Computational Method Course CHEG 220

Week_2_Lec_2

Programming with MATLAB

Previously

in CHEG220

• Mathematical description of an

engineering problem

• Construction of numerical algorithms

• Programming

Outline

• Designing and developing programs

• Relational Operators and Logical Variables

• Logical operators and Functions

• Conditional Statements

• Loops and Switch Structures

• Application to programming

Designing and developing programs (1)

• Construct MATLAB programs to solve complex problems

• Structure and manage the design of MATLAB programs

We need a general and efficient systematic approach

Designing and developing programs (2)

Algorithms and control structures

An Algorithm is an ordered sequence of instructions that performs

desired task in a finite amount of time. An algorithm has the ability to

alter the order of its instructions using control structures.

Algorithmic operations can be sequential instructions, conditional instructions , or iterative instructions

Designing and developing programs (3)

Sequential operations

*Compute the perimeter p and the area A of a triangle whose sides are a, b and c* a=input (‘Enter the value of side a: ’); b=input (‘Enter the value of side b: ’); c=input (‘Enter the value of side c: ’); p= a + b + c A= sqrt((p/2)*(p/2 - a)* (p/2 – b)*(p/2 – c)); disp (‘The perimeter is:’) disp(p) disp (‘The area is:’) disp(A)

Designing and developing programs (4)

Conditional operations

*Compute the square root b if a real number a*

a=input (‘Enter the value of a: ’);

if a>= 0

b=sqrt(a);

else

b=sqrt(abs(a));

end

disp (‘The square root is:’)

disp(b)

Designing and developing programs (5)

Iterative operations

*Determine how many terms are required for the sum of the series

10k2-4k+2, k=1,2,3,… to exceed 20,000. What is the sum for this many

terms?*

total=0;

k=0;

while total < 20000

k= k+ 1;

total=total+10*k2-4*k+2;

end

disp (‘The number of terms :’)

disp (k)

disp (‘The sum is:’)

disp (total)

Designing and developing programs (6)

Structured Programming

It is a technique for designing programs in which a hierarchy of

modules is used.

In MATLAB these modules can be built-in or user-defined functions.

Structured programs are:

• Easy to write, understand and maintain

• Reusable codes that can be used for other applications

• Easy to debug and their modules can be tested separately

Designing and developing programs (7)

Top-down design

• It is a method for creating structured programs. Its purpose is to describe the aim

of a program at a very high level initially and then partition it into more detailed levels until the program structure become enough understood to be coded.

• The process of top-down design consists of the following steps:

Define the problem mathematically

Specify the “input “

Specify the “output”

Use a simpler set of data to work out the solution steps by hand

Write a program

Run it

Compare the solution with your hand solution

Run the program with your input data

Designing and developing programs (8)

An example of top-down design (This example can be found in the presentation 2 of week 1)

Main Program

Input A,B Output X X=A-1*B

Matrix Inverse give A get A-1

Matrix Determinant give A

get det (A)

Matrix Product give A-1 and B

get X

Designing and developing programs (9)

Good habits when writing a program include:

• Proper selection of variable names and functions to reflect the

quantities they represent. Example: call the function inversing

matrices INV_MATRIX

• Use of comments within the program. Example: “here we

compute the matrix determinant ”

• Divide your program to a main part and many functions or

modules to make it easy to write, understand and maintain

Relational Operators and Logical Variables (1)

MATLAB has 6 relational operators to make comparison between arrays:

< Less than

<= Less than or equal to

> Greater than

>= Greater than or equal to

== Equal to

~= Not equal to

The single = sign is the assignment, or replacement operator in MATLAB

The result of the comparison is 0 (false) or 1 (true)

Relational Operators and Logical Variables (2)

The results of comparison using the relational operators can be used as variable.

Example 1 : a=4 and b=7

typing z = (a<b) : z=1

typing z = (a==b) : z=0

Example 2 : x[6,3,9], y[14,2,9]

typing z = x(x<y) : z = 6

Example 3 : (arithmetic operator have precedence over the relational operators. Parentheses can be used to change the order of the precedence )

typing z =5>2+7 : z=0

typing z =(5>2) +7 : z=8

Relational Operators and Logical Variables (3)

The results of comparison using the relational operators can be used as variable.

Example 4 : (The relational operators have equal precedence among themselves. They are evaluated in order from left to right )

z = 5>3 ~= 1

z = (5>3) ~= 1

z=0

Relational Operators and Logical Variables (4)

The logical class z = (2==3) is a logical variable. It is a data type and MATLAB class

Logical variable such z may have only the value 1 (true) and 0 (false)

The logical function B = logical (A) returns a logical array B. A is a numeric array

D = double (C) returns a numeric array D. C is a logical array

Questions

In three words, define a well written MATLAB program