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Matlab Basics

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Workspace, Windows

Command window

Enter commands anddata, display results

Prompt >> Graphics (Figure) window

Display plots and graphs

Created

in

respon

se to graphics command

s M-file editor/debugger window

Create and edit scripts of commands called M-files

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Scalar Mathematics

Fixed point: Decimal form, with an optional

decimal point. For example:

2.6349 -381 0.00023 Floating point: Scientific notation,

representing m 10e

For example: 2

.6349 105 is represented as2.6349e5

Operators

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>>3 + 4

ans =

7

>>3 - 3ans =

0

>>4/5

ans =

0.8000

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>>4^3

ans =

64

>>56/8ans =

7

>>8\56

ans =

7

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Precedence of operations (order of

evaluation)

1. Parentheses, innermost first

2.Exponentiation (^), left to right

3. Multiplication (*) anddivision (/ or \) withequal precedence, left to right

4. Addition (+) and subtraction () with equal

precedence, left to right

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Variables and Assignment Statements

variable = numbervariable = expression

>> screws = 32

screws =

32

>> bolts = 18bolts =

18

>> rivets = 40;

>> items = screws + bolts + rivets

items =90

>> cost = screws * 0.12 + bolts * 0.18 + rivets * 0.08

cost =

10.2800

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Special variables

ans: default variable name

pi: ratio of circle circumference to its diameter, = 3.1415926...

eps: smallest amount by which two numbers candiffer

inf or Inf : infinity, e.g.1/0

nan or NaN : not-a-number, e.g. 0/0

date: current date in a character string format,such as 19-Mar-1998.

flops: count of floating-point operations

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Example 2.2 Listing andclearing variables

>> who

Your variables are:

21

average_cost cost rivets

bolts items screws

>> whos

Name Size Bytes Class

average_cost 1x1 8 double array

bolts 1x1 8 double array

cost 1x1 8 double arrayitems 1x1 8 double array

rivets 1x1 8 double array

screws 1x1 8 double array

Grand total is 6 elements using 48 bytes

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Command reuse and editing

Press the up arrow cursor key() to scrolls backwardthrough previous commands.

Press Enter to execute the selected command.

The down arrow cursor key() scrolls forward through

commands The left() and right arrow() cursor keys movewithin a command at the Matlab prompt, allowing thecommand to be edited.

The mouse can also be usedto reposition the command

cursor, by positioning the mouse cursor and pressingthe left mouse button.

Other standard editing keys, such as delete Del,backspace BkSp

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Copy

Ctrl+C

PasteCtrl+V

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Punctuation and Comments

Semicolon (;) at the end of a command suppresses thedisplay of the result

Commas and semicolons can be used to place multiple

commands on one line, with commasproducing display of results, semicolons suppressing

Percent sign (%) begins a comment, with all text up tothe next line ignored by Matlab

Three periods (...) at the end of a command indicatesthat the command continues on the next line. Acontinuation cannot be given in the middle of avariable name.

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Use of punctuation

>> screws = 36

screws =

36>> items

items =

90

>>items = screws + bolts + rivetsitems =

94

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>> screws=32, bolts=18; rivets=40; % multiplecommands

screws =

32>> items = screws + bolts + rivets;

>> cost = screws*0.12 + bolts*0.18 + rivets*0.08;

>> average_cost = cost/... % command continuation

itemsaverage_cost =

0.1142

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Basic Mathematical Functions

abs(x) Absolute value |x|

sign(x) Sign, returns 1 if x < 0, 0 if x = 0, 1 if x> 0

exp(x) Exponential ex

log(x) Natural logarithm ln x

log10(x) Common (base 10) logarithm log10 x

sqrt(x) Square root x

rem(x,y) Remainder ofx/y. For example,rem(100,21) is 16. Also called the modulusfunction.

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x =2/2

y =1/2*e(x2/2)

z = 20log10 y

>> x = sqrt(2)/2

x =0.7071

>> y = exp(-(x^2)/2)/sqrt(2*pi)

y =

0.3107

>> z = 20*log10(y)z =

-10.1533

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Arrays: vectors and matrices

A matrix is a rectangular object (e.g. a table)consisting of rows and columns

Enter a statement like

x = [13 0 -15] You can put commas instead of spaces between

vector elements if you like. Try this:

a = [5,6,7]

And what about this?a = [13 7];

a = [a 0 -1];

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Elements in the list must be enclosed in

square not round brackets.

Eleme

nts i

nthe list must be separate

deitherby spaces or by commas.

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Initializing vectors: the colon operator

x = 1:10

x =

1 2 3 4 5 6 7 8 9 10

x = 1:0.5:4x =

1.0000 1.5000 2.0000 2.5000 3.00003.5000 4.0000

x = 10:-1:1x =

10 9 8 7 6 5 4 3 2 1

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linspace

The function linspace can be used to initialize

a vector of equally spaced

values, e.g. linspace(0, pi/2, 10)

creates a vector of10 equally spaced points

from 0 to /2 (inclusive).

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Transposing vectors

Enter x = 1:5 and then enter x to display the

transpose of x. Note that x itself remains a

row vector.

you can create a column vector directly:

y = [148 0 -1]

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Subscripts

1.Enter r = rand(1,7) This gives you a row vector of sevenrandom numbers.

r =

0.9501 0.2311 0.6068 0.4860 0.8913 0.7621 0.4565

2. Now enter r(3)

This will display the third element of r. The number3 is thesubscript.

3. Now enter r(2:4)

This should give you the second, third and fourth elements.

4. What about r(1:2:7)?

5. And r([1 7 26])?6. You can use an empty vector to remove elements from a vector, e.g.

r([1 7 2]) = [ ]

will remove elements 1, 7 and2.

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a = [248];

b = [322];

a .* b

a ./ b

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Assignment

Evaluate the following MATLAB expressionsyourself (before you use MATLAB to check!).

2/2 * 3

2/3 2

(2/3) 2

2 + 3 * 4 4

2 2 * 3/4 + 3

2 (2 * 3)/ (4 + 3) 2 * 3 + 4

2 3 2

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Assignment

Use MATLAB to evaluate the followingexpressions. The answers are in round

brackets again.

a. 2

b.3 + 4/5 + 6

c.Find the sum of5 and3divided by theirproduct

d.232 e.Find the square of2

f.22

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Assignment

g.1/2

h.1/2

i.Find the cube root of the product of2.3 and4.5

j.(1 2/(3+2))/(1 + 2/(32))

k.1000(1 + 0.15/12)60 l. (0.0000123+5.678103)0.4567104

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Assignment

Water freezes at 32 and boils at 212 on the

Fahrenheit scale. IfC and F are Celsius and

Fahrenheit temperatures, the formula

F = 9C/5 +32

converts from Celsius to Fahrenheit.

Use the MATLAB command line to convert

temperature of37C (normal human

temperature) to Fahrenheit (98.6).

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Try to avoid using unnecessary brackets in an

expression. Can you spot the errors in the

following expression (test your corrected

version with MATLAB):

(2(3+4)/(5*(6+1))2

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Set up a vector n with elements 1, 2, 3, 4, 5.

Use MATLAB array operations on the vector n

to set up the following four vectors, each with

five elements:

a.2, 4, 6, 8, 10

b.1/2, 1, 3/2, 2, 5/2

c.1, 1/2, 1/3, 1/4, 1/5

d.1, 1/22, 1/32, 1/42, 1/52

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Suppose a and b are defined as follows:

a = [2 -15 0];

b = [32 -14];

Evaluate by hand the vector c in the following statements. Check youranswers with MATLAB.

a. c = a - b;b. c = b + a - 3;

c. c = 2 * a + a . b;

d. c = b ./ a;

e. c = b .\ a;

f. c = a . b;g. c = 2. b+a;

h. c = 2*b/3.*a;

i. c = b*2.*a;

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Assignment

Use MATLAB array operations to do the

following:

1. Add

1 to each elemen

t of the vector [23 -1].2. Multiply each element of the vector [148]by

3.

3.Find the array product of the two vectors [12

3]and [0 -11].

4. Square each element of the vector [231].

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Write a program to calculate x, where

x = (b +(b2 4ac))/2a

anda=2, b=10, c=12 (Answer3.0)