MATLAB2 Beamer

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N.M. 2.1

Lecture N.M. 2Introduction to MATLABPart 2

CHE 4163 Transport Phenomena and Numerical Methods

Ravi JagadeeshanDepartment of Chemical Engineering

Monash University

Lecture Aims

Built-in functions

Graphics

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Programming withMATLABObjectives

Example problem

M-FilesScript files

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N.M. 2.2

Aims of todays lecture and examples

1 Learning about MATLAB’s built-in functions

2 Quick start guide to Graphics with MATLAB

3 Basics of developing M-files in MATLAB

4 Distinguishing between script files and function files

5 Example problems on script files and function files

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.3

Table of Contents

1 Built-in functions

2 Graphics

3 Help

4 Programming with MATLABObjectivesExample problem

5 M-FilesScript filesFunction filesExample

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.4

Built-in functions

• MATLAB and its Toolboxes have a rich collection of built-infunctions

• You can use online help to find out more about them

• For example, if you want to learn about the logfunction, type in:>> help log

• For a list of all the elementary functions, type>> help elfun

• One of the important properties of MATLAB’ s built-infunctions is that they will operate directly on vector andmatrix quantities

• For example, try>> log (A)

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.5

Built-in functions

• The natural logarithm function is applied in array style,element by element, to the matrix A

• Most functions, such as sqrt, abs, sin, acos, tanh, andexp, operate in array fashion

• Certain functions, such as exponential and square root,have matrix definitions also

• MATLAB will evaluate the matrix version when the letter mis appended to the function name

• Try>> sqrtm(A)

• A common use of functions is to evaluate a formula for aseries of arguments

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.6

Built-in functions

• Consider the function,

v(t) =gmc

(1− e−(c/m)t)

where v is velocity (m/s), g is the acceleration due togravity (9.81 m/s2), m is mass (kg), c is the drag coefficient(kg/m), and t is time (s)

• Create a column vector t that contains values from 0 to200 in steps of 2>> t = [0:2:200]’;

• Check the number of items in the t array with the lengthfunction>> length(t)

• Assign values to the parameters:>> g = 9.81; m = 8.1; c = 0.25;

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.7

Built-in functions

• MATLAB allows you to evaluate a formula such asv = f(t), where the formula is computed for each valueof the t array, and the result is assigned to acorresponding position in the v array:>> v = (g*m/c)*(1 - exp(-(c/m)*t));

Graphics

• MATLAB allows graphs to be created quickly andconveniently

• For example, to create a graph of the t and v arrays fromthe data above, enter>> plot (t, v)

• The graph appears in the graphics window and can beprinted or transferred via the clipboard to other programs

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.8

Graphics

• You can customize the graph a bit with commands such asthe following:>> title( ’plot of v versus t’)>> xlabel (’Values of t’)>> ylabel (’Values of v’)>> grid

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.9

Graphics

• The plot command displays a solid line by default

• If you want to plot each point with a symbol, you caninclude a specifier enclosed in single quotes in the plotfunction

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.10

Graphics

• For example, if you want to use open circles enter>> plot (t, v, ’o’)

• MATLAB allows you to display more than one data set onthe same plot. For example, if you want to connect eachdata marker with a straight line you could type>> plot (t, v, t, v, ’o’)

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.11

Graphics

• There are other features of graphics that are useful—forexample, plotting objects instead of lines, families ofcurves plots, plotting on the complex plane, multiplegraphs windows, log-log or semilog plots,three-dimensional mesh plots, and contour plots.

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.12

Help

• The MATLAB package includes an extensive Help facilitythat can be accessed by clicking on the Help menu in thecommand window

• It also provides access to a number of instructive demos

• Help is also available in interactive mode by typing the helpcommand followed by the name of a command or function

• If you do not know the name, you can use the lookforcommand to search the MATLAB Help files foroccurrences of text

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.13

Help

• For example, suppose that you want to find all thecommands and functions that relate to logarithms, youcould enter>> lookfor logarithm

• You can obtain help from The Math Works, Inc., website atwww.mathworks.com, and other links on the coursewebsite

• Sometimes, if you can’t figure out why MATLAB is spewingout error messages at you, just ask it why - it may help...

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.14

Programming with MATLAB

Objectives

• Learn how to create well-documented M-files in the editwindow and invoke them from the command window

• Understand how to set up M-files so that they interactivelyprompt users for information and display results in thecommand window

• Learn how to write clear and well-documented M-files byemploying structured programming constructs toimplement logic and repetition

• Understand what is meant by vectorization and why it isbeneficial

• Understand how functions can be passed to M-files.

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.15

A free-falling Bungee Jumper

Example problem

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.16

Example problem

• We can use a force balance to develop a mathematicalmodel to predict the fall velocity of a bungee jumper

• This model takes the form of the following differentialequation:

dvdt

= g − cm

v (1)

• The numerical solution of this equation could beobtained with Euler’s method:

v(ti+1) = v(ti) +dvi

dt∆t (2)

• This equation can be implemented repeatedly to computevelocity as a function of time

• However, to obtain good accuracy, many small steps mustbe taken

• With the aid of MATLAB, such extremely laborious andtime consuming calculations can be performed easily

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.17

M-Files

• The most common way to operate MATLAB is by enteringcommands one at a time in the command window

• M-files provide an alternative way of performing operationsthat greatly expand MATLAB’s problem-solving capabilities

• An M-file contains a series of statements that can be runall at once

• The nomenclature "M-file" comes from the fact that suchfiles are stored with a . m extension

• M-files come in two flavors:

• script files

• function files

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.18

Script files

• A script file is merely a series of MATLAB commands thatare saved on a file

• The script can be executed by typing the file name in thecommand window or by invoking the menu selections inthe edit window: Debug, Run

Example

Problem Statement:

Develop a script file to compute the velocity of the free-fallingbungee jumper.

Solution:

• Open the editor with the menu selection: File, New, M-file

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.19

Solution contd...

• Type in the following statements to compute the velocity ofthe free-falling bungee jumper at a specific time:

g = 9.81; m=8.1; t = 12; c = 0.25;

v = (g*m/c)*(1 - exp(-(c/m)*t))

• Save the file as scriptdemo.m

• Return to the command window and type in: scriptdemo

• Remember to set the path so MATLAB can find the M-file!

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.20

Function files

• Function files are M-files that start with the wordfunction

• In contrast to script files, they can accept inputarguments and return outputs

• They are analogous to user-defined functions inprogramming languages such as Fortran, Visual Basic orC

• The syntax for the function file can be representedgenerally as

function outvar = funcname(arglist)% helpcommentsstatementsoutvar = value

where the various terms are explained below.

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.21

Function files

function outvar = funcname(arglist)% helpcommentsstatementsoutvar = value

1 outvar = the name of the output variable,

2 funcname = the function’s name,

3 arglist = the function’s argument list (i.e.,

comma-delimited values that are passed into the function),

4 helpcomments = text that provides the user with

information regarding the function (these can be invoked

by typing Help funcname in the command window),

5 statements = MATLAB statements that compute the

value that is assigned to outvar

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.22

Function files

• The M-file should be saved as funcname.m

• The function can then be run by typing funcname in the

command window as illustrated in the following example

• Even though MATLAB is case-sensitive, your computer’s

operating system may not be. Whereas MATLAB would

treat function names like freefallvel and

FreeFallVel as two different variables, your operating

system might not

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.23

Example

Problem Statement:

As in the previous example, compute the velocity of the

free-falling bungee jumper, but now use a function file for

the task

Solution:

Type the following statements in the file editor:

function velocity = freefallvel(m, c, t)% freefallvel(m, c, t)% computes the free-fall velocity (mps)% of an object with second-order drag.% input:% m = mass (kg)% c = drag coefficient (kg/m)% t = time (s)

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.24

Solution contd....

% output:% velocity = downward velocity (m/s)g = 9.81; % acceleration of gravityvelocity = (g*m/c)*(1 - exp(-(c/m)*t));

• Save the file as freefallvel.m

• To invoke the function, return to the command window andtype:freefallvel(8.1,0.25,12)

• To invoke the help comments type:help freefallvel

• The first few lines of all m-files begin with a “%" sign,which indicates a comment statement

• All comments are ignored by MATLAB

Lecture Aims

Built-in functions

Graphics

Help

Programming withMATLABObjectives

Example problem

M-FilesScript files

Function files

Example

N.M. 2.25

• Comments have at least two very important uses:

• They can help other users (and very frequently, yourself!)understand what is going on.

• They can be used to “block" out lines of code that you don’twant executed.

• Function M-files can return more than one result

• In such cases, the variables containing the results arecomma-delimited and enclosed in brackets

• For example, the following function, stats.m, computesthe mean and the standard deviation of a vector:

function [mean, stdev] = stats(x)n = length (x);mean = sum(x)/n;stdev = sqrt(sum((x-mean).^2/(n-1)));