1. Chapter 1: Brief Overview of MATLAB 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. 2

3. 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 3 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

4. 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 4

5. 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 >> 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*b c = 32 77 80 54 62 105 64 41 100 >> d=a/b d = 2.3934 2.0164 -2.1639 0.1475 0.1311 0.6885 5.0820 1.2951 -2.9508 >> c=a*b c = 32 77 80 54 62 105 64 41 100 >> d=a/b d = 2.3934 2.0164 -2.1639 0.1475 0.1311 0.6885 5.0820 1.2951 -2.9508 Matrix Arithmetic, Eigen Analysis,... 5

6. Graphics & Visualization 6

7. Graphical User Interface Try them for yourself! 7 xpbombs fifteen fdatool

8. Toolboxes 8

9. SIMULINK Model-based design environment 9 Ref: Help – Video and Image Processing Blockset – Demos – Motion Detection

10. 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 10 Ref: Help – MATLAB – Getting Started – Introduction – Product Overview

11. The MATLAB System The 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 11 Ref: Help – MATLAB – Getting Started – Introduction – Product Overview

12. What is Symbolic Computing Position of an oscillating mass: Velocity? 12 General Solution View underlying mathematics Ref: Webinar – Symbolic Computing Tools for Academia

13. Symbolic Math Usage in Academia 13 Ref: Webinar – Symbolic Computing Tools for Academia

14. Working w/t Symbolic Math Toolbox From MATLAB Perform symbolic computations using familiar MATLAB syntax 14 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

15. Dynamic Equation Initial Conditions Symbolic Math Solution Demo: Mass-Spring-Damp System 15 mass_spring_damp_system.mn Ref: Webinar – Symbolic Computing Tools for Academia

16. 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 16 Linear Algebra Operations Eigenvalues Special Functions Bernoulli, Bessel, Beta, … Fresnel sine/cosine integral, Gamma Variable Precision Arithmetic Plotting 2-D 3-D contour, surface, mesh Animations Ref: Webinar – Symbolic Computing Tools for Academia