The Very Basics of MATLAB

MAM1043H

What is MATLAB?

• MATrix LABoratory• “MATLAB is a numerical computing

environment…” (Google)

• Useful for numerical scientific and engineering calculations

• MANY useful toolboxes available for a wide variety of applications.

Why do I need it?

• Very few real world problems can be solved analytically!

• Have to resort to computational methods to solve problems.

• MATLAB is a powerful environment for solving such problems.

Example – Parallel Plate Capacitor

Example – Golf ball with spin

The MATLAB Desktop

Command WindowFor entering commands

WorkspaceFor keeping track of variables

So what do I do???

• MATLAB behaves like a really cool calculator! (That can be programmed to perform complex calculations)

• Simply enter commands in the command window.

• Try:

>>5*3

>>sin(pi/2)

Statements

• A statement is some instruction for the computer to perform some task.

• Example:

>>a=2

Tells the MATLAB to create a new variable ‘a’ and assign it a value of 2.

Key Idea:“=“ means to assign a value obtained on the RHS to the variable on the LHS

Statements

• Can then modify a variable:

>>a=a*3

Tells MATLAB to take the value of what was in the variable a, multiply it by 3, and then assign the result to a again.

Key Idea:Variables will keep their value until some instruction is given to change it.

Some Useful Commands

• clc – Clears the command window• clear – Clears variables from the workspace• close all – Closes all figure windows• who – Lists all the variables in the workspace

Basic Math Operators

• Addition: >>a=2+3• Subtraction: >>a=2-3• Multiplication: >>a=2*3• Division: >>a=2/3• Powers: >>a=2^3

Variables

• Rules for variable names:– Consist of letters (a..z), numbers (0..9) and

underscore ( _ )

– Must start with a letter (a..z)

– Variables are case sensitive, so velocity and Velocity are different variables!

• Ok: a, a2, a_2• NOT Ok: a 2, 2a, a#

Types of Variables

• Scalars:>>a=2

• Vectors:>>v=[1 2 3]

• Matrices:>>A=[1 2 3; 4 5 6; 7 8 9]

Key Idea:All variables in MATLAB are matrices!!

Operations on Vectors

• For the vector:>>v=[1 2 3]

try the following operations:– Addition: >>v=v+3

– Subtraction: >>v=v-1

– Multiplication: >>v=v*4

– Division: >>v=v/2

– Powers: >>v=v^2

Operations on Vectors

• The power operation gives an error! Why?? Does this make sense?

>>[1 2 3]^2

which means>>[1 2 3]*[1 2 3]

• How do we multiply vectors together? Is there a unique way of doing this?...

The answer is NO!!

Array Operators

• Performs operation on each component in two vectors (must be the same size!):

>>[1 2 3].*[1 2 3]

>>[2 8 27]./[1 2 3]

>>[1 2 3].^2

Constructing Arrays

• Use the colon “:” operator:

>>x=1:10

same as x=[1 2 3 4 5 6 7 8 9 10]

• If want smaller increments, use

>>x=1:0.5:4

same as x=[1 1.5 2 2.5 3 3.5 4]

Built in functions

• MATLAB has many built in functions, for example:– Trigonometric (sin(),cos(), etc)– Exponentials, logs (log(),exp())– Roots (sqrt())– Plotting (plot(),surf(), etc)– Vector product (dot(), cross() )

• plus more…• And you can create your own!! (Later….)

Plotting Graphs

• Must create vectors to plot:>>x=0:pi/10:2*pi;

>>y=sin(x);

• Now just plot!>>plot(x,y);

Playing with the Graph

• Add a grid: >>grid on;

• Add a title: >>title(‘My Sine Graph’);• Add labels: >>xlabel(‘\theta’);

>>xlabel(‘sin(\theta)’);

• Colours, etc: >>plot(x,y,’r’);

>> plot(x,y,’rx’);

An exercise in dropping a ball

• Know: x=x0 + v0t + ½ a t2

• Plot for t from 0 to 5 sec

• Dropped from height of 100m….

Still to come

• Creating our own functions.

• How can we solve linear system of equations?

• Making decisions and repeating steps.

What if I get stuck?

• Don’t just keep trying the same thing.• Read a textbook(s).• Use the MATLAB help. • Ask somebody else.But most importantly

Don’t give up!• EVERYBODY makes mistakes and

struggles when programming.