Welcome to EGR 106 Foundations of Engineering II

Course information Today’s specific topics:

– Computation and algorithms– MATLAB

Basics Demonstrations

Material in textbook chapter 1

Computation

What is computation?

Examples: 3 + 2

tan 40o

Computation = “transformation from one or more inputs to an output”

Human Computation

“Simple” computations (trivial to us)– Adding 2 single digit numbers– Recognizing a letter of the alphabet– Comparing 2 numbers for <, =, >

“Harder” computations (based on simple)– Adding 3 or more numbers – Reading a word– Sorting a list of numbers

Algorithms

Definition: “a set of directions for carrying out a computation in terms of other, simpler computations”

“Simpler computations” = ones that we already know how to do

Example

Memorizing addition tables in grammar school

0 1 2 3 4 5 6 7 8 9

0 0 1 2 3 4 5 6 7 8 9

1 1 2 3 4 5 6 7 8 9 10

2 2 3 4 5 6 7 8 9 10 11

3 3 4 5 6 7 8 9 10 11 12

4 4 5 6 7 8 9 10 11 12 13

5 5 6 7 8 9 10 11 12 13 14

6 6 7 8 9 10 11 12 13 14 15

7 7 8 9 10 11 12 13 14 15 16

8 8 9 10 11 12 13 14 15 16 17

9 9 10 11 12 13 14 15 16 17 18

Permits multi-digit addition

Computer Computation

Very fast at arithmetic operations Algorithms = computer programs

– Need to understand what computations are “simple” for the computer

– Need to write a clear set of directions to be followed

– Build more complicated computations from intermediate ones

Examples

Find the smallest in a list of number Sort a list of numbers Some for discussion/thought

(first two from Kaplan, Introduction to Scientific Computation and Programming)

Find the Smallest of a List:

S et P =1, S =first num ber on list

S et S equal to the sm aller of S and theP th num ber on the list

Done withlist?

S top

no

yes

S tart with the list and 2 variab les, P and S

Increase P by 1

Example: list = 7,1,5

Step P S

1 1 S = 7

2 2

3 S = smaller(7,1) = 1

4 3

5 S = smaller(1,5) = 1

6 stop

Sort a List of Numbers:

S tart with your list and an em pty list

Let S = the sm allest num ber in the list

Done withlist?

S top

no

yes

Delete S from the old list;A ppend S to the new list

Note reuse!

Example: list = 8,5,1,2

Step S Orig List New List

1 1

2 8,5,2 1

3 2

4 8,5 1,2

5 5

6 8 1,2,5

7 8

8 1,2,5,8

Some Others….

Adding numbers expressed in Roman numerals

LXVI + XXXIV = ???

Find the 2nd smallest number in a list Convert the month/day into day of the year

Feb 15 = day 46

MATLAB – What is it ?

Name is from matrix laboratory Powerful tool for

– Computation and visualization of engineering and science mathematics

– Communication of ideas– Programming:

Built-in editor, debugger, and help Many predefined functions (grouped in toolboxes) Interpreted or compiled programs

Today is “beginning MATLAB”, sort of like “beginning French”:

– We start with basic terminology– We consider the simplest of computations– We do computation in interpreter mode (the

“enter” key invokes/runs/executes the operation requested)

Chapter 1 of Gilat– Pages 5-22

The MATLAB Environment

Data represented in arrays– Organized by row and column indices– Use variable names for them

Multi-paned desktop: – Command window– Workspace browser– Current directory– Other windows: Figure, File Editor, Help, …..

More next week

The Command Window

Command prompt >> Basic math operations are available:

addition + subtraction – division /

multiplication * exponentiation ^

“enter” key “executes” or “runs” or “invokes” the operation

Operator precedence: PEMDAS5 – 4 + 3 ^ 4 / ( 3 – 1 ) = ?

Finite precision mathematics !!

By default, 5 significant digits are shown, with exponential notation as needed

Results of NaN, Inf, possible

Allows Stored Variables

The equal sign is an assignment operator c = 7.5 bob3 = 3.7789

There are naming restrictions:Connected symbols, starting with a letter Make them unique Some are predefined for special values or

uses: pi inf flops j i ans for

Combining Operations and =

Generally, computation requires 3 pieces of information:– The operator?– The inputs?– What to do with the output?

MATLAB storing the result in a variable Accomplished by the equal sign, =

Specified on the right hand side of an equal sign

For these examples, 2 and 4 are the input and addition is the operation

No specification of the output; the default is to put it into the variable named ans

The output is assigned to the variable named bob

bob is again the destination of the result, we’ve just used functional style notation for the computation

Note that = is not really an equal sign, but is an assignment operator

The computation on the right can be trivial

Here the computation is done using bob, then the result is put into variable bob

An error results since we’ve got things on the wrong sides of the assignment operator

Other Useful Operations

abs(x) ceil(x) exp(x) fix(x) sign(x) floor(x) log(x) round(x) sqrt(x) conj(x) log10(x) rem(x,y) sin(x)sinh(x) tan(x) atan2(x,y) asin(x) acosh(x) atan(x) sec(x) sind(x) many more exist !!

Examples

Square roots

Note that trig functions generally work in radians, not degrees

In general, all variables are complex numbers

Bits and Pieces

Other useful system commands: – clear, clc – diary – help, lookfor – who, whos

Semicolon (;) suppresses the displaying of the result of a computation

Arrow keys allow for editing of prior commands PC version (network license) is available from ECC

help desk for $10

Plotting Basics

Figure window commands:

figure, figure(3), clf, close plot(x,y) in which x and y are “arrays” Annotation commands:

title('the title goes here')

xlabel('the x axis label goes here')

ylabel('the y axis label goes here')

Now for Some Demos!

Simple demos of variables and math “Demos” at the command line A simple gui of a bouncing ball