CLASS: 01 - Bangladesh University of Engineering and...

CLASS: 01

ME 262: Numerical Analysis Sessional

Department of Mechanical Engineering, BUETDepartment of Mechanical Engineering, BUET

Tentative Schedule

Class TOPICS

1 Introduction: MATLAB

2 Root Finding

3 Solution of Linear and Non-linear Algebraic Equations

4 Curve Fitting and Numerical Interpolation

5 Numerical Differentiation and Integration

6 Solution of Differential Equations

7 Final Quiz

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ME262 Numerical Analysis Sessional 4 December 2009

Reference Books

� Numerical Methods using MATLAB

- John H Mathews & Kurtis D Fink

� An Introduction to Programming and Numerical Methods in MATLAB

- S.R. Otto and J.P. Denier

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Overview4

� Basic Matlab Operation

– Starting Matlab

– Using Matlab as a calculator

– Introduction to variables and functions

� Matrices and Vectors [All variables are matrices]

– Creating matrices and vectors

– Subscript notation

– Colon notation


Overview5

� Working with Matrices and Vectors

– Some basic linear algebra

– Vectorized operations

– Array operators

� Graphics

– Plotting


Overview6

� Scripts and Functions m-files

– Creating m-files

– Syntax of I/O parameters

– Primary and secondary functions

� Flow control

– Relational operators

– Conditional execution of blocks

– Loops


MATLAB Desktop7


MATLAB as a Calculator8


MATLAB as a Calculator9


Built-in Variables10


Built-in Functions11


Suppress output with ‘;’12


Suppress output with ‘;’13


Multiple Statements per line14


MATLAB Variables Names15


Built-in MATLAB Variables16


Matrices and Vectors17


Creating MATLAB Variables

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Creating Matrices & Vectors


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Matrix

Column vector

Row vector

Creating Matrices & Vectors


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[it will create a row vector of 100 element]

Transpose Operator


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Example:


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Colon Notation


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Colon Notation


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[J:K is the same as (J, J+1, ..., K)]

Try this25

� Create the following column vector without using manual input

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4t

3

2

=


Functions to Create Matrices


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27



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Subscript Notation

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Vector Addition & Subtraction

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Array Operators

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Using Array Operators

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The MATLAB Workspace

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The MATLAB Workspace

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Plotting [x,y] Data

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Plotting [x,y] Data

Line & Symbol Types


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Plot Annotation

Example:

a = [0 1 2 3 4 5]; b = a + 2;

plot(a,b,'ro-');

xlabel('a');

ylabel('b');

title('b versus a');

legend('b'); grid;

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Script Files

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ME262 Numerical Analysis Sessional

Script to plot tan(ϴ)

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Script to plot tan(ϴ)

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Function .m Files

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Function .m Files

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Function .m Files

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Function Input & Output

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Examples:

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Examples:

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Examples:

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Text Input & Output

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Text Output with disp

Take values of three different variables as input and

display their summation

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Prompting for User Input

function [x, y, z] = newfunc (a, b)

x = a + b; y = a – b; z = a * b;

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Function .m File

Do this

� Find f(x) of an real number x which is taken as input

function value should be calculated in a separate .m file

f(x)=x2-6x+15

function s=f(x)s=x^2-6*x+15;

f.m command window

>> f (input('Enter value x = '))Enter value x = 510

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function [x, y, z] = newfunc (a, b)

x = a + b; y = a – b; z = a * b;

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Flow Control

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Relational Operators

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Relational Operators

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Logical Operators

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Conditional Execution

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if Constructs

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if .. else

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if .. elseif

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Flow Control

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for Loops

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for Loop Variations

Do this

� Find Summation of an odd number series starting from 1 to n (odd number) which is taken by an input function.

function odd(n)sum = 0;for i = 1 : 2: n

sum = sum + i;enddisp(sum);

factorial.m command window

>> odd(input('Enter value n = '))Enter value n = 925

>> a=odd (input('Enter value n = '))Enter value n = 5??? Error using ==> factorialToo many output arguments.

>> odd(9)25

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Do this

� Find Factorial of an real number n which is taken by an input function.

function sum = odd(n)sum = 0;for i = 1 : 2: n

sum = sum + i;enddisp(sum);

factorial.m command window

>> a=odd(input('Enter value n = '))Enter value n = 925

a =25

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while Loops

The break Command


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The return Command


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Comparison of break & return

CLASS: 01 - Bangladesh University of Engineering and...

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