Chapter1_Cơ Sở Matlab

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Lecture 1: Introduction

Lecture series based on the text:

Essential MATLABfor Engineers and ScientistsBy

Hahn & Valentine

2007 Daniel Valentine. All rights reserved. Published by

Elsevier.

http://www.mediafire.com/?y5dz4zjxrj0z4

Email: [email protected]

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MATLAB desktop

Command Window

Command History

Window

Workspace Window

Current Directory

Window

Start Button

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Command Window

The Command Windowon the right is the mainpanel where you interact with MATLAB.

You key (or type) and commands after

the prompt >>; MATLAB executes the

commands and displays results (if requested).

Some commonly used tools and commands:

(up arrow) returns last command input, can be

repeated clcclears the screen

whosshows list of variables

clearclears variables

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Evaluation of MATLAB

HANDS-ON with MATLAB

Type

>>

2+3

into the Command Window

>> clc

>>whos

Throughout the lecture, yellow text indicateswhat you should type into MATLAB.

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Command History Window

The Command History Windowlogs all of thecommands you enter in MATLAB.

It should have logged 2+3.

Use the Command History Window to reenter2+3in the command window (use copy-and-paste or double click on 2+3).

This is useful to retrieve past commands.

Use Shiftkey to select multiple lines.

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Arithmetic with MATLAB

Let us explore by doing exercises:

>> 32

>> 3*2 >> 3/2

>> 3\2

>> 3^2

>> 2/0

>> 0/2

>> 3*Inf

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Algebraic-numeric computations

Let us explore by doing exercises:

>> a = 3

>>b = 2

>> a b

>> a / b

>> a^2

>> c = a * b >> d = c^(b+1)

>>who

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Hiding Output

Let us explore by doing exercises:>> clear; clc

>>whos

>> a = 3; >>b = 2;

>> c = a * b;

>> d = c^(b+1);

>>who

>> % a, b, c, d are in workspace

>>a, b, c, d

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Plotyversusx

Introduction to plotting & displaying data:

>> clear; clc

>> x = 0:0.1:1;

>> y = x.^2; >> whos

>> plot(x,y,x,y,o)

>> disp(' '),disp('...... x ........ y .....'),disp([x y'])

>> x

>>y

>> % x and y are 1-by-11 arrays of numbers!

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Write a Simple Program

Consider computing the volume of a cone:Volume = (pi.*r.^2.*h)./3

radius = 6 inches

height = 12 inches

In the command window key in:>> clear; clc

>>r = 6

>>h = 12 >>v = (pi.*r.^2.*h)./3

>>whos

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Editor & M-Files

An M-filein MATLAB is analogous to a txt-file in Microsoft Notepad.

An M-file is created in MATLAB text editor.

M-files: You can save your programs (i.e., list of

executable commands) as M-files.

You can reopen and modify your program. They are useful for debugging (correcting

errors) as you develop your programs (yourtechnical computing tools).

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Comments in programs

Every time you write a program to be saved, it ishelpful for you to comment(i.e., describe)it well.

To insert a comment on a line in the editor or inthe Command Window, use the comment

operator %, then type your comment. MATLAB:

will not run lines that begin with the comment operator(in the editor comments appear in green).

Comments Comments allow you (and others) to more easily

understand your program.

When your lines of code are easy to understand, yourcode will be easier to use later.

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Art of well-written code

A well-written program is like literature; itcontains comments explaining:

what your program requires as input.

what the variables in the program represent. what your program computes and displays.

It is useful for you to add a set of headercomments that include the name of theprogram, your name (as the programmer),and the date the program was created ormodified.

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Saving code in an M-File

Open the editor by: Entering the command editin the command window.

Or click the white-sheet-of-paper icon in the upper left

hand corner directly below file.

Now enter the lines of code to find the volume of a cone:rr = 4

h = 12

v = (pi.*r.^2.*h)./3

REMARK: If you save it, add header comments and commentsexplaining what the program does.

After you have typed in the code, save it as cone.m.

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This is cone.m in the editor

%% Tool to compute the volume of a cone.% A simple sample for a first lecture.% B.H.& Daniel........... January 2007%rr = 4; % radius of the coneh = 12; % height of the conev = (pi.*r.^2.*h)./3 % Volume of the cone

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Execute an M-file as a Command

Now execute (or run) the program by pushingF5, or by typing on the command line>> cone

or by clicking the run button. (Note that the run buttonlookslike a page with a down arrow to its left. It can be found below help on

the toolbar of the edit window.) If you entered the code as written on the

previous slide you will get an error!

What went wrong?

Repair your program (Changerr = 4to r = 4.), save it,and run it again.

Now change the height to 24, save and run yourprogram again.

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Summary

MATLAB can be used like a hand calculator todo arithmetic.

You can define (or assign) variables with

numbers and expressions to do calculations asillustrated by the volume-of-cone example.

The advantage of saving programs as M-filesisthat you open it, make changes and/or execute it

again without having to type it all over again. This concludes our overview of MATLAB and a

taste of things to come!

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Lecture 2

MATLAB fundamentalsVariables, Naming Rules,

Arrays (numbers, scalars, vectors, matrices),

Arithmetical Operations,

Defining and manipulating arrays


Elsevier.

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Variables

What are variables?You name the variables(as the programmer)

and assign them numerical values.

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Variable Naming Rules

Must begin with a LETTER

May only contain letters, numbers andunderscores ( _ )

No spaces or punctuation marks allowed!

Only the first 63 characters are significant;

beyond that the names are truncated. Case sensitive(e.g. the variables aandA

are not the same)

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Which variable names are valid?

12oclockRock

tertiarySector

blue cows

Eiffel65

red_bananas

This_Variable_Name_Is_Quite_Possibly_Too_Lo

ng_To_Be_Considered_Good_Practice_However_It_Will_Work % (the green part is not part ofthe recognized name)

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Variable Naming Conventions

There are different ways to name variables. Thefollowing illustrate some of the conventions used:

lowerCamelCase

UpperCamelCase

underscore_convention

If a variable is a constant, some programmers use allcaps:

CONSTANT

It does not matter which convention you choose to workwith; it is up to you.

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In MATLAB, a variableis stored as an array of

numbers. When appropriate, it is interpreted as a

scalar, vectoror matrix.

The size of an array is specified by the number of

rows and the number of columns in the array, with

the number of rows indicated first.

Variables as Arrays

scalar1 1

vectorn 1 or 1 n

matrixn m

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Scalarsare 11 arrays.

They contain a single value, for example:

r = 6r = 6

width = 9.07width = 9.07

height = 5.3height = 5.3

Scalars

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Vectors

A vectoris a list of numbers expressed as a 1

dimensional array.

A vector can be n1 or 1n.

Columns are separated by commas (or spaces):

Rows are separated by semicolons:

v = [1; 2; 3]v = [1; 2; 3]

h = [1, 2, 3]h = [1, 2, 3]

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m = [3.0, 1.8, 3.6; 4.6,m = [3.0, 1.8, 3.6; 4.6, --2.0, 21.3; 0.0,2.0, 21.3; 0.0,

--6.1, 12.8; 2.3, 0.3,6.1, 12.8; 2.3, 0.3, --6.1]6.1]

Matrices

A matrixis a twodimensional array ofnumbers.

For example, this is a43 matrix:

1 2 3

1 3.0 1.8 3.6

2 4.6 -2.0 21.3

3 0.0 -6.1 12.8

4 2.3 0.3 -6.1

Columns

Row

s

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m(2,3)m(2,3)

Indexed-location of numbers in anarray

Each item in an arrayis located in the

(row, column).

1 2 3

1 3.0 1.8 3.6

2 4.6 -2.0 21.3

3 0.0 -6.1 12.8

4 2.3 0.3 -6.1

Columns

Rows

ans =21.3000

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Enter the following into MATLAB:

Scalar:

Vectors:

Matrix:d = [5, 4, 3; 0, 2, 8]d = [5, 4, 3; 0, 2, 8]

b = [1, 0, 2]b = [1, 0, 2]

c = [1 0 2]c = [1 0 2]

a = 1a = 1

Examples

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Examples

Enter (input) the following matrix into MATLAB:

-7 21 6

2 32 0

-5 0 -18.5

whiteRabbit =

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Scalar Operations

Operation AlgebraicSyntax

MATLAB Syntax

Addition a + b a + b

Subtraction a - b a b

Multiplication a b a .* b

Division a b a ./ b ora.\ b

Exponentiation ab a .^ b

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Array Operations

Arrays of numbers in MATLAB can be interpreted asvectors and matrices if vector or matrix algebra is to beapplied. Recall that matrices are mathematical objectsthat can be multiplied by the rules of matrices. To do

matrix multiplication, you need to use the standard *, /,and ^ operators [without the preceding .(dot)]. They arenotfor array multiplication, division and exponentiation.

To deal with arrays on an element-by-elementlevel we

need to use the following arrayor dot-operators:

.* ,./ and.^

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Array operations & dot-operators

Because scalars are equivalent to a 11array, you can either use the standard or

the dot-operatorswhen doingmultiplication, division and exponentiationof scalars (i.e., of single numbers).

It is okay for you to always use the dot-operators, unless you intend to performvector or matrix multiplication or division.

.*, ./ and.^

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Example:

z = x .* yresults in [10, 6; 21, 32]; this is array multiplication

z = x * y

results in [17, 20; 43, 50]; this is matrix multiplication

So, do NOT forget the dot when doing arrayoperations! (.* ./ .^)

x = [2, 1; 3, 4]x = [2, 1; 3, 4]

y = [5, 6; 7, 8]y = [5, 6; 7, 8]

Array vs. Matrix Operations

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Hierarchy of Operations

Just like in mathematics the operations are done in thefollowing order: Left to rightdoing what is in

Parentheses & Exponents first, followed by

Multiplication & Division, and thenAddition & Subtraction last.

An example:

c = 2+3^2+1/(1+2) 1st c = 2+3^2+1/3

c = 2+3^2+1/(1+2) 2nd

c = 2+9+1/3c = 2+3^2+1/(1+2) 3rd c = 2+9+0.33333

c = 2+3^2+1/(1+2) 4th c = 11+0.33333

c = 2+3^2+1/(1+2) 5th c = 11.33333

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Hands-on

Enter these two arrays into MATLAB:

Multiply, element-by-element, a b.

Since this is an array operation, the .*multiplication operation is implied by therequest.

a =10 5 52 9 0

6 8 8

b =1 0 20 0 0

1 1 0

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Defining & manipulating arrays

All variables in MATLAB are arrays!

Single number array & scalar: 1 1

Row array & row vector: 1 n

Column array & column vector: n x 1Array of n rows x m columns & Matrix: n m

Naming rules

Indexed by (row, column) Remark:vectors and matrices are special

mathematical objects, arrays are lists ortables of numbers.

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The equal sign assigns

Consider the command lines:>> ax = 5;

>> bx = [1 2];

>> by = [3 4];>> b = bx + by;

The equal sign (=) commands that the

number computed on the right of it isinput to the variable named on the left;thus, it is an assignment operation.

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An arraycan be defined by typing in a list of numbersenclosed in square brackets:

Commasor spacesseparate numbers.

Semicolonsindicate a new row.

A = [12, 18,A = [12, 18, --3]3] oror A = [12 18A = [12 18 --3]3]

B = [2, 5, 2; 1 , 1, 2; 0,B = [2, 5, 2; 1 , 1, 2; 0, --2, 6]2, 6]

Defining (or assigning) arrays

A =12 18 -3

B =2 5 21 1 20 -2 6

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D =12 18 -3 12 18 -3

2 5 2 2 5 2

1 1 2 1 1 2

0 -2 6 0 -2 6

C = [A; B]C = [A; B]

D = [C, C]D = [C, C]

Defining arrays continued

You can define an array in terms of another array:

C =

12 18 -3

2 5 21 1 2

0 -2 6

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Create an array of zeros:

Create an array of ones:

Note: Placing a single number inside either function will return an n narray.e.g. ones(4)will return a 4 4 array filled with ones.

E = zeros(3,5)E = zeros(3,5)

F = ones(2,3)F = ones(2,3)

Creating Zeros & Ones arrays

E =0 0 0 0 0

0 0 0 0 00 0 0 0 0

F =

1 1 11 1 1

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Indexa number used to identify elements in an array

Retrieving a value from an array:

G(3,2)G(3,2)G(2,1)G(2,1)

G = [1, 2, 3; 4, 5, 6; 7, 8, 9]G = [1, 2, 3; 4, 5, 6; 7, 8, 9]

Retrieving Values in an Array

ans = 4 ans = 8

G =1 2 34 5 67 8 9

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You can change a value in an element in an array with indexing:

You can extend an array by defining a new element:

Notice how undefined values of the array are filled with zeros

A(2) = 5A(2) = 5

A(6) = 8A(6) = 8

Changing Values in an Array

A =

12 5 -3

A =12 5 -3 0 0 8

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Colon notationcan be used to define evenly spaced vectors in theform:

first : last

The default spacing is 1, so to use a different increment, use the form:

first : increment : last

The numbers now increment by 2

I = 1:2:11I = 1:2:11

H = 1:6H = 1:6

Colon Operator

H =1 2 3 4 5 6

I =1 3 5 7 9 11

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G(2,:)G(2,:)G(:,1)G(:,1) G(:,3)G(:,3)

Extracting Data with the ColonOperator

The colon represents an entire row or column when usedin as an array index in place of a particular number.

G =1 2 3

4 5 67 8 9

ans =

1

4

7

ans =

3

6

9

ans =

4 5 6

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G(1,2:3)G(1,2:3)G(2:3,:)G(2:3,:)

Extracting Data with the ColonOperator Continued

The colon operator can also be used to extract a rangeof rows or columns:

G =1 2 3

4 5 67 8 9

ans =2 3

G =4 5 67 8 9

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J'J'J = [1 , 3, 7]J = [1 , 3, 7]

Manipulating Arrays

The transpose operator, an apostrophe,changes all of an arrays rows to columnsand columns to rows.

J =1 3 7

ans =

137

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Manipulating Matrices Continued

The functions fliplr()and flipud()flip amatrix left-to-right and top-to-bottom,respectively.

Experiment with these functions to see howthey work.

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W = [1:5; 10:2:18; 6:W = [1:5; 10:2:18; 6:--1:2]1:2]

Hands-on exercise:

Create the following matrix using colon notation:W =

1 2 3 4 510 12 14 16 186 5 4 3 2

All three rows are evenly spaced The first row ranges from 1 to 5 in increments of 1

1:5

The second row ranges from 10 to 18 in increments of 2

10:2:18 The third row ranges from 6 to 2 in increments of -1 6:-1:2

All together:

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Hands-on continued

Create the following matrix using colon notation:

X =

1.2 2.3 3.4 4.5 5.6

1.9 3.8 5.7 7.6 9.5

0 -3 -6 -9 -12

Transpose this matrix and assign it to variable Y.

>> Y = x

Extract the 2nd row from Y and assign it to variable Z.

>> Z = Y(2,:)

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Summary (1 of 2)

Naming a variable: Start with letterfollowed by any combination of letters,numbers and underscores (up to 63 of

these objects are recognized).Arrays are rows and columns of numbers.

Array operations (element-by-element

operations with the dot-operators)

Hierarchy of arithmetic operations.

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Summary (2 of 2)

Command lines that assign variablesnumerical values start with the variablename followed by = and then the defining

expressionAn array of numbers is the structure of

variables in MATLAB. Within one variablename, a set of numbers can be stored.

Array, vector and matrix operations areefficient MATLAB computational tools.

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Lecture 3

Creating M-filesProgramming tools:

Input/output(assign/graph-&-display)

Repetition (for)

Decision (if)


Elsevier.

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Review

Arrays List of numbers in brackets

A comma or space separates numbers (columns) A semicolon separates row

Zeros and ones Matrices:

zeros() ones()

Indexing (row,column)

Colon Operator: Range of Data first:last or first:increment:last

Manipulating Arrays & Matrices Transpose

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Input

Examples of input to arrays:

Single number array & scalar: 1 1

>> a = 2

Row array & row vector: 1 n

>> b = [1 3 2 5]

Column array & column vector: n x 1

>> b = b % This an application of the transpose.Array of n rows x m columns & Matrix: n m

>> c = [1 2 3; 4 5 6; 7 6 9] % This example is 3 x 3.

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Basic elements of a program

Input

Initialize, define or assign numerical values tovariables.

Set of command expressions Operations applied to input variables that lead

to the desired result.

Output Display (graphically or numerically) result.

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An example of technical computing

Let us consider using the hyperbolic tangentto model a down-hill section of a snowboardor snow ski facility.

Let us first examine the hyperbolic tangentfunction by executing the command:

>> ezplot(tanh(x))

We get the following graph:

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Ezplot(tanh(x))

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Problem background

Let us consider the design of a slope thatis to be modeled by tanh(X). Consider therange -3


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Formula for snow hill shape

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Problem statement

Find the altitude of the hill at 0.5 meterintervals from -5 meters to 5 meters usingthe shape described and illustrated in theprevious two slides.

Tabulate the results.

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Structure plan

Structure plan Initialize the range of X in 0.5 meter intervals.

Compute y, the altitude, with the formula:

y = 1tanh(3*X/5). Display the results in a table.

Implementation of the structure plan Open the editor by typing editin the

command window.

Translate plan into the M-file language.

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This is from editor: It is lec3 m

%% Ski slope offsets for the% HYPERBOLIC TANGENT DESIGN% by D.T. Valentine...January 2007%% Points at which the function

% is to be evaluated:% Step 1: Input xx = -5:0.5:5;

% Step 2: Compute the y offset,% that is, the altitude:

y = 1 - tanh(3.*x./5);

%% Step 3: Display results in a table%disp(' ') % Skips a linedisp(' X Y')disp([x' y'])

Command window OUTPUT

X Y

-5.0000 1.9951

-4.5000 1.9910

-4.0000 1.9837

-3.5000 1.9705

-3.0000 1.9468

-2.5000 1.9051

-2.0000 1.8337

-1.5000 1.7163

-1.0000 1.5370

-0.5000 1.2913

0 1.0000

0.5000 0.7087

1.0000 0.4630

1.5000 0.2837

2.0000 0.16632.5000 0.0949

3.0000 0.0532

3.5000 0.0295

4.0000 0.0163

4.5000 0.0090

5.0000 0.0049

SOLUTION TO IN-CLASS EXERCISE

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Use of repetition (for)

Repetition: In the previous example, thefastest way to compute y was used. Analternative way is as follows:

Replace:y = 1 - tanh(3.*x./5); % This is vectorized approach.

With:

for n=1:21

y(n) = 1 - tanh(3*x(n)/5);

end

Remark: Of course, the output is the same.

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This is from editor: It is lec3_2 m

%% Ski slope offsets for the% HYPERBOLIC TANGENT DESIGN% by D.T. Valentine...January 2007%% Points at which the function

% is to be evaluated:% Step 1: Input xx = -5:0.5:5;

% Step 2: Compute the y offsetfor n=1:21

y(n) = 1 - tanh(3*x(n)/5);

end%% Step 3: Display results in a tabledisp(' ') % Skips a linedisp(' X Y')disp([x' y'])

Command window OUTPUT

X Y

-5.0000 1.9951

-4.5000 1.9910

-4.0000 1.9837

-3.5000 1.9705

-3.0000 1.9468

-2.5000 1.9051

-2.0000 1.8337

-1.5000 1.7163

-1.0000 1.5370

-0.5000 1.2913

0 1.0000

0.5000 0.7087

1.0000 0.4630

1.5000 0.2837

2.0000 0.16632.5000 0.0949

3.0000 0.0532

3.5000 0.0295

4.0000 0.0163

4.5000 0.0090

5.0000 0.0049

SOLUTION TO IN-CLASS EXERCISE

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Decision: Application of if

Temperature conversion problem:

Convert C to F or F to C.

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%% Temperature conversion from C to F% or F to C as requested by the user%

Dec = input(' Which way?: 1 => C to F? 0 => F to C: ');Temp = input(' What is the temperature you want to convert? ');%% Note the logical equals sgn (==)if Dec == 1

TF = (9/5)*Temp + 32;disp(' Temperature in F: ')disp(TF)

elseTC = (5/9)*(Temp-32);disp(' Temperature in C: ')disp(TC)

end


Temperature conversion problem:

Convert C to F or F to C. SOLUTION:

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Summary

Introduced, by an example, the structureplan approach to design approaches tosolve technical problems.

Input: Assignment with and without inpututility.

Output: Graphical & tabular were shown.

Illustrated array dot-operation, repetition(for) and decision (if) programming tools.

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Chapter1_Cơ Sở Matlab