MuPAD Pro Computing Essentials

by Miroslaw Majewski

Overview

This book explains basic principles of MuPAD commands. It teaches how to write simple programs and develop interactive environments for teaching mathematics. The text gives a large number of useful examples from different areas of undergraduate mathematics developed by the author during his long teaching experience. All the book examples are available online. Flash, SVG and JVX formats are used to display interactive and animated graphics.

Product Details

ISBN-13:	9783540219439
Publisher:	Springer Berlin Heidelberg
Publication date:	05/21/2004
Edition description:	Second Edition 2004
Pages:	538
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

1.1 For whom this book was written.- 1.2 The goal.- 1.3 Why we should care about MuPAD.- 1.4 What is inside.- 1.5 Style conventions.- 1.6 Writing “between”.- A Quick Introduction to MuPAD.- 2.1 The Very First Look.- 2.2 Getting Started.- 2.3 A Quick Look at MuPAD’s Interface.- 2.4 Formatting Documents in MuPAD.- 2.5 Getting Help.- 2.6 Chapter Summary.- 2.7 Review Exercises.- Programming in MuPAD — Declarations.- 3.1 Writing Formulae in MuPAD.- 3.2 Declaring Variables and Constants.- 3.3 Declaring Functions and Operations.- 3.4 Writing More than One Line of Code.- 3.5 The Basics of the Domain Concept.- 3.6 Chapter Summary.- 3.7 Review Exercises.- Programming in MuPAD — Control Structures.- 4.1 Decisions.- 4.1.1 MuPAD Syntax: the “if” Statement.- 4.1.2 Indentation in MuPAD.- 4.1.3 Quadratic Equation Example.- 4.1.4 Formatting Output and Input.- 4.1.5 “elif” a Useful Shortcut.- 4.2 Programming Itcrations in MuPAD.- 4.2.1 The “for” Loop.- 4.2.2 MuPAD Syntax: the “for” Loop.- 4.2.3 The “while” and “repeat” Loops.- 4.2.4 MuPAD Syntax: the “while” and “repeat” Loops.- 4.3 What is Wrong with my Loops and Conditions.- 4.4 Selections.- 4.4.1 MuPAD Syntax: the “case” Structure.- 4.5 Chapter Summary.- 4.6 Programming Exercises.- Programming in MuPAD — Procedures.- 5.1 What is a Procedure.- 5.2 Examples of Procedures.- 5.3 Getting Output from Procedures.- 5.4 Returning Unevaluated or Symbolic Expressions.- 5.5 Shall We use Global or Local Variables?.- 5.6 Introduction to Types and Domains.- 5.7 Using MuPAD Types and Domains.- 5.8 Using Procedures to Produce Data Structures.- 5.8.1 Sequences.- 5.8.2 Lists.- 5.8.3 Sets.- 5.8.4 Strings.- 5.8.5 Vectors and Matrices.- 5.9 Procedures with a Variable Number of Input Parameters.- 5.10 Recursive Procedures.- 5.11 Using Libraries.- 5.12 User Defined Libraries of Procedures.- 5.13 Final Comments on MuPAD Coding Guidelines.- 5.13.1 Magic Numbers.- 5.13.2 Comments.- 5.13.3 Braces.- 5.14 Chapter Summary.- 5.15 Programming Exercises.- to MuPAD Graphics.- 6.1 Obtaining Quick Plots.- 6.1.1 Procedure plotfunc2d.- 6.1.2 Your First Animation with MuPAD.- 6.1.3 Procedure plotfunc3d.- 6.2 General Concept of MuPAD Plots.- 6.2.1 Object Attributes’ Options.- 6.3 Canvas, Scene and Coordinate System Options.- 6.3.1 Options for Canvas.- 6.3.2 Options for Scene2d.- 6.3.3 Options for Sccnc3d.- 6.3.4 The Coordinate System in 2D and 3D.- 6.4 Options Related to Primitives.- 6.4.1 Basic Options for Primitives.- 6.4.2 Working with Color.- 6.4.3 Mesh and Other Options.- 6.5 Operations on Graphical Objects.- 6.5.1 Operation modify.- 6.6 Chapter Summary.- 6.7 Programming Exercises.- Interactive Graphics’ Animation with VCam.- 7.1 Learning the Virtual Camera Environment.- 7.2 Using VCam to Improve 2D Graphs.- 7.3 Using VCam to Improve 3D Graphs.- 7.4 Interactive Development of Animations.- 7.5 Saving MuPAD Graphs.- 7.6 Chapter Summary.- 7.7 Exercises.- Exploring Mathematical Curves and Surfaces.- 8.1 Plots in 2D Space’ Plot Types.- 8.1.1 Class Function2d.- 8.1.2 Class Curve2d.- 8.1.3 Developing Polar Plots.- 8.1.4 Developing Implicit Plots.- 8.2 Plots in 3D Space.- 8.2.1 Class Function3d.- 8.2.2 Class Surface.- 8.2.3 Class Spherical.- 8.2.4 Class Cylindrical.- 8.2.5 Class Implicit3d.- 8.2.6 Classes Curve3d and Tube.- 8.3 Chapter Summary.- 8.4 Programming Exercises.- A Few Applications of MuPAD Graphics.- 9.1 Calculus Graphics.- 9.1.1 Plotting Contours.- 9.1.2 Developing Density Plots.- 9.1.3 Vector Fields.- 9.1.4 Plotting Areas.- 9.1.5 Surfaces of Revolution.- 9.2 Presentation Graphics.- 9.3 Working with Geometry Objects.- 9.4 Transformations of Graphical Objects.- 9.5 Turtle Graphics & L-systems.- 9.5.1 Turtle Graphics in MuPAD.- 9.5.2 Plotting L-systems.- 9.6 Chapter Summary.- 9.7 Programming Exercises.- Exploring Numbers with MuPAD.- 10.1 Integers in MuPAD.- 10.2 Rational Numbers in MuPAD.- 10.3 Real Numbers in MuPAD.- 10.4 Complex Numbers in MuPAD.- 10.5 Chapter Summary.- 10.6 Programming Exercises.- Elementary Algebra and Trigonometry in MuPAD.- 11.1 Polynomials.- 11.2 Rational Expressions.- 11.3 Algebraic Expressions.- 11.4 Trigonometric and Other Functions.- 11.5 Solving Equations and Inequalities.- 11.6 Chapter Summary.- 11.7 Programming Exercises.- Working with Sets and Sentences MuPAD.- 12.1 Logic in MuPAD.- 12.1.1 Polish Notation.- 12.2 Working with Sets.- 12.3 Chapter Summary.- 12.4 Programming Exercises.- Exploring Calculus with MuPAD.- 13.1 Limits.- 13.2 Derivatives.- 13.3 Working with Integrals.- 13.4 Infinite Series and Products.- 13.5 Calculus of Two Variables.- 13.5.1 Limits of Functions of Two Variables.- 13.5.2 Partial Derivatives.- 13.6 Chapter Summary.- 13.7 Programming Exercises.- A Short Introduction to Linear Algebra.- 14.1 Checking Resources.- 14.2 Solving Linear Equations.- 14.3 Matrices and Operations on Matrices.- 14.3.1 Declaring Matrices in MuPAD.- 14.3.2 Global Operations on Matrices.- 14.3.3 Local Matrix Operations.- 14.4 Determinants.- 14.5 Chapter Summary.- 14.6 Programming Exercises.- Appendix 1: MuPAD Libraries and Procedures.- MuPAD Libraries (ver. 3.0, 21/02/2004).- Operators Represented by Symbols.- MuPAD Standard Collection.- Procedures in Standard Collection.- Functions in Standard Collection.- Library ‘adt’ — — Abstract Data Types.- Library ‘Ax’ — — Basic Axiom Constructors.- Library ‘Cat’ — — Category Constructors.- Library ‘combinat’ — — Combinatorial Functions.- Library ‘detools’ — — Methods for Differential Equations.- Library ‘Dom’ — — Domain Constructors.- Library ‘fp’ — — Utilities for Functional Programming.- Library ‘generate’ — — Generate Foreign Formats.- Library ‘Graph’ — — Utilities for Directed and Undirected Graphs.- Library ‘groebner’ — — Utilities for Groebner Bases.- Library ‘import’ — — Utilities for Reading Data.- Library ‘intlib’ — — Definite and Indefinite Integration.- Library ‘linalg’ — — the Linear Algebra Package.- Library ‘linopt’ — — Tools for Linear Optimization.- Library ‘listlib’ — Operations on Lists.- Library ‘matchlib’ — Pattern Matching Tools.- Library ‘module’ — Module Management Tools.- Library ‘numeric’ — Tools for Numerical Methods.- Library ‘numlib’ — Elementary Number Theory.- Library ‘orthpoly’ — Orthogonal Polynomials.- Library ‘output’ — Tools for the Output of Data.- Library ‘plot’ — 2D and 3D Graphical Objects.- Library ‘polylib’ — Tools for Polynomials.- Library ‘prog’ — Programming Utilities.- Library ‘property’ — Properties of Identifiers.- Library ‘RGB’ — Color Names and Color Functions.- Library’ series’ — Tools for Series Expansions.- Library’ solvclib’ — Tools for Solving Equations.- Library’ stats’ — Statistical Functions.- Library’ stringlib’ — Tools for String Manipulation.- Library’ student’ — the Student Package.- Library ‘transform’ — Integral Transformations.- Library ‘Type’ — Predefined Types.- MuPAD Environmental Variables.- Appendix 2: MuPAD Resources.