1. Chapter 2: First Steps in MuPAD MATLAB for Scientist and Engineers Using Symbolic Toolbox

2. You are going to See the difference between numerical computing and symbolic computing Say hello to MuPAD notebook Enjoy the kind help system of MuPAD Taste the sweet power of symbolic computing Create basic 2-D, 3-D graphs and animations Be glad to know that MuPAD is there for you 2

3. Numerical Computations Problem solving by number calculations Approximate solutions as fast as possible Numbers are stored by floating-point representation. The only way when no closed form solution 3

4. Computer Algebra Problem solving by symbolic computations Exact solution as fast as possible Numbers are stored by integer fractions. Requires more computing power and storage Can help numerical computation by simplifying the expressions. 4

5. MuPAD Software Originally developed by the MuPAD research group at the University of Paderborn, Germany. University of Paderborn A computer algebra system to manipulate formulas symbolicallycomputer algebra system Program packages for linear algebra, differential equations, number theory, statistics, functional programminglinear algebradifferential equations number theorystatisticsfunctional programming An interactive graphic system that supports animations and transparent areas in 3D Classic and verified numerical analysis in discretionary accuracynumerical analysis A programming language that supports object orientation and functional programmingprogramming languageobject orientation 5 Ref: http://en.wikipedia.org/wiki/MuPAD

6. Other Options Mathematica, www.wolfram.comwww.wolfram.com Maple, www.maplesoft.comwww.maplesoft.com IDL, www.ittvis.com/ProductServices/IDL.aspx www.ittvis.com/ProductServices/IDL.aspx, www.gnu.org/software/octave/www.gnu.org/software/octave/ M, www.ptc.com/products/mathcad/www.ptc.com/products/mathcad/ Ref: http://amath.colorado.edu/computing/mmm/ http://amath.colorado.edu/computing/mmm/ 6

7. Starting MuPAD Two ways of starting MuPAD 1. Type mupad in the command window. 2. Start button 7

8. MuPAD Notebook >> mupad 8 Format Toolbar Standard Toolbar Output Region Command Bar Menu Bar Input Region Ctr-I Text Region Ctr-T

9. Working with Input Regions 9 Enter Shift + Enter Evaluate and show the results. Evaluate and show the results. Evaluate but do not show the results. Evaluate but do not show the results. The expressions continues to the next line The expressions continues to the next line

10. Evaluation after Modification Once you change the value of variable, you can re-evaluate the other dependent expressions. 10

11. Accessing Help Completing Commands: Tool Tips: mouse over the command 11 Space Ctrl + Complete Help: right mouse click

12. Computing Numbers 12 real number! Assignment! Convert to a real number! Convert to a real number! Change precision. Change precision. delete DIGITS PI E E

13. Complex Numbers 13 imaginary real magnitude in radian

14. Differentiation 14 D(f) f'

15. Integration 15 No closed form solution ! No closed form solution ! Numeric integration

16. Solving Equations solve 16 Solve Algebraic Equations Solve Ordinary Differential Equations Solve Inequalities

17. Graphics 2-D Function Plotting 2-D Animation 3-D Function Plotting 3-D Animation 17

18. Manipulating Expressions Simplifying the expressions Factoring, Expanding, Collecting, and etc. 18

19. Basic Plotting Options With plot command, you can Create 2-D and 3-D function plots Specify plotting range Create plots for piecewise functions Create multiple function plots in one graph Create animated 2-D and 3-D function plots 19

20. Creating 2-D Plots 20 Set range. Parameter assignment. Parameter assignment. Sequence of plots. Sequence of plots.

21. Creating 2-D Plots (cont.) 21 Multiple Plots Piecewise Functions

22. Creating 3-D Plots 22 Three Dim. Sequence of 3D Plots Sequence of 3D Plots Animation Control

23. Animated 2-D Plots 23 Additional parameter is regarded as the animation parameter. Additional parameter is regarded as the animation parameter. 2-D point 2-D curve Animation parameter Animation parameter

24. Animated 3-D Plots 24

25. Key Takeaways Now, you are able to tell the differences between numerical computing and symbolic computing, expand your knowledge on MuPAD by yourself using MuPAD help system, apply differentiation, indefinite integrals, definite integrals on math expressions and functions, solve an equation or a set of equations, manipulate math expressions at your will, and to create basic 2-D and 3-D graphs and animations 25

26. MuPAD Commands Review 26 mupad := : : float PI E E abs rectform Re Im arg conjugate diff int infinity assuming solve factor expand simplify collect partfrac ode Simplify Shift Enter + Ctr Space + Ctr T T + I I +

27. Notes 27

28. Notes 28