Selected Examples From the Book (1st Edition)

In my book there are many examples. Some of them are spread out on many pages with  comments between lines of code. Typing these examples can be not only time consuming but also a bit difficult.  For example, if you miss parts of the code then the whole example may not work. In order to save time of my readers and avoid confusion I enclosed here the code of some of the most interesting or elaborated examples. There are still a few examples that were not enclosed here. These are very short and simple examples or those with heavy comments.  

At the time of publishing this web site all code works properly. However, I wish to remind you that different versions of MuPAD may produce slightly different output or in rare cases due to changes in the syntax the enclosed code may not work. For testing of these examples I used MuPAD version 2.5.    

How to use MuPAD Examples

Using these examples is very simple. Select the example code the same way like you select text on a web page, copy it and paste into MuPAD notebook. Then execute the code in MuPAD. If something does not work or you are getting strange messages, then check if you copied properly the whole code. For example, omitting colon or semicolon ending MuPAD command may give you a lot of trouble.  Any way, if still an example does not work, you can always write to me.  

In most of these examples you may try to experiment  and produce results for different initial data. For example, you can change parameters of the equation and produce solutions for it, or you can change equation of a function of two variables and get a plot of a new surface. Try this. Certainly you will find many interesting things.  Happy hunting for a new ideas in undergraduate mathematics!

Chapter 5. Programming in MuPAD - Procedures and Libraries

• Example 5.0 - Quadratic Equation
• Example 5.1 - Heron Formula
• Example 5.2 - The Euclid algorithm to find GCD of two integers
• Example 5.3 - To produce a sequence
• Example 5.4  - To produce list or set of numbers
• Example 5.5 - To produce a matrix of any dimension
• Example 5.6 - To produce a recursive procedure
• Example 5.7 - User defined library of MuPAD procedures

Chapter 6. Introduction to MuPAD Graphics

• Example 6.1 - First MuPAD plot
• Example 6.2 - Graphical solutions of equations
• Example 6.3 - Plotting surfaces
• Example 6. 4 - Developing MuPAD scenes
• Example 6.6 - Using functions to define colors for 3D plots
• Example 6.7 - Showing how grid values influence plot quality
• Example 6.8 - Various plot styles for function of one variable

Chapter 7. Exploring Mathematical Curves and Surfaces

• Example 7.2 - Plotting parametric curves
• Example 7.3 - Plotting curves given in polar coordinates
• Example 7.4 - Plotting curves given by implicit equations 
• Example 7.5 - Family of curves and their asymptote
• Example 7.6 - Plotting  surfaces of functions of two variables
• Example 7.8 - Plotting surfaces given by user defined complex functions
• Example 7.9 - Plotting surfaces given by parametric equations
• Example 7.10 - Another example of surface given by parametric equations
• Example 7.11 - Plotting in spherical coordinates
• Example 7.12 - Plot in cylindrical coordinates
• Example 7.14 - Plot of a curve in 3D

Chapter 8. A Few Applications of MuPAD Graphics

• Example 8.1 - Plotting contours
• Example 8.2 - Density plots
• Example 8.3 - Vector fields
• Example 8.4 - Plotting inequalities
• Example 8.5 - Plotting sequences
• Example 8.9 - Plotting points and lines
• Example 8.10 - Plotting solids
• Example 8.10a - Demonstration of turtle graphics
• Example 8.11 - Plotting L-systems

Chapter 9. Exploring Numbers with MuPAD

• Example 9.1 - Checking factorials
• Example 9.2 - Arithmetic modulo m
• Example 9.3 - Continued Fractions
• Example 9.4 - To calculate sqrt(2)
• Example 9.5 - Roots of complex numbers

Chapter 10. Elementary Algebra and Trigonometry in MuPAD

• Example 10.1 - To Produce Polynomials
• Example 10.2 - Two simple procedures to convert between radians and degrees
• Example 10.3 - Multiple Roots

Chapter 11. Working with Sets and Sentences MuPAD

• Example 11.2 - Polish Notation in Logic
• Example 11.3 - Checking Subsets
• Example 11.4 - Cartesian Product

Chapter 12. Exploring Calculus with MuPAD

• Example 12.1 - Plotting Sequences
• Example 12.2 - Local minimum and maximum values 
• Example 12.3 - Plotting Asymptotes of Functions 
• Example 12.3a - Visualization of an Integral using the Riemann Method
• Example 12.5 - Taylor Polynomials 
• Example 12.7 - Finding Extremes of Function of two Variables 

Chapter 13. Linear Equations, Matrices and Determinants

• Example 13.3 Cramer's Rule