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IMS 3253: Math
1Dr. Lawrence West, MIS Dept., University of Central [email protected]
Topics
• Five Fundamental Math Operations• Precedence of Math Operations
– Using Parentheses to override precedence• Writing and Interpreting VB Calculation
Statements• Mathematical Functions
“A computer lets you make more mistakes faster than any invention in human history—with the possible exceptions of handguns and tequila”
Mitch Ratcliffe
IMS 3253: Math
2Dr. Lawrence West, MIS Dept., University of Central [email protected]
Numeric Operations in Computer Code
• Computers were invented to process large quantities of numeric data
• Computers perform arithmetic operations on numeric values incredibly rapidly
• All computer operations can be performed using the basic operations of addition, subtraction, multiplication, and division.
• Most computer languages also provide for exponentiation
• Most also provide built in functions for more complex operations
IMS 3253: Math
3Dr. Lawrence West, MIS Dept., University of Central [email protected]
Objectives
• Understand the five fundamental arithmetic operations in VB
• Understand how to write and interpret mathematical calculations in VB
• Understand the precedence of mathematical operations in computers and how parenthetical grouping affects calculation order
• Understand the use of predefined mathematical functions available in VB
IMS 3253: Math
4Dr. Lawrence West, MIS Dept., University of Central [email protected]
Five Fundamental Arithmetic Operations
• VB supports five built-in arithmetic operations:
Operation Conventional Notation Computer
Symbol
– Addition 3 + 4 3 + 4– Subtraction 3 - 4 3 - 4– Multiplication 3 x 4 3 * 4– Division 3 3 / 4– Exponentiation 34 3 ^ 4
IMS 3253: Math
5Dr. Lawrence West, MIS Dept., University of Central [email protected]
The Assignment Operation
• Many times the results of a calculation or other operation are assigned to a variable, property, or other value holder
intSum = intFirstValue + intSecondValue
intSum = Val(txtFirst.Text) + Val(txtSecond.Text)
MainMenu.Top = (Screen.Height - MainMenu.Height) / 3
• The calculation on the right of the equal sign is performed first and assigned to the location on the left
• The Equal Sign is an assignment operator
IMS 3253: Math
6Dr. Lawrence West, MIS Dept., University of Central [email protected]
Using Numeric Calculations
• Legal statements
x = 4
y = 2
z = x + 5
t = x * 2
txtPrice.Text = x + y
Const Pi = 3.14
dblDiameter = Pi * sglRadius
dSqrt = x ^ .5
• Illegal statements
4
x + y
z% = x% + txtInput.Text
sglPrice = $1,456.98
IMS 3253: Math
7Dr. Lawrence West, MIS Dept., University of Central [email protected]
Precedence of Numeric Calculations
• Q: What is the result of 3 + 5 * 2?A:
• Numeric operations have a defined hierarchy or precedence of calculation
1. Exponentiation
2. Multiplication and division
3. Addition and subtraction
4. Left to right within categories– Because multiplication precedes addition 5 is
multiplied by two giving 10 first after which the three is added to give 13
IMS 3253: Math
8Dr. Lawrence West, MIS Dept., University of Central [email protected]
Precedence Exercises
x + y / 2
y ^ 3 / 4
x + 2 * y - 2 * x
8 + x * y / 3
-8 + y ^ -2
16 ^ (1 / 4)
What are the results of the following calculations if x = 12 and y = 4?
IMS 3253: Math
9Dr. Lawrence West, MIS Dept., University of Central [email protected]
Using Parentheses to Group Calculations
• Operations grouped in parentheses are performed first, regardless of the natural order of calculation3 + 5 * 2 = 13(3 + 5) * 2 = 16
• Parentheses may be nested((3 + 5) * 8) / (2 * 4) = ?
• Parentheses may be used to visually format mathematical expressions even if no change to the calculation order is needed
Inner parentheses areevaluated first
IMS 3253: Math
10Dr. Lawrence West, MIS Dept., University of Central [email protected]
More Precedence Exercises
Write computer expressions for each mathematical expression
dcb
baz
23 yxz
xb b ac
a 2 4
2
IMS 3253: Math
11Dr. Lawrence West, MIS Dept., University of Central [email protected]
Numeric Functions
• VB (and most other programming languages) provide predefined numeric calculations in the form of functions
• Functions often operate on a value and return some transformation of the value
• E.g. in x = 25y = Sqrt(x)
Sqr( ) is a predefined function which returns the square root of its argument (x in this case)
IMS 3253: Math
12Dr. Lawrence West, MIS Dept., University of Central [email protected]
Functions and Expressions as Arguments
• Functions may be nested
E.g., in Math.Sqr(Math.Abs(x))
the absolute value of x is determined first and then becomes the argument of the square root function
• A calculation may be performed inside the argument of a function
E.g., in Math.Sqr(x ^ 2)
the value of x is first squared and then the square root of the result is taken
• Functions are always calculated from the inside out
IMS 3253: Math
13Dr. Lawrence West, MIS Dept., University of Central [email protected]
Empty Variables in Mathematical Operations
• Variables which have never been assigned a value are said to be ‘empty’
• If a mathematical operation is performed on an empty variable the variable behaves as if its value is zero
• Be very careful as division by zero results in a runtime error which will crash the program.
• NB: Variables loaded from databases may sometimes contain a null value which is different from empty.
IMS 3253: Math
14Dr. Lawrence West, MIS Dept., University of Central [email protected]
Converting Data Types
• VB will automatically convert many numeric data types before performing calculations– Single precision values can be multiplied by
integers, assigned to currency variables etc.• Some conversions cannot take place
– String values cannot be assigned to explicitly declared numeric variables (non variants)
– Commonly arises when using text boxes, list boxes, grid controls, etc.
Introducesinefficiency
IMS 3253: Math
15Dr. Lawrence West, MIS Dept., University of Central [email protected]
The Val( ) Function
• Val( ) returns the numeric value of its argument– Argument is typically a string but may be a number– Val converts strings to numbers
• A common use of Val is to convert values which must be treated as text into numbersintQty = Val(txtQty.Text)intCourse = Val(cboCourseNumber.Text)sglPrice = Val(InputForm.Tag)
• Or use the Convert method
Some properties always contain characters
IMS 3253: Math
16Dr. Lawrence West, MIS Dept., University of Central [email protected]
The Val ( ) Function: Examples
• Val (“123.54”) 123.54
• Val (““) 0
• Val(“123A45”) 123
• Val(“A123”) 0
• Val(“ 123 456”) 123456
IMS 3253: Math
17Dr. Lawrence West, MIS Dept., University of Central [email protected]
Methods of the Math Class
Name Description
Abs Overloaded. Returns the absolute value of a specified number.
Acos Returns the angle whose cosine is the specified number.
Asin Returns the angle whose sine is the specified number.
Atan Returns the angle whose tangent is the specified number.
Atan2 Returns the angle whose tangent is the quotient of two specified numbers.
BigMul Produces the full product of two 32-bit numbers.
Ceiling Overloaded. Returns the smallest integer greater than or equal to the specified number.
Cos Returns the cosine of the specified angle.
Cosh Returns the hyperbolic cosine of the specified angle.
DivRem Overloaded. Calculates the quotient of two numbers and also returns the remainder in an output parameter.
Exp Returns e raised to the specified power.
Floor Overloaded. Returns the largest integer less than or equal to the specified number.
IMS 3253: Math
18Dr. Lawrence West, MIS Dept., University of Central [email protected]
Methods of the Math Class (cont.)
IEEERemainder Returns the remainder resulting from the division of a specified number by another specified number.
Log Overloaded. Returns the logarithm of a specified number.
Log10 Returns the base 10 logarithm of a specified number.
Max Overloaded. Returns the larger of two specified numbers.
Min Overloaded. Returns the smaller of two numbers.
Pow Returns a specified number raised to the specified power.
Round Overloaded. Rounds a value to the nearest integer or specified number of decimal places.
Sign Overloaded. Returns a value indicating the sign of a number.
Sin Returns the sine of the specified angle.
Sinh Returns the hyperbolic sine of the specified angle.
Sqrt Returns the square root of a specified number.
Tan Returns the tangent of the specified angle.
Tanh Returns the hyperbolic tangent of the specified angle.
Truncate Overloaded. Calculates the integral part of a number.
