Chapter 1:Brief Overview of MAT-

LAB

MATLAB for Scientist and Engineers

Using Symbolic Toolbox

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You are going to Expose yourself to the history of MATLAB, See what MATLAB provides, Look at a symbolic math example.

Old History of MATLAB 1967: "Computer solution of linear algebraic equations", Forsythe and Moler

1976: "Matrix Eigensystem Routines, EISPACK Guide" in FORTRAN 1976~9: "LINPACK" in FORTRAN 1977~: "MATLAB Environment", Cleve Moler

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J.H.Wilkinson, UK(1919~1986)

Cleve Moler(1939~)

Jack Little

1971: "Handbook for automatic computations" in ALGOL,

J. H. Wilkinson et. al.

1979: "Numerical analysis" lecture at Stanford, met with Jack Little, then an engineering student 1984: MathWorks founded by Jack and Moler

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Further Digging Resources Video: The Origins of MATLAB at MathWorks.com

http://www.mathworks.com/company/aboutus/founders/clevemoler.html

Meet Mr Matlab at Scientific Computing World http://www.scientific-computing.com/features/feature.php?feature_id=15

Cleve Moler at Wikipedia http://en.wikipedia.org/wiki/Cleve_Moler

BLAS at Netlib.org http://www.netlib.org/blas/

Maple at Wikipedia and Maplesoft.com http://en.wikipedia.org/wiki/Maple_(software) http://www.maplesoft.com/index1.aspx

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MATLAB? Matrix Laboratory

>> b=floor(10*rand(3))b = 1 5 3 6 1 8 3 6 8>> a=magic(3)a = 8 1 6 3 5 7 4 9 2

>> c=a*bc = 32 77 80 54 62 105 64 41 100>> d=a/bd = 2.3934 2.0164 -2.1639 0.1475 0.1311 0.6885 5.0820 1.2951 -2.9508

Matrix Arithmetic, Eigen Analysis, ...

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Graphics & Visualization

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Graphical User Interface

Try them for yourself! xp-bombs

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fdatool

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Toolboxes

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SIMULINK Model-based design environment

Ref: Help – Video and Image Processing Blockset – Demos – Motion Detection

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They Use MATLAB for … Math and computation Algorithm development Data acquisition Modeling, simulation, and prototyping Data analysis, exploration, and visualization Scientific and engineering graphics Application development, including graphical

user interface building

Ref: Help – MATLAB – Getting Started – Introduction – Product Overview

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The MATLAB SystemThe MATLAB system consists of these main parts: Desktop Tools and Development Environment Mathematical Function Library The Language Graphics External Interfaces; API+ Toolboxes: MATLAB function packages Simulink: Model-based design Blocksets: Simulink model packages

Ref: Help – MATLAB – Getting Started – Introduction – Product Overview

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What is Symbolic Computing Position of an oscillating mass:

Velocity? 2Position cos(6 ) sin(6 )te t t

General Solution

View underlying mathematics

Ref: Webinar – Symbolic Computing Tools for Academia

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Symbolic Math Usage in Academia

Ref: Webinar – Symbolic Computing Tools for Academia

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Working w/t Symbolic Math ToolboxFrom MATLAB

Perform symbolic computations using familiar MATLAB syntax

From Notebook Interface

Conveniently manage & document symbolic computations

Math notation, embedded text, graphics Access complete MuPAD language

15+libraries of symbolic math functions

Sharing

Ref: Webinar – Symbolic Computing Tools for Academia

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Dynamic Equation

Initial Conditions

Symbolic Math Solution

Demo: Mass-Spring-Damp System

( ) ( ) ( ) 0mx t Rx t kx t

(0) 0, (0) 1x x

mass_spring_damp_system.mnRef: Webinar – Symbolic Computing Tools for Academia

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Symbolic Math Toolbox Libraries Calculus

Differentiation Integrals Jacobian Taylor series Limits

Solving Equations Algebraic Equations Differential Equations

Transforms Fourier transform Laplace transform Z-transform

Simplification Polynomial Expansion Substitution

Linear Algebra Operations Eigenvalues

Special Functions Bernoulli, Bessel, Beta, … Fresnel sine/cosine inte-

gral, Gamma

Variable Precision Arith-metic

Plotting 2-D 3-D contour, surface, mesh Animations

Ref: Webinar – Symbolic Computing Tools for Academia