Least Squares
17 сент. 2013 г. The MAtlAB function polyfit computes least squares polynomial fits by setting up the design matrix and using backslash to find the ...
Magic Squares
2 окт. 2011 г. Write a MAtlAB function ismagic(A) that checks if A is a magic square. 10.2 Magic sum. Show that. 1 n n2. ∑ k=1 k = n3 + n. 2 . 10.3 durerperm ...
Some important Built-in function in MATLAB 1. Square root b=sqrt(x
14 мар. 2020 г. Some important Built-in function in MATLAB. 1. Square root b=sqrt(x) b=sqrt(4). 2. 2. Remainder of dividing x/y a=rem(xy) a=rem(10
Objective 1 Triangular Wave 2 Square Wave 3 Discrete Time
2 Square Wave. MATLAB has a built-in function square to generate a periodic square waveform. Following example will help you draw such a waveform. 2.1
- 1 - Some MATLAB Built-in Functions Function Description sqrt(x
Some MATLAB Built-in Functions. Function. Description sqrt(x). Square root of x nthroot(xn) nth root of x abs(x). Absolute value of x exp(x). Exponential (ex).
Eigenvalues and Singular Values
16 сент. 2013 г. The Matlab function condeig computes eigenvalue condition numbers. ... The qr function in Matlab factors any matrix real or complex
Quadrature
area—plot the function on graph paper and count the number of little squares that The function functions in Matlab itself usually expect the first argument to.
Iteration
2 окт. 2011 г. Matlab responds with x = 3. Next enter this statement x = sqrt(1 + x). The abbreviation sqrt is the Matlab name for the square root function.
Total Least Squares Approach to Modeling: A Matlab Toolbox
In this section we show some applications of the TLS method in static and dynamical modeling by using the created Matlab functions [14]. 3.1 Linear regression
Implementing the 2D square lattice Boltzmann method in Matlab
23 февр. 2023 г. In contrast to LGA. LBM deals with distribution function values instead of single particles. The exact denomination for the following described ...
General Linear Least-Squares and Nonlinear Regression
Applied Numerical Methods with MATLAB for Engineers Chapter 15 & Teaching The least-squares ... function that returns the sum of the squares of the.
Objective 1 Triangular Wave 2 Square Wave 3 Discrete Time
MATLAB has a built-in function sawtooth to generate a periodic triangular waveform. Following example will help you draw such a waveform. 1.1 Example. Generate
Magic Squares
2011?10?2? An n-by-n magic square is an array containing the integers from 1 to n2 ... squares of order n but the MAtlAB function magic(n) generates a ...
Least Squares
2013?9?17? The MAtlAB function polyfit computes least squares polynomial fits by setting up the design matrix and using backslash to find the ...
Some important Built-in function in MATLAB 1. Square root b=sqrt(x
2020?3?14? Some important Built-in function in MATLAB. 1. Square root b=sqrt(x) b=sqrt(4). 2. 2. Remainder of dividing x/y a=rem(xy) a=rem(10
Eigenvalues and Singular Values
2013?9?16? A singular value and pair of singular vectors of a square or ... qr function in Matlab factors any matrix real or complex
Iteration
2011?10?2? The abbreviation sqrt is the Matlab name for the square root function. The quantity on the right. /. 1 + x
DEPARTMENTS OF MATHEMATICS
1999?1?4? MAtlAB has included since at least version 3 a function sqrtm for computing a square root of a matrix. The function works by reducing the ...
INTRODUCTION TO MATLAB FOR ENGINEERING STUDENTS
The function diary is useful if you want to save a complete MATLAB session. of vectors in MATLAB are enclosed by square brackets and are separated by ...
Total Least Squares Approach to Modeling: A Matlab Toolbox
In this section we show some applications of the TLS method in static and dynamical modeling by using the created Matlab functions [14]. 3.1 Linear regression
MATLAB Basic Functions Reference - MathWorks
Tasks represent a series of MATLAB commands To see the commands that the task runs show the generated code Common tasks available from the Live Editor tab on the desktop toolstrip: • Clean Missing Data • Clean Outlier • Find Change Points • Find Local Extrema • Remove Trends • Smooth Data mathworks com/help/matlab
Chapter 10 Magic Squares - MathWorks
Ann-by-nmagic square is an array containing the integers from 1 ton2arranged so that each of the rows each of the columns and the two principaldiagonals have the same sum For eachn >2 there are many di?erent magicsquares of ordern but theMatlabfunctionmagic(n)generates a particular one Matlabcan generate Lo Shu with = magic(3) which produces
MATLAB Function Example Handout - University of Wyoming
ical function libraries The Matlab Optimization and Curve Fitting Toolboxes include functions for one-norm and in?nity-norm problems We will limit ourselves to least squares in this book 5 3 censusgui The NCM program censusgui involves several di?erent linear models The data
Chapter 1 Iteration - MathWorks
In Matlab and most other programming languages the equals sign is the assignment operator It says compute the value on the right and store it in the variable on the left So the statement x = sqrt(1 + x) takes the current value of x computes sqrt(1 + x) and stores the result back in x
Functions and Scripts - Electrical Engineering and Computer
Many functions are programmed inside MATLAB as built-in functions and can be used in mathematical expressions simply by typing their name with an argument; examples are sin(x) cos(x) sqrt(x) and exp(x) MATLAB has a plethora of built-in functions for mathematical and scientific computations
Chapter 1 Introduction to MATLAB - MathWorks
MATLAB An introduction to MATLAB through a collection of mathematical and com-putational projects is provided by Moler’s free online Experiments with MATLAB [6] A list of over 1500 Matlab-based books by other authors and publishers in several languages is available at [12] Three introductions to Matlab are of par-
MATLAB Getting Started Guide - Massachusetts Institute of
The load function reads binary files containing matrices generated by earlier MATLAB sessions or reads text files containing numeric data The text file should be organized as a rectangular table of numbers separated by blanks with one row per line and an equal number of elements in each row
MATLAB Function Tips - Michigan State University
function [xsqrd xcubd] = square(x) xsqrd = x^2 xcubd = x^3 There are two possible places to position this code If you are using MATLAB 5 0 or later this function code can be placed at the end of the main program in the same file as the main program It could also be placed in its own file which must use the function name or for our example
Matlab Introduction - California State University Long Beach
The batch commands in a file are then executed by typing the name of the file at the Matlab command prompt The advantage to using a ' m' file is that you can make small changes to your code (even in different Matlab sessions) without having to remember and retype the entire set of commands
6057 Introduction to MATLAB Homework 2 - MIT OpenCourseWare
Use magenta square symbols of marker size 10 and line width 4 and no line connecting them You may have to change the x limits to see all 6 symbols (xlim) If the relationship really is exponential it will look linear on a log plot 2 Subplot and axis modes Make a new Square Tight 100 100 200 figure that has a 2x2 grid of axes () subplot 200
MATLAB Commands and Functions - College of Science and
MATLAB Commands – 11 M-Files eval Interpret strings containing Matlab expressions feval Function evaluation function Creates a user-defined function M-file global Define global variables nargin Number of function input arguments nargout Number of function output arguments script Script M-files Timing cputime CPU time in seconds
Searches related to function square matlab filetype:pdf
MATLAB is installed on the engineering instructional facility You can find it in the Start>Programs menu You can also install MATLAB on your own computer This is a somewhat involved process –you need to first register your name at mathworks then wait until they create an account for you there then download MATLAB and activate it
What are the functions of MATLAB?
- MATLAB Function Example Handout. MatLab is a high performance numeric computing environment, which includes numerical analysis, matrix computation, signal processing, and graphics to provide answers to the most troubling of mathematical problems. This handout provides different examples to show the different aspects of MatLab.
How to generate unit step function in MATLAB?
- function [x]=unitstep (x) %This is a unit step "function". The vector keeping track of time is the %input. If time is negative then a zero is returned. If time is zero than %0.5 is returned.
How to generate square wave in MATLAB?
- Square wave is generated using “square” function in Matlab. The command sytax – square (t,dutyCycle) – generates a square wave with period for the given time base. The command behaves similar to “ sin ” command (used for generating sine waves), but in this case it generates a square wave instead of a sine wave.
INTRODUCTION TO MATLAB FOR
ENGINEERING STUDENTS
David Houcque
Northwestern University
(version 1.2, August 2005)Contents
1Tutorial lessons 1
1 1.1Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2Basic features
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3A minimum MATLAB session
. . . . . . . . . . . . . . . . . . . . . . . . . . 21.3.1 Starting MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3.2 Using MATLAB as a calculator . . . . . . . . . . . . . . . . . . . . . 4
1.3.3 Quitting MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4Getting started
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4.1 Creating MATLAB variables . . . . . . . . . . . . . . . . . . . . . . . 5
1.4.2 Overwriting variable . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.3 Error messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.4 Making corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.5 Controlling the hierarchy of operations or precedence . . . . . . . . . 6
1.4.6 Controlling the appearance of °oating point number . . . . . . . . . . 8
1.4.7 Managing the workspace . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4.8 Keeping track of your work session . . . . . . . . . . . . . . . . . . . 9
1.4.9 Entering multiple statements per line . . . . . . . . . . . . . . . . . . 9
1.4.10 Miscellaneous commands . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.11 Getting help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5Exercises
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2Tutorial lessons 2
12 2.1Mathematical functions
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.1.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
i 2.2Basic plotting
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.1 overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.2 Creating simple plots . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.3 Adding titles, axis labels, and annotations . . . . . . . . . . . . . . . 15
2.2.4 Multiple data sets in one plot . . . . . . . . . . . . . . . . . . . . . . 16
2.2.5 Specifying line styles and colors . . . . . . . . . . . . . . . . . . . . . 17
2.3Exercises
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5Matrix generation
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5.1 Entering a vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5.2 Entering a matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5.3 Matrix indexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.5.4 Colon operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5.5 Linear spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5.6 Colon operator in a matrix . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5.7 Creating a sub-matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.5.8 Deleting row or column . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5.9 Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5.10 Continuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5.11 Transposing a matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5.12 Concatenating matrices . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5.13 Matrix generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5.14 Special matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.6Exercises
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3Array operations and Linear equations
303.1
Array operations
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.1.1 Matrix arithmetic operations . . . . . . . . . . . . . . . . . . . . . . . 30
3.1.2 Array arithmetic operations . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 Solving linear equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1 Matrix inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
ii3.2.2 Matrix functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3Exercises
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4Introduction to programming in MATLAB
354.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 M-File Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2.2 Script side-e®ects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3 M-File functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3.1 Anatomy of a M-File function . . . . . . . . . . . . . . . . . . . . . . 38
4.3.2 Input and output arguments . . . . . . . . . . . . . . . . . . . . . . . 40
4.4 Input to a script ¯le . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.5 Output commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.6Exercises
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5Control °ow and operators
435.1
Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.2Control °ow
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.2.1 The``if...end''structure . . . . . . . . . . . . . . . . . . . . . . . 43
5.2.2 Relational and logical operators . . . . . . . . . . . . . . . . . . . . . 45
5.2.3 The``for...end''loop . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2.4 The``while...end''loop . . . . . . . . . . . . . . . . . . . . . . . 46
5.2.5 Other °ow structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.2.6 Operator precedence . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.3Saving output to a ¯le
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.4Exercises
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 6Debugging M-¯les
496.1
Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.2Debugging process
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.2.1 Preparing for debugging . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.2.2 Setting breakpoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
iii6.2.3 Running with breakpoints . . . . . . . . . . . . . . . . . . . . . . . . 50
6.2.4 Examining values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.2.5 Correcting and ending debugging . . . . . . . . . . . . . . . . . . . . 51
6.2.6 Ending debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.2.7 Correcting an M-¯le . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
ASummary of commands
53B
Release notes for Release 14 with Service Pack 2
58B.1
Summary of changes
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 B.2Other changes
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 B.3Further details
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 CMain characteristics of MATLAB
62C.1
History
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 C.2Strengths
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 C.3Weaknesses
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 C.4Competition
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 ivList of Tables
1.1 Basic arithmetic operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Hierarchy of arithmetic operations . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Elementary functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Prede¯ned constant values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Attributes forplot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Elementary matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5 Special matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1 Array operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Summary of matrix and array operations . . . . . . . . . . . . . . . . . . . . 32
3.3 Matrix functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1 Anatomy of a M-File function . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2 Di®erence between scripts and functions . . . . . . . . . . . . . . . . . . . . 39
4.3 Example of input and output arguments . . . . . . . . . . . . . . . . . . . . 40
4.4dispandfprintfcommands . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.1 Relational and logical operators . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2 Operator precedence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
A.1Arithmetic operators and special characters
. . . . . . . . . . . . . . . 53 A.2Array operators
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 A.3Relational and logical operators
. . . . . . . . . . . . . . . . . . . . . . 54 A.4Managing workspace and ¯le commands
. . . . . . . . . . . . . . . . . 55 A.5Prede¯ned variables and math constants
. . . . . . . . . . . . . . . . . 55 v A.6Elementary matrices and arrays
. . . . . . . . . . . . . . . . . . . . . . 56 A.7Arrays and Matrices: Basic information
. . . . . . . . . . . . . . . . . 56 A.8Arrays and Matrices: operations and manipulation
. . . . . . . . . . 56 A.9 Arrays and Matrices: matrix analysis and linear equations . . . . . 57 viList of Figures
1.1 The graphical interface to the MATLAB workspace . . . . . . . . . . . . . . 3
2.1 Plot for the vectors x and y . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Plot of the Sine function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Typical example of multiple plots . . . . . . . . . . . . . . . . . . . . . . . . 17
viiPreface
\Introduction to MATLAB for Engineering Students" is a document for an introductory course in MATLAB R°1and technical computing. It is used for freshmen classes at North- western University. This document is not a comprehensive introduction or a reference man- ual. Instead, it focuses on the speci¯c features of MATLAB that are useful for engineering classes. The lab sessions are used with one main goal: to allow students to become familiar with computer software (e.g., MATLAB) to solve application problems. We assume that the students have no prior experience with MATLAB. The availability of technical computing environment such as MATLAB is now reshaping the role and applications of computer laboratory projects to involve students in more intense problem-solving experience. This availability also provides an opportunity to easily conduct numerical experiments and to tackle realistic and more complicated problems. Originally, the manual is divided into computer laboratory sessions (labs). The lab document is designed to be used by the students while working at the computer. The emphasis here is \learning by doing". This quiz-like session is supposed to be fully completed in 50 minutes in class. The seven lab sessions include not only the basic concepts of MATLAB, but also an in- troduction to scienti¯c computing, in which they will be useful for the upcoming engineering courses. In addition, engineering students will see MATLAB in their other courses. The end of this document contains two useful sections: a Glossary which contains the brief summary of the commands and built-in functions as well as a collection of release notes. The release notes, which include several new features of the Release 14 with Service Pack2, well known as R14SP2, can also be found in Appendix. All of the MATLAB commands
have been tested to take advantage with new features of the current version of MATLAB available here at Northwestern (R14SP2). Although, most of the examples and exercises still work with previous releases as well. This manual re°ects the ongoing e®ort of the McCormick School of Engineering and Applied Science leading by Dean Stephen Carr to institute a signi¯cant technical computing in the Engineering FirstR°2courses taught at Northwestern University.
Finally, the students - Engineering Analysis (EA) Section - deserve my special grati- tude. They were very active participants in class.David Houcque
Evanston, Illinois
August 2005
1 MATLABR°is a registered trademark of MathWorks, Inc.2Engineering FirstR°is a registered trademark of McCormick
School of Engineering and Applied Science (Northwestern University) viiiAcknowledgements
I would like to thank Dean Stephen Carr for his constant support. I am grateful to a number of people who o®ered helpful advice and comments. I want to thank the EA1 instructors (Fall Quarter 2004), in particular Randy Freeman, Jorge Nocedal, and Allen Ta°ove for their helpful reviews on some speci¯c parts of the document. I also want to thank Malcomb MacIver, EA3 Honors instructor (Spring 2005) for helping me to better understand the animationof system dynamics using MATLAB. I am particularly indebted to the many students (340 or so) who have used these materials, and have communicated their comments and suggestions. Finally, I want to thank IT personnel for helping setting up the classes and other computer related work: Rebecca Swierz, Jesse Becker, Rick Mazec, Alan Wol®, KenKalan, Mike Vilches, and Daniel Lee.
About the author
David Houcque has more than 25 years' experience in the modeling and simulation of struc- tures and solid continua including 14 years in industry. In industry, he has been working as R&D engineer in the ¯elds of nuclear engineering, oil rig platform o®shore design, oil reser- voir engineering, and steel industry. All of these include working in di®erent international environments: Germany, France, Norway, and United Arab Emirates. Among other things, he has a combined background experience: scienti¯c computing and engineering expertise. He earned his academic degrees from Europe and the United States. Here at Northwestern University, he is working under the supervision of Professor Brian Moran, a world-renowned expert in fracture mechanics, to investigate the integrity assess- ment of the aging highway bridges under severe operating conditions and corrosion. ixChapter 1
Tutorial lessons 1
1.1Introduction
The tutorials are independent of the rest of the document. The primarily objective is to help you learnquicklythe ¯rst steps. The emphasis here is \learning by doing". Therefore, the best way to learn is by trying it yourself. Working through the examples will give you a feel for the way that MATLAB operates. In this introduction we will describe how MATLAB handles simple numerical expressions and mathematical formulas. The name MATLAB stands for MATrix LABoratory. MATLAB was written originally to provide easy access to matrix software developed by the LINPACK (linear system package) and EISPACK (Eigen system package) projects. MATLAB [1] is a high-performance language for technical computing. It integrates computation,visualization, andprogrammingenvironment. Furthermore, MATLAB is a modern programming language environment: it has sophisticateddata structures, contains built-in editing anddebugging tools, and supportsobject-oriented programming. These factors make MATLAB an excellent tool for teaching and research. MATLAB has many advantages compared to conventional computer languages (e.g., C, FORTRAN) for solving technical problems. MATLAB is an interactive system whose basic data element is anarraythat does not require dimensioning. The software package has been commercially available since 1984 and is now considered as a standard tool at most universities and industries worldwide. It has powerfulbuilt-inroutines that enable a very wide variety of computations. It also has easy to use graphics commands that make the visualization of results immediately available. Speci¯c applications are collected in packages referred to astoolbox. There are toolboxes for signal processing, symbolic computation, control theory, simulation, optimiza- tion, and several other ¯elds of applied science and engineering. In addition to the MATLAB documentation which is mostly available on-line, we would 1 recommend the following books: [2], [3], [4], [5], [6], [7], [8], and [9]. They are excellent in their speci¯c applications. 1.2Basic features
As we mentioned earlier, the followingtutoriallessons are designed to get you started quickly in MATLAB. The lessons are intended to make you familiar with the basics of MATLAB. We urge you to complete theexercisesgiven at the end of each lesson. 1.3A minimum MATLAB session
The goal of thisminimumsession (also calledstartingandexitingsessions) is to learn the¯rst steps:
How to log on
Invoke MATLAB
Do a few simple calculations
How to quit MATLAB
1.3.1 Starting MATLAB
After logging into your account, you can enter MATLAB by double-clicking on the MATLAB shortcuticon(MATLAB 7.0.4) on your Windows desktop. When you start MATLAB, a special window called the MATLAB desktop appears. The desktop is a window that contains otherwindows. The major tools within or accessible from the desktop are:TheCommand Window
TheCommand History
TheWorkspace
TheCurrent Directory
TheHelp Browser
TheStartbutton
2 Figure 1.1: The graphical interface to the MATLAB workspace 3 When MATLAB is started for the ¯rst time, the screen looks like the one that shown in the Figure 1.1. This illustration also shows the default con¯guration of the MATLAB desktop. You can customize the arrangement of tools and documents to suit your needs. Now, we are interested in doing some simple calculations. We will assume that you have su±cient understanding of your computer under which MATLAB is being run. You are now faced with the MATLAB desktop on your computer, which contains the prompt (>>) in the Command Window. Usually, there are 2 types of prompt: >> for full versionEDU> for educational version
Note: To simplify the notation, we will use this prompt,>>, as a standard prompt sign, though our MATLAB version is for educational purpose.1.3.2 Using MATLAB as a calculator
As an example of a simple interactive calculation, just type the expression you want to evaluate. Let's start at the very beginning. For example, let's suppose you want to calculate the expression, 1 + 2£3. You type it at the prompt command (>>) as follows, >> 1+2*3 ans = 7 You will have noticed that if you do not specify an output variable, MATLAB uses a default variableans, short foranswer, to store the results of the current calculation. Note that the variableansis created (or overwritten, if it is already existed). To avoid this, you may assign a value to a variable or output argument name. For example, >> x = 1+2*3 x = 7 will result inxbeing given the value 1 + 2£3 = 7. This variable name can always be used to refer to the results of the previous computations. Therefore, computing 4xwill result in >> 4*x ans =28.0000
Before we conclude this minimum session, Table 1.1 gives the partial list of arithmetic operators. 4Table 1.1: Basic arithmetic operators
Symbol Operation Example
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