction to Loops: For Loops

Name:___________________________ Date:_____________ Period:__________

Learning Targets:

MATLAB.21 – Be able to explain how a for loop works in MATLAB and other programming

languages.

MATLAB.22 – Be able to utilize for loops in MATLAB scripts.

What is a Loop? (MATLAB.21)

There may be situations where we want parts of a program to be used multiple times (e.g.,

performing a series of calculations on a list of numbers, run a program multiple times based on

user input). To achieve this functionality, we can use what is commonly referred to as a loop in

computer programming.

Loops are structures that allow code to be ___________________ until certain conditions are

met.


One type of loop that can be used is a for loop (Figure and Figure ). A for loop will repeat code

_________________________________________________________________________

Logic of a For Loop (MATLAB.21)

For Loops in MATLAB (MATLAB.21)

The syntax for a for loop in MATLAB is as follows:

1) for index/counter = array/values 1) The index/counter is a ___________ that stores

the values to be iterated through the loop. Line

must begin with the keyword ________.

Start

Define Array:

(x = start:increment:end)

Check Condition:

Are there anymore

elements in the array?

Run code in loop body for

the selected element

True

Increment Index:

(Move to next element of Array)

False

End

Figure 22: For Loop in MATLAB® Created by author.

Initialize Index/Counter:

(x = 0)

Check Condition:

Is counter’s value less

than a given value?

Run code in loop body

True

Increment Counter

(x = x + 1)

False

Start

End

Figure 23: Traditional For Loop. Created by author.


2) statement(s) 2) The statements are the commands that MATLAB

will run using the values stored in the

___________________.

3) end 3) Every for loop block must end with the keyword

__________.

Example of For Loop in MATLAB (MATLAB.21)

In this example, i represents the ___________________ of the for loop, and its values range

from ______________.

Beginning with i = 1, the statements in the loop body are executed:

d = i + 12

disp(d)

Once the body is completed, the program returns to the first line and changes the value of i to

__________________________________________________, or i = ________. The process

continues in this manner until all values specified by the index/counter have been used.

Here is what the example would look like as a flowchart (Figure 24):



Determine how many times the output in each program will be displayed.

A)

B)

C)

i = 2

d = 2 + 12 =

14

i = 3

d = 3 + 12 =

15

i = 4

d = 4 + 12 =

16

i = 1

d = 1 + 12 =

13

For i = 1:5

No more

elements

in array

End For Loop

i = 5

d = 5 + 12 =

17

i = 6?

Figure 15: For Loop Flowchart Example



What sequence of numbers will the following loop print? Explain why this code does what it

does.


A) What value will be displayed when this script is ran?

B) How could we find this answer more quickly using math?


A) Create a for loop that will take the values from -5 to 5 and multiply them by 3.


a

b

c

B) Create a for loop that will evaluate the function 𝑦 = 2𝑥2 − 3𝑥 + 1 for all values of x from 1

and 10.

C) Use a for loop to graph 𝑦 = cos (2𝜋𝑓𝑡) for values of t from 0 to 4 and for the following values

of f: 0.5, 1, 1.8, and 2.6.


Suppose you are modifying an RC car and are designing wheels that will achieve a given travel

speed. The radius (in inches) of the wheel is represented by r, and the rotations per second by

the wheel is represented by w. The speed of the car (s) in inches per second can be found by

using the formula 𝑠 = 2𝜋𝑟𝑤.

On a single graph, create plots of the relationship between s and w for the following r values:

0.4 in., 0.7 in., 1.3 in., 3.2 in., and 4.0 in.


The following table represents different lengths of the legs of a right triangle.

Use a for loop and the Pythagorean Theorem to determine the length of the hypotenuse (c) for

each pair of leg values.

a b

1 1

2 3

4 2

7 3

a

b

c







MATLAB®.

Practice Problems

1) Determine how many times the output in each program will be displayed.

A)

B)

C)

2) Create a loop in the MATLAB editor that will complete each of the following tasks.

A) Take the values from -2 to 8 and find three more than double of each value.


B) Plot the graph of ℎ = −4.9𝑡2 + 45𝑡 + 3 for the t-values of 0, 1.7, 2.9, and 4.

3) Use the distance formula, 𝑑 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2 , to determine the distance

between each set of consecutive points in the table.

4) Suppose a cylinder has a height h and base diameter of b, and you want to find out how

many ping-pong balls of diameter d could fit into the cylinder. To figure this out, we need to

learn how to compute the lower bound on the number of ping-pong balls.

A lower bound for this problem can be found using the following:

𝑁𝐿 – Lower bound on the number of balls that fit into the cylinder. 𝑁𝐿 =𝑉𝑐𝑦𝑙

𝑉𝑐𝑢𝑏𝑒

𝑉𝑐𝑦𝑙 – The volume of the cylinder. 𝑉𝑐𝑦𝑙 = 𝜋 (𝑏

2)2

ℎ

𝑉𝑐𝑢𝑏𝑒 – The volume of a cube that encloses a single ball. 𝑉𝑐𝑢𝑏𝑒 = 𝑑3

x y

1 1

2 -4

3 8

4 5

5 -1

6 3


A) Use the command line prompt to determine the lower bound of the ping-pong balls given

that d = 1.54 in., b = 8 in., and h = 14 in.

B) Create a script that would allow you to solve the problem in A).

C) Add a for loop to your script to compute 𝑁𝐿 for b = 8 in. and h = 14 in. Let the values of d

range from 1 in. to 2 in., incrementing each value by 0.1 in.

D) Add a plot function to your script to plot 𝑁𝐿 as a function of d for b = 8 in. and h = 14 in.

E) Modify your script to compute 𝑁𝐿 for d = 1.54 in. and various values of b and h (at least 10

values for each)

8.6. ANSWER KEYS

8.6.1. GUIDED NOTES


Introduction to Loops: For Loops

Name:___________________________ Date:_____________ Period:__________

Learning Targets:

MATLAB.21 – Be able to explain how a for loop works in MATLAB and other programming

languages.

MATLAB.22 – Be able to utilize for loops in MATLAB scripts.

What is a Loop? (MATLAB.21)

There may be situations where we want parts of a program to be used multiple times (e.g.,

performing a series of calculations on a list of numbers, run a program multiple times based on


user input). To achieve this functionality, we can use what is commonly referred to as a loop in

computer programming.

Loops are structures that allow code to be repeated until certain conditions are met.

One type of loop that can be used is a for loop (Figure and Figure ). A for loop will repeat code a

specific number of times based on a value of the index variable/counter.

Logic of a For Loop (MATLAB.21)

For Loops in MATLAB (MATLAB.21)

The syntax for a for loop in MATLAB is as follows:

Start

Define Array:

(x = start:increment:end)

Check Condition:

Are there anymore

elements in the array?

Run code in loop body for

the selected element

True

Increment Index:

(Move to next element of Array)

False

End

Figure 22: For Loop in MATLAB®

Initialize Index/Counter:

(x = 0)

Check Condition:

Is counter’s value less

than a given value?

Run code in loop body

True

Increment Counter

(x = x + 1)

False

Start

End

Figure 23: Traditional For Loop


1) for index/counter = array/values 1) The index/counter is a variable that stores

the values to be iterated through the loop. Line

must begin with the keyword for.

2) statement(s) 2) The statements are the commands that MATLAB

will run using the values stored in the

index/counter.

3) end 3) Every for loop block must end with the keyword

end.

Example of For Loop in MATLAB (MATLAB.21)

In this example, i represents the index/counter of the for loop, and its values range from 1 to 5.

Beginning with i = 1, the statements in the loop body are executed:

d = i + 12 d = 1 + 12 = 13

disp(d) 13

Once the body is completed, the program returns to the first line and changes the value of i to

the next value of the index/counter, or i = 2. The process continues in this manner until all

values specified by the index/counter have been used.




Determine how many times the output in each program will be displayed.

A)

‘Video games are fun!’ will be displayed 20 times.

B)

‘Kon’nichiwa sekai!’ will be displayed 59 times.

C)

‘How can you figure this out?’ will be displayed 15 times.


i = 2

d = 2 + 12 =

14

i = 3

d = 3 + 12 =

15

i = 4

d = 4 + 12 =

16

i = 1

d = 1 + 12 =

13

For i = 1:5

No more

elements

in array

End For Loop

i = 5

d = 5 + 12 =

17

i = 6?

Figure 24: For Loop Flowchart Example. Created by author.


What sequence of numbers will the following loop print? Explain why this code does what it

does.

Sequence: 6, 5, 4, 3, 2, 1, 0

In this code, a starts with a value of 7. The loop counter will execute from 1 to 7, for a total of 7

times. Each time the loop body executes, it takes the current value of a and subtracts 1 from it.

This new value is re-stored in a and is displayed on the screen.

When 7 is passed through the loop for the first time, its value becomes 6 (i.e., a = 7 – 1), and is

displayed before the loop body executes again. The table below (Table 8) shows how the

variable values change throughout the loop.

j (index/counter) a a = a – 1 disp(a)

1 7 7 – 1 6

2 6 6 – 1 5

3 5 5 – 1 4

4 4 4 – 1 3

5 3 3 – 1 2

6 2 2 – 1 1

7 1 1 – 1 0 Table 8: Example 2 Loop Analysis



A) What value will be displayed when this script is ran?

3000

B) How could we find this answer more quickly using math?

Determine the number of times each loop will activate and multiply the values together (i.e., a

will loop 5 times, b will loop 10 times, c will loop 20 times, and d will loop 3 times):

5 ∗ 10 ∗ 20 ∗ 3 = 3000


A) Create a for loop that will take the values from -5 to 5 and multiply them by 3.

B) Create a for loop that will evaluate the function 𝑦 = 2𝑥2 − 3𝑥 + 1 for all values of x from 1

and 10.

C) Use a for loop to graph 𝑦 = cos (2𝜋𝑓𝑡) for values of t from 0 to 4 and for the following values

of f: 0.5, 1, 1.8, and 2.6.


a

b

c


Suppose you are modifying an RC car and are designing wheels that will achieve a given travel

speed. The radius (in inches) of the wheel is represented by r, and the rotations per second by

the wheel is represented by w. The speed of the car (s) in inches per second can be found by

using the formula 𝑠 = 2𝜋𝑟𝑤.

On a single graph, create plots of the relationship between s and w for the following r values:

0.4 in., 0.7 in., 1.3 in., 3.2 in., and 4.0 in.


The following table represents different lengths of the legs of a right triangle.

Use a for loop and the Pythagorean Theorem to determine the length of the hypotenuse (c) for

each pair of leg values.

a b

1 1

2 3

4 2

7 3

a

b

c



Practice Problems

1) Determine how many times the output in each program will be displayed.

A)

‘Good Morning,’ will be displayed 27 times.

B)

‘Good night,’ will be displayed 49 times.

C)

101,250 (i.e., 10 * 15 * 25 * 27)

2) Create a loop in the MATLAB editor that will complete each of the following tasks.

A) Take the values from -2 to 8 and find three more than double of each value.

B) Plot the graph of ℎ = −4.9𝑡2 + 45𝑡 + 3 for the t-values of 0, 1.7, 2.9, and 4.


3) Use the distance formula, 𝑑 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)

2 , to determine the distance

between each set of consecutive points in the table.

4) Suppose a cylinder has a height h and base diameter of b, and you want to find out how

many ping-pong balls of diameter d could fit into the cylinder. To figure this out, we need to

learn how to compute the lower bound on the number of ping-pong balls.

A lower bound for this problem can be found using the following:

𝑁𝐿 – Lower bound on the number of balls that fit into the cylinder. 𝑁𝐿 =𝑉𝑐𝑦𝑙

𝑉𝑐𝑢𝑏𝑒

𝑉𝑐𝑦𝑙 – The volume of the cylinder. 𝑉𝑐𝑦𝑙 = 𝜋 (𝑏

2)2

ℎ

𝑉𝑐𝑢𝑏𝑒 – The volume of a cube that encloses a single ball. 𝑉𝑐𝑢𝑏𝑒 = 𝑑3

A) Use the command line prompt to determine the lower bound of the ping-pong balls given

that d = 1.54 in., b = 8 in., and h = 14 in.

x y

1 1

2 -4

3 8

4 5

5 -1

6 3


B) Create a script that would allow you to solve the problem in A).

C) Add a for loop to your script to compute 𝑁𝐿 for b = 8 in. and h = 14 in. Let the values of d

range from 1 in. to 2 in., incrementing each value by 0.1 in.

D) Add a plot function to your script to plot 𝑁𝐿 as a function of d for b = 8 in. and h = 14 in.


E) Modify your script to compute 𝑁𝐿 for d = 1.54 in. and various values of b and h (at least 10

values for each).

8.7. RESOURCES










9. INTRODUCTION TO LOOPS: WHILE LOOPS

9.1. INTRODUCTION

In this lesson, students will continue their work with loops, advancing on to while loops.

Students will learn about the structure of while loops, how to step through and explain each

line of code in a while loop, as well as how to create while loops to perform small programming

tasks.

9.2. MATERIALS



Copy of Introduction to MATLAB® - Introduction to Loops: While Loops guided notes





Copy of Introduction to Loops: While Loops answer key





Be able to explain how a while loop works in MATLAB® and other programming languages.

Just like for loops from the previous lesson, while loops are structures that are used to repeat a

specific section of code. While loops are used quite extensively in MATLAB® as well as other

programming languages.

A for loop iterates over a section of code a specific number of times (i.e., the index variable has

a start and end value), whereas a while loop will continue to iterate until a specific condition is

met or fails. It is important that the students understand the logic that drives a while loop and

be able to explain what happens at various points when a while loop executes.





Be able to utilize while loops in MATLAB® scripts.

After this lesson, students should be able to create while loops for a variety of situations

including divisibility tests and simple games. This lesson only covers a small sample of while

loop problems, but many more exist. In fact, many problems containing a for loop could be

reconfigured to use a while loop too.

Loops can be difficult for students, especially students with little to no programming

background. This lesson may take a few days for students to complete. As students begin to

create their own while loops, encourage them to step through the code line by line either

mentally or, preferably, on paper. This will not only help with troubleshooting should problems

arise in their code but will also help students process the logical steps that occur during a while

loop.

9.4. GUIDED NOTES


Introduction to Loops: While Loops

Name:___________________________ Date:_____________ Period:__________

Learning Targets:

MATLAB.23 – Be able to explain how a while loop works in MATLAB and other programming

languages.

MATLAB.24 – Be able to utilize while loops in MATLAB scripts.

What is a While Loop? (MATLAB.23)

A while loop is a loop (Figure 28) that will execute a body of code until a specific

_______________________________ is met.


Logic of a While Loop (MATLAB.23)

While Loops in MATLAB (MATLAB.23)

The syntax for a while loop in MATLAB is as follows:

1) while <expression> 1) The expression is a logical expression (i.e., it is

either true or false) that determines if the loop

body is executed. Line must begin with the

keyword _____________.

2) statement(s) 2) The statements are the commands that MATLAB will

run only when the logical expression from the while

statement is _____________.

Start

Check Condition:

A logical expression that

evaluates to true or false

Run code in loop body for the

selected element

True

Update Variable Values

False

End

Figure 16: While Loop in MATLAB®. Created by author.


Figure 17: Sample While Loop

3) end 3) Every while loop block must end with the keyword

___________.

Example of While Loop in MATLAB (MATLAB.23)

In this example (Figure 29), the variables a, b, and total are ____________________, meaning

that they are given values prior to entering the loop. This must be done as the program will

NOT recognize them when it begins the loop otherwise.

Once the program reaches the while loop, it checks to see if the sum of a and b is

________________________ total. When this condition is true, the loop body is executed.

First run of while loop:

a = 3, b = 2, total = 40

Check Condition: a + b < 40? TRUE / FALSE

If true:

a = a * 2

b = b * 2

fprintf(…)


Once the body is completed, the program returns to the while loop statement and checks to

see if ____________________________. The program will continue this process until this

condition is false.



Determine the number of times each string will be printed in each script.

A)

B)

a = 12

b = 8 a = 24

b = 16

a = 12 * 2 = 24

b = 8 * 2 = 16

FalTr

True

a = 3 * 2 = 6

b = 2 * 2 = 4

a = 3, b = 2

total = 40

(Initialize)

Condition:

a + b < total?

a = 6

b = 4

End While

Loop

Condition:

a + b < total?

a = 6 * 2 = 12

b = 4 * 2 = 8

Condition:

a + b < total? Condition:

a + b < total?

True True False

Figure 18: While Loop Flowchart Example. Created by author.



Determine the number of times the string will be printed in the following script.

Why does the script act the way that it does? Explain.


What values will the following code print?


Use a while loop to solve each of the following problems.

A) Create a script that asks the user to input a value that is greater than 0. The script should

keep asking until a valid number is entered.

B) Create a script that asks the user to enter two numbers and determines if the sum of the

numbers is even. An even number is one that is divisible by 2. The script should continue asking

for two numbers until their sum is even.


NOTE: You will need to use the b = mod(a,m) mathematical function (mod is short for modular

arithmetic). Mod calculates the remainder of a / m.

Examples:

mod(10,2) = 0 mod(10,3) = 1 mod(8,3) = 2 mod(125,6) = 5

C) Create a number guess game where a random integer from 1 to 20 is chosen, and the player

gets a maximum of three chances to guess the correct number. After each guess, the player

should receive feedback that tells them whether their guess was too low or too high. The

program should congratulate the player if they guess the correct number within the guess limit;

and the program should tell the player what number it had chosen if three incorrect guesses

have been made.

NOTE: To generate a random integer, use the randi(imax) function of MATLAB. The function

works by replacing imax with a positive integer value. The program will then select a random

integer between 1 and the value imax is equal to.

Example: a = randi(10) The value of a will be number selected randomly from 1 to 10.






MATLAB®.

Practice Problems


1) Determine the number of times each string will print in the following scripts.

A)

B)

C)

D)

2) Use a while loop to solve each of the following problems.

A) Create a script that displays the consecutive integers from 10 to 20.


B) Create a script that asks the user to enter two numbers and determines if the difference of

the numbers is a multiple of 6 (e.g., 6, 12, 18, 24… are multiples of 6). The script should

continue asking for two numbers until their difference is a multiple of 6.

3) Create a game of rock-paper-scissors in MATLAB. Here are the requirements:

Utilize a while loop to determine when the game is over

Player should be able to choose rock, paper, or scissors on his/her turn

o NOTE: You may use numeric values to represent each item (e.g., “Press 1 for

rock,…”), but be sure to communicate this clearly to players through your

program

The computer will randomly pick rock, paper, or scissors for each round

The program should compare the choices made by the player and computer to see who

wins the round

o Rules: rock beats scissors, paper beats rock, scissors beat paper

One point is awarded to the player who wins a round

The game is over when either the player or computer earns three points

When the game is over, a message should display based on whether a player won or lost

o Example: “Congratulations!” or “Nice try!”

Your program will require the use of a while loop, conditional statements, input functions, and

other topics covered throughout the previous lessons. Good luck!

9.6. ANSWER KEYS

9.6.1. GUIDED NOTES


Introduction to Loops: While Loops

Name:___________________________ Date:_____________ Period:__________

Learning Targets:


MATLAB.23 – Be able to explain how a while loop works in MATLAB and other programming

languages.

MATLAB.24 – Be able to utilize while loops in MATLAB scripts.

What is a While Loop? (MATLAB.23)

A while loop is a loop (Figure 28) that will execute a body of code until a specific condition is

met.

Logic of a While Loop (MATLAB.23)

While Loops in MATLAB (MATLAB.23)

The syntax for a while loop in MATLAB is as follows:

Start

Check Condition:

A logical expression that

evaluates to true or false

Run code in loop body for the

selected element

True

Update Variable Values

False

End

Figure 19: While Loop in MATLAB®


Figure 20: Sample While Loop. Created by author.

1) while <expression> 1) The expression is a logical expression (i.e., it is

either true or false) that determines if the loop

body is executed. Line must begin with the

keyword while.

2) statement(s) 2) The statements are the commands that MATLAB will

run only when the logical expression from the while

statement is true.

3) end 3) Every while loop block must end with the keyword end.

Example of While Loop in MATLAB (MATLAB.23)

In this example (Figure 29), the variables a, b, and total are initialized, meaning that they are

given values prior to entering the loop. This must be done as the program will NOT recognize

them when it begins the loop otherwise.

Once the program reaches the while loop, it checks to see if the sum of a and b is less than

total. When this condition is true, the loop body is executed.

First run of while loop:

a = 3, b = 2, total = 40

Check Condition: a + b < 40? TRUE / FALSE since 3 + 2 < 40 is a true statement

If true:

a = a * 2 a = 3 * 2 = 6 new value of a is 6


b = b * 2 b = 2 * 2 = 4 new value of b is 4

fprintf(…)

Once the body is completed, the program returns to the while loop statement and checks to

see if a + b < 40 is true for the new values of a and b. The program will continue this process

until this condition is false.



Determine the number of times each string will be printed in each script.

A)

‘Hola! Como estas?’ will be displayed 5 times.

B)

a = 12

b = 8 a = 24

b = 16

a = 12 * 2 = 24

b = 8 * 2 = 16

FalTr

True

a = 3 * 2 = 6

b = 2 * 2 = 4

a = 3, b = 2

total = 40

(Initialize)

Condition:

a + b < total?

a = 6

b = 4

End While

Loop

Condition:

a + b < total?

a = 6 * 2 = 12

b = 4 * 2 = 8

Condition:

a + b < total? Condition:

a + b < total?

True True False

Figure 21: While Loop Flowchart Example. Created by author.


‘Hello World!’ will be displayed 7 times.


Determine the number of times the string will be printed in the following script.

Why does the script act the way that it does? Explain.

The word ‘Loop’ will keep being displayed and never stop (this is called an infinite

loop). In this script, n must be greater than -2 for the loop to execute. Since n is initialized at 3

and 1 is added to n in the loop body, n’s value will never be below -2. Therefore, the while

statement (n > -2) will never be false, and the loop body will continuously be executed.


What values will the following code print?

The code will print the values of a: 2, 6, 24, 120


Use a while loop to solve each of the following problems.

A) Create a script that asks the user to input a value that is greater than 0. The script should

keep asking until a valid number is entered.


B) Create a script that asks the user to enter two numbers and determines if the sum of the

numbers is even. An even number is one that is divisible by 2. The script should continue asking

for two numbers until their sum is even.

NOTE: You will need to use the b = mod(a,m) mathematical function (mod is short for modular

arithmetic). Mod calculates the remainder of a / m.

Examples:

mod(10,2) = 0 mod(10,3) = 1 mod(8,3) = 2 mod(125,6) = 5

C) Create a number guess game where a random integer from 1 to 20 is chosen, and the player

gets a maximum of three chances to guess the correct number. After each guess, the player

should receive feedback that tells them whether their guess was too low or too high. The

program should congratulate the player if they guess the correct number within the guess limit;

and the program should tell the player what number it had chosen if three incorrect guesses

have been made.

NOTE: To generate a random integer, use the randi(imax) function of MATLAB. The function

works by replacing imax with a positive integer value. The program will then select a random

integer between 1 and the value imax is equal to.

Example: a = randi(10) The value of a will be number selected randomly from 1 to 10.



Practice Problems

1) Determine the number of times each string will print in the following scripts.

A)

‘STEM for the win!’ will be displayed 7 times.


B)

‘Tricky’ will be displayed 4 times.

C)

Nothing is displayed since g is never less than h.

D)

‘How long does this go?’ will be constantly displayed (infinite loop).

2) Use a while loop to solve each of the following problems.

A) Create a script that displays the consecutive integers from 10 to 20.

B) Create a script that asks the user to enter two numbers and determines if the difference of

the numbers is a multiple of 6 (e.g., 6, 12, 18, 24… are multiples of 6). The script should

continue asking for two numbers until their difference is a multiple of 6.


3) Create a game of rock-paper-scissors in MATLAB. Here are the requirements:

Utilize a while loop to determine when the game is over

Player should be able to choose rock, paper, or scissors on his/her turn

o NOTE: You may use numeric values to represent each item (e.g., “Press 1 for

rock,…”), but be sure to communicate this clearly to players through your

program

The computer will randomly pick rock, paper, or scissors for each round

The program should compare the choices made by the player and computer to see who

wins the round

o Rules: rock beats scissors, paper beats rock, scissors beat paper

One point is awarded to the player who wins a round

The game is over when either the player or computer earns three points

When the game is over, a message should display based on whether a player won or lost

o Example: “Congratulations!” or “Nice try!”

Your program will require the use of a while loop, conditional statements, input functions, and

other topics covered throughout the previous lessons. Good luck!

There are many possible ways this program could be created. Here is one possible solution.


9.7. RESOURCES






9.8. IMAGE CREDITS

All images are screenshots taken by the author from The MathWorks©,Inc.: MATLAB© R2018a,

including all Command Windows provided throughout.




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Introduction to MATLAB® · The first lesson of Introduction to MATLAB® provides an overview of the MATLAB® programming environment, performing mathematical calculations in the