Engr/Math/Physics 25
Chp1 MATLAB
OverView: Part-1
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering/Math/Physics 25: Computational Methods
1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
MATLAB Command Window
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Example Cmd Window Session
>> %Use MATLAB As Calculator
>> (7+11)*2.5
>> 17*19
ans =
ans =
45
323
>> L = 14.4
>> 77/19 -4.3
L =
ans =
14.4000
-0.2474
>> W = 13.3
>> 64^(1/3) + 32^0.2
ans =
W =
13.3000
6
>> Area = L*W
Area =
Engineering/Math/Physics 25: Computational Methods
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191.5200
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Script/Function File Editor
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Arithmetic Scalar Operations
Symbol
^
*
/
\
+
-
Operation
exponentiation: ab
multiplication: ab
right division: a/b
left division: b/a
addition: a + b
subtraction: a - b
MATLAB
a^b
a*b
a/b
a\b
a + b
a - b
 LEFT-Division A\b read from
Right-to-Left as: “b divided by A”
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Precedence Examples
>> 8+3*5
>> 4^2-12-8/4*2
ans =
ans =
23
4
0
>> 8 + (3*5)
ans =
23
>>(8 + 3)*5
>> 4^2-12-8/(4*2)
ans =
1
3
ans =
55
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Precedence Examples cont.
>>27^(1/3) + 32^0.2
>> 3*4^2 + 5
ans =
48
ans =
5
53
>>27^1/3 + 32^0.2
>>(3*4)^2 + 5
ans =
144
149
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3
ans =
9
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
“=“ → 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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Work Session Commands
Command
Description
clc 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
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Work Session Commands cont.1
Command
who
Description
Lists the variables currently in
memory
Lists the current variables and sizes,
whos and indicates if they have imaginary
parts.
Generates an array having regularly
: (Colon)
spaced elements
, (Comma) Separates elements of an array
; (Semicolon)
Suppresses screen printing; also
denotes a new row in an array
… (Ellipsis) Continues a line
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
whos on First???
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Special VARS & const’s
Command
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)
Indicates an undefined numerical result;
a.k.a., Not a Number
pi The number pi (3.14159...)
NaN

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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
The Complex Plane
Im (i or j)
F  A  Bi or F  A  Bj
Re
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Complex-Number Operations
 The number c1 = 1 – 2i is entered as:
c1 = 12i 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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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)
>> Log_Z = log10(Z2)
ln_Z =
Log_Z =
2.6922 + 1.0769i
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1.2485 + 0.1242i
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Special VARS & const’s
Command
Description
Four decimal digits (the default);
format short
13.6745
format long 16 digits; 17.27484029463547
format short e
format long e
Five digits (four decimals) plus
exponent; 6.3792e+03
16 digits (15 decimals) plus exponent;
6.379243784781294e–04
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Discrete Math Funtions
Command
factor(n)
gcd(m,n)
Description
Returns a row vector containing the
prime factors of n.
Finds the Greatest Common
Divisor/Factor of m & n
Finds the Least Common Multiple for
m&n
Returns the factorial of n; i.e., returns
factorial(n)
n! = 1*2*3…(n-2)*(n-1)*n
lcm(m,n)
primes(n) Finds all prime numbers less than n
isprime(n) Determines if n is a prime number
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Discrete Math Examples
factor777 = factor(777)
P93 = primes(93)
factor777 =
P93 =
3
7
37
Columns 1 through 12
GCF = gcd(1001, 1105)
GCF =
13
11
29
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3
17
37
5
19
7
23
Columns 13 through 24
F7 = factorial(7)
F7 =
5040
2
13
31
59
79
41
61
83
43
67
89
47
71
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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73
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  2
with special
properties
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
5th Order Polynomial
 Find the roots of the 5th Order function
g  y   y  9 y  35 y  65 y  64 y  26  0
5
4
3
2
>> r5 = [1,-9,35,-65,64,-26];
>> roots(r5)
ans =
3.0000 + 2.0000i
3.0000 - 2.0000i
1.0000 + 1.0000i
1.0000 - 1.0000i
 The roots of g(y)
• y1,2 = 3 ± 2j
• y3,4 = 1 ± j
• y5 = 1
1.0000
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Common Math Functions
Fcn
MATLAB
Fcn
ex exp(x)
√x sqrt(x)
ln x log(x)
log10 x log10(x)
cos x cos(x)
MATLAB
sin x sin(x)
tan x tan(x)
cos-1 x acos(x)
sin-1 x asin(x)
tan-1 x atan(x)
 Note that MATLAB Trig functions
Operate on RADIANS
• Convert using Ratio: -rads per 180°
 rad    
 rads
180
;
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e.g., 73
 rads
180
 1.274 rads
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
The “d” Trig Comands for Degrees
>> T1 = sind(77)
>> T4 = asind(.497)
T1 =
T4 =
0.9744
>> T2 = cosd(19)
>> T5 = acosd(0.629)
T2 =
T5 =
0.9455
51.0236
>> T3 = tand(53)
>> T6 = atand(1.73)
T3 =
T6 =
1.3270
Engineering/Math/Physics 25: Computational Methods
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29.8017
59.9706
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Printing From Command Window - 1
Text
to
Print
 Note: MATLAB “Comments” Start with
the “%” Sign
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Printing From Command Window - 2
SELECT
Text to
Print
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Printing From Command Window - 3
 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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Alternative Cmd Window Printing
 Perform MATLAB
Operation
 Select Desired Text
 COPY text to the
Windows Paste
Buffer
 PASTE the MATLAB
Text Into the Text
Processor
 Print from the Text
Processor as Usual
 Open Text
application
• MSWord, WordPad,
NotePad, etc.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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')
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
System, Directory, File Cmnds
Command
Description
Adds the directory dirname to the
addpath dirname
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Plotting with MATLAB
 Plot over
573°
q p   cos p  
1.73 ln  p  1
QP  cosP  1.73 ln P  1
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
MATLAB Plotting Commands
Command
Description
Generates a plot of the array y versus
plot(x,y)
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
DeskTop Recovery
to UnScramble the DeskTop
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
DeskTop “Recovery”
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Example Problem 1-21
 Plot This Function
T  6 ln t  7e
0.2t
• Where
– T  Temperature (°C)
– t  time (minutes)
• For: 1  t  3
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
All Done for Today
Tutorial on
HomeWork
Construction
Next Time
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Engr/Math/Physics 25
Appendix
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Example Demo Session
>> %Use MATLAB As Calculator
>> (7+11)*2.5
>> 17*19
ans =
ans =
45
323
>> L = 14.4
>> 77/19 -4.3
L =
ans =
14.4000
-0.2474
>> W = 13.3
>> 64^(1/3) + 32^0.2
ans =
W =
13.3000
6
>> Area = L*W
Area =
Engineering/Math/Physics 25: Computational Methods
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191.5200
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Prob 1-22 Plot
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Problem 1-22
-6
Temperature (°C)
-6.5
-7
-7.5
-8
-8.5
-9
1
1.2
1.4
1.6
1.8
2
2.2
time (min)
Engineering/Math/Physics 25: Computational Methods
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2.4
2.6
2.8
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
3
System, Directory, File Cmnds
Command
Description
pwd Displays the current directory
Changes the current directory to
dirname
Removes the directory dirname from
rmpath dirname
the search path.
cd dirname
Lists the MATLAB-specific files found in
the current working directory. Most data
what
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
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_OverView-1.ppt