MATLABfor Scientist and Engineers

using Symbolic Toolbox

Byoung-Jo CHOI, PhDUniversity of Incheon

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References Symbolic Math Toolbox™ 5 MuPAD® Tutorial, MathWorks Symbolic Math Toolbox™ 5 User's Guide Mastering MATLAB 7, Duane Hanselman and Bruce Littlefield,

Pearson/Prentice Hall, 2005 Numerical Computing with MATLAB, Cleve Moler, MathWorks 임종수의 MATLAB7, 높이깊이 , 2009 MATLAB: An Introduction with Applications, Amos Gilat, John Wiley

& Sons, Inc., 2004 Graphics and GUIs with MATLAB, 3rd Ed, Patrick Marchand and O.

Thomas Holland, Chapman & Hall/CRC, 2003

Course Introductions

MATLAB for Scientist and Engineers

Using Symbolic Toolbox

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

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Course Overview Symbolic Computing using MuPAD

7 Weeks + MidTerm Exam Text: MuPAD Tutorial available in PDF

http://www.mathworks.com/access/helpdesk/help/pdf_doc/symbolic/mupad_tutorial.pdf

Ref: Symbol Math Toolbox 5 – User's Guidehttp://www.mathworks.com/access/helpdesk/help/pdf_doc/symbolic/symbolic_tb.pdf

Numeric Computing using MATLAB 7 Weeks + Final Exam Text: MATLAB, an Introduction with Applications,

3rd Ed, Amos Gilat, John Wiley, 2008 Ref: 임종수의 MATLAB7, 2009, 임종수 ,

높이깊이

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Overview: Symbolic Computation First Taste of MuPAD (Ch1~4) MuPAD Language (Ch 5~9) Graphics (Ch 10) Applications (Ch 11~13)

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Overview: Numeric Computation Basic Computing in MATLAB M-File Script and Excel File Read/Write Handling Arrays and Matrices Plotting Graphs M-File Function Programming 3D Graphics Data Analysis / Interpolation / Optimization GUI Development

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Lecture Layout Lecture: 1hr

Study the lecture material in advance using lec-ture notes and video recording. On-line quiz

Report Review: 10 min Preview Quiz: 20 min Review: Revisit the core topics covered in the

video recording – 10 min Q&A Session: 10 min

LAB1: 1hr – demo / on-line submission LAB2: 1hr – demo / on-line submission

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How to Get Good Grades Fall in love with MATLAB. Be adventurous! Try different possibilities! Don't miss on-line quiz / preview quiz / LABs. Use MATLAB for other courses. Ask during the classes. Ask your friends to help you. Come and visit me as often as you can. Do not just copy others' work. Do not miss midterm exam and final exam.

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Contact Lecturer

Byoung-Jo CHOI bjc97r@incheon.ac.kr 032-835-8765 / 010-6737-1536 IT BD Room 7-327

Assistant Seok-Beom KIM (MSc Student) mms1274@gmail.com 032-835-4680 / 010-9100-5365 IT BD Room 7-330

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Notes