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Chapter 1: Brief Overview of MATLAB. MATLAB for Scientist and Engineers Using Symbolic Toolbox. 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 - PowerPoint PPT Presentation
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Chapter 1:Brief Overview of MAT-
LAB
MATLAB for Scientist and Engineers
Using Symbolic Toolbox
2
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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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