BMayer@ChabotCollege.edu ENGR-25_MATLAB_OverView-1.ppt 1 Bruce Mayer, PE Engineering/Math/Physics...

BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt1

Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

BMayer@ChabotCollege.edu

Engr/Math/Physics 25

Chp1 MATLABOverView:

Part-1

Learning Goals

Turn On MATLAB and use as a calculator

Create Basic Cartesian Plots Write and Save simple “Script”

Program-files Execute Conditional Statements

• IF, THEN, ELSE, >, <, >=, etc.

Execute Loop Statements• FOR & WHILE

MATLAB Environment

TWO Interaction Modes• INTERACTIVE

– Type in the COMMAND WINDOW– Often Called a Command-Window “Session”– Interaction is NOT Saved to Disk

Commands (NOT results) Stored in “Command History” Buffer Window

• STORED → Two Types– SCRIPT Files– FUNCTION Files

MATLAB Command Window

Example Cmd Window Session>> %Use MATLAB As Calculator

>> 17*19

>> 77/19 -4.3

-0.2474

>> 64^(1/3) + 32^0.2

>> (7+11)*2.5

>> L = 14.4

14.4000

>> W = 13.3

13.3000

>> Area = L*W

Area =

191.5200

Script/Function File Editor

Script & Function Files (m-files) SCRIPTS and FUNCTIONS in MATLAB

are stored in text files that end with the extension “.m”• These files are called m-files

SCRIPTS (a.k.a. “programs”)• Scripts files are useful for automating tasks

that may need to be repeated.• They have no input/output parameters• They can (but probably shouldn’t) share

variables with the command workspace

Script & Function Files (m-files) SCRIPTS (cont.)

• Scripts are sequences of interactive statements stored in a file– i.e., They look liked Stored versions of Command Window

Sessions

FUNCTIONS (a.k.a. “subroutines”)• Function m-files are MATLAB subprograms

analogous to FORTRAN Subroutines, or C functions• They communicate with the command window and

other functions via a list of INPUT and OUTPUT PARAMETERS or ARGUMENTS

Script & Function Files (m-files) FUNCTIONS (cont.)

• Functions COMMUNICATE with the COMMAND WINDOW and other m-files via a list of input and output variables

• LOCAL variables are variables defined INSIDE the function– They only can be used inside the function in

which they reside.• The number of output parameters used

when a function is called must match the number of outputs that the function is expected to return

Entering Commands & Expressions MATLAB retains your previous keystrokes. Use the up-arrow (↑) key to scroll back

through the commands. Press the key (↑) once to see the previous

entry, and so on. Use the down-arrow (↓) key to scroll forward. Edit a line using the left (←) & right (→) arrow

keys the Backspace key, and the Delete key. Press the Enter key to execute the command

Arithmetic Scalar Operations

Symbol Operation MATLAB

^ exponentiation: ab a^b

* multiplication: ab a*b

/ right division: a/b a/b

\ left division: b/a a\b

+ addition: a + b a + b

- subtraction: a - b a - b

LEFT-Division A\b read from Right-to-Left as: “b divided by A”

Math Op Precedence (PEMDAS)

Precedence Operation

First Parentheses, evaluated starting with the innermost pair.

Second Exponentiation, evaluated from left to right.

Third Multiplication and Division with EQUAL precedence, evaluated from left to right.

Fourth Addition and Subtraction with EQUAL precedence, evaluated from left to right.

Precedence Examples

>> 8+3*5

>> 8 + (3*5)

>>(8 + 3)*5

>> 4^2-12-8/4*2

>> 4^2-12-8/(4*2)

Precedence Examples cont.

>> 3*4^2 + 5

>>(3*4)^2 + 5

>>27^(1/3) + 32^0.2

>>27^1/3 + 32^0.2

“=“ → Assignment Operator Typing x = 3 ASSIGNS the value 3 to

the variable x. We can then type x = x + 2. This assigns

the value 3 + 2 = 5 to x. But in algebra this implies that 0 = 2.

In algebra we can write x+2 = 20, but in MATLAB we cannot.

In MATLAB the LEFT side of the = operator MUST be a SINGLE variable.

The Right side must be a computable value

Work Session Commands

Command Descriptionclc Clears the Command window

clear Removes all variables from memory

clear v1 v2 Removes the variables v1 and v2 from memory

exist(‘var’) Determines if a file or variable exists having the name ‘var’

quit Stops MATLAB

Work Session Commands cont.1

Command Description

who Lists the variables currently in memory

whosLists the current variables and sizes, and indicates if they have imaginary parts.

: (Colon) Generates an array having regularly spaced elements

, (Comma) Separates elements of an array

; (Semicolon) Suppresses screen printing; also denotes a new row in an array

… (Ellipsis) Continues a line

whos on First???

Special VARS & const’sCommand Description

ans Temporary variable containing the most recent answer

eps Specifies the accuracy of floating point precision

i,j The imaginary unit (-1)

Inf Infinity (unbounded magnitude)

NaN Indicates an undefined numerical result; a.k.a., Not a Number

pi The number pi (3.14159...) NaN returns the IEEE arithmetic representation for Not-a-Number

(NaN). These result from operations which have undefined numerical results;. e.g., try Q = 0/0

The Complex PlaneIm (i or j)

BjABiA FF or

Complex-Number Operations The number c1 = 1 – 2i is entered as: c1 = 1 2i or c1 = 1-2j

An Asterisk is NOT needed between i or j and a NUMBER, although it is required with a VARIABLE, such as c2 = 5 - i*c1.

Be careful. The expressions • y = 7/2*i and x = 7/2j

give two DIFFERENT results: • y = (7/2)i = 3.5i• and x = 7/(2j) = –3.5j

Complex Arithmetic>> Im_Pwr = Z1^3.84

Im_Pwr =

-1.6858e+004 -2.5886e+004i

>> e_to_Z = exp(Z2)

e_to_Z =

6.8518e+006 -2.3163e+007i

>> ln_Z = log(Z1)

ln_Z =

2.6922 + 1.0769i

>> Log_Z = log10(Z2)

Log_Z =

1.2485 + 0.1242i

Special VARS & const’s

Command Description

format short Four decimal digits (the default); 13.6745

format long 16 digits; 17.27484029463547

format short e Five digits (four decimals) plus exponent; 6.3792e+03

format long e 16 digits (15 decimals) plus exponent; 6.379243784781294e–04

Discrete Math Funtions

Command Description

factor(n)Returns a row vector containing the prime factors of n.

gcd(m,n) Finds the Greatest Common Divisor/Factor of m & n

lcm(m,n) Finds the Least Common Multiple for m & n

factorial(n)Returns the factorial of n; i.e., returns n! = 1*2*3…(n-2)*(n-1)*n

primes(n) Finds all prime numbers less than n

isprime(n) Determines if n is a prime number

Discrete Math Examplesfactor777 = factor(777)

factor777 =

3 7 37

GCF = gcd(1001, 1105)

GCF = 13

F7 = factorial(7)

F7 = 5040

P93 = primes(93)

Columns 1 through 12

2 3 5 7 11 13 17 19 23 29 31 37

Columns 13 through 24

41 43 47 53 59 61 67 71 73 79 83 89

Arrays

An ARRAY is an ORDERED SET of Numbers of with n DIMENSIONS• A regular Number (a SCALAR) is an

Array of Dimension ZERO

a VECTOR is a 1-Dim Array a MATRIX

is an ARRAY of Dim 2with specialproperties

Arrays in MATLAB The numbers 0, 0.1, 0.2, …, 10 can be

assigned to the array variable u by typing • u = [0:0.1:10]

To compute w = 5 sin u for u = 0, 0.1, 0.2, 0.3, 0.4,…, 10, the command session is; • >>u = [0:0.1:10];• >>w = 5*sin(u);

The single line, w = 5*sin(u), computed the formula, w = 5 sin(u), 101 times.

Array Index >>u(7) ans = 0.6000 >>w(7) ans = 2.8232 Use the LENGTH function to determine how

many values are in an array. >>m = length(w) m = 101

Polynomial Roots MATLAB has a Way-Cool Polynomial

Root Finder Find the roots of x3 − 7x2 + 40x − 34 = 0

• >>a = [1,-7,40,-34];• >>roots(a)• ans =• 3.0000 + 5.000i• 3.0000 - 5.000i• 1.0000

The roots are x = 1 and x = 3 ± 5i

5th Order Polynomial

Find the roots of the 5th Order function

0266465359 2345 yyyyyyg>> r5 = [1,-9,35,-65,64,-26];

>> roots(r5)

3.0000 + 2.0000i

3.0000 - 2.0000i

1.0000 + 1.0000i

1.0000 - 1.0000i

1.0000

The roots of g(y)• y1,2 = 3 ± 2j

• y3,4 = 1 ± j

• y5 = 1

Common Math FunctionsFcn MATLAB Fcn MATLAB

ex exp(x) sin x sin(x)

√x sqrt(x) tan x tan(x)

ln x log(x) cos-1 x acos(x)

log10 x log10(x) sin-1 x asin(x)

cos x cos(x) tan-1 x atan(x)

Note that MATLAB Trig functions Operate on RADIANS• Convert using Ratio: -rads per 180°

rads 274.1180

73 e.g., ;180

radsrads

The “d” Trig Comands for Degrees>> T1 = sind(77)

0.9744

>> T2 = cosd(19)

0.9455

>> T3 = tand(53)

1.3270

>> T4 = asind(.497)

29.8017

>> T5 = acosd(0.629)

51.0236

>> T6 = atand(1.73)

59.9706

Printing From Command Window - 1

Note: MATLAB “Comments” Start with the “%” Sign

TexttoPrint

SELECTText toPrint

Send to printer from Print Dialog Box

Caveat• In a COMMAND

WINDOW session once you Hit Enter () you can NOT Go back to Edit the Text– Can Save your

command sequence as an m-file SCRIPT

Alternative Cmd Window Printing

Perform MATLAB Operation Select Desired Text COPY text to the Windows Paste Buffer Open Text application

• MSWord, WordPad, NotePad, etc.

PASTE the MATLAB Text Into the Text Processor

Print from the Text Processor as Usual

DIARY Function to Record Cmnds Keeping a Session Log → The diary Function

• The diary function creates a copy of your session in MATLAB on a disk file, including keyboard input and system responses, but excluding graphics. You can view and edit the resulting text file using any text editor, such as the MATLAB Editor. To create a file on your disk called sept23.out that contains all the functions you enter, as well as output from MATLAB, enter– diary('sept23.out')

• To stop recording the session, use– diary('off')

• To view the file, run• edit('sept23.out')

Command Execution Hierarchy When you type problem1

1. MATLAB first checks to see if problem1 is a variable and if so, displays its value.

2. If not, MATLAB then checks to see if problem1 is one of its own commands, and executes it if it is.

3. If not, MATLAB then looks in the current directory for a file named problem1.m and executes problem1 if it finds it.

4. If not, MATLAB then searches the directories in its search path, in order, for problem1.m and then executes it if found.

System, Directory, File Cmnds Command Description

addpath dirname Adds the directory dirname to the search path.

cd dirname Changes the current directory to dirname

dir Lists all files in the current directory

dir dirname Lists all the files in the directory dirname

path Displays the MATLAB search path

pathtool Starts the Set Path tool

HINT: Consider putting ALL your m-files in ONE Folder/Directory

Plotting with MATLAB

Plot over 573°

1ln73.1

1ln73.1cos PPPQ

MATLAB Plotting Commands

Command Description

plot(x,y)Generates a plot of the array y versus the array x on rectilinear axes

title(’text’) Puts text in a title at the top of the plot

xlabel(’text’) Adds a text label to the horizontal axis (the abscissa).

ylabel(’text’) Adds a text label to the vertical axis (the ordinate).

grid Puts grid lines on the plot

gtext(’text’) Enables placement of text with the mouse

DeskTop Recoveryto UnScramble the DeskTop

DeskTop “Recovery”

Example Problem 1-21

Plot This Function

tetT 2.07ln6 • Where

– T Temperature (°C)– t time (minutes)

• For: 1 t 3

All Done for Today

Tutorial onHomeWork

ConstructionNext Time

A VERY IMPORTANT MEETING

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

BMayer@ChabotCollege.edu

Engr/Math/Physics 25

Appendix

Example Demo Session>> %Use MATLAB As Calculator

>> 17*19

>> 77/19 -4.3

-0.2474

>> 64^(1/3) + 32^0.2

>> (7+11)*2.5

>> L = 14.4

14.4000

>> W = 13.3

13.3000

>> Area = L*W

Area =

191.5200

Prob 1-21 Command Script

From the Command Window

>> t = [1:0.02:3];

>> T = 6*log(t) - 7*exp(0.2*t);

>> plot(t,T), xlabel('time (min)'),ylabel('Temperature (°C)'), title('Problem 1-21'), grid

Prob 1-22 Plot

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3-9

time (min)

Problem 1-22

System, Directory, File Cmnds Command Description

pwd Displays the current directory

cd dirname Changes the current directory to dirname

rmpath dirname Removes the directory dirname from the search path.

Lists the MATLAB-specific files found in the current working directory. Most data files and other non-MATLAB files are not listed. Use dir to get a list of all files

what dirname Lists the MATLAB-specific files in directory dirname

BMayer@ChabotCollege.edu ENGR-25_MATLAB_OverView-1.ppt 1 Bruce Mayer, PE Engineering/Math/Physics...

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