MuPAD Tutorial

1.Introduction.- 1.1 Numerical Computation.- 1.2 Computer Algebra.- 1.3 Characteristics of Computer Algebra Systems.- 1.4 Existing Systems.- 1.5 MuPAD.- 2 First Steps in MuPAD.- 2.1 Explanations and Help.- 2.2 Computing with Numbers.- 2.3 Symbolic Computation.- 3 The MuPAD Libraries.- 3.1 Information About a Particular Library.- 3.2 Exporting Libraries.- 3.3 The Standard Library.- 4 MuPAD Objects.- 4.1 Operands: the Functions op and nops.- 4.2 Numbers.- 4.3 Identifiers.- 4.4 Symbolic Expressions.- 4.5 Sequences.- 4.6 Lists.- 4.7 Sets.- 4.8 Tables.- 4.9 Arrays.- 4.10 Boolean Expressions.- 4.11 Strings.- 4.12 Functions.- 4.13 Series Expansions.- 4.14 Algebraic Structures: Fields, Rings, etc.- 4.15 Vectors and Matrices.- 4.16 Polynomials.- 4.17 Null Objects: null(), NIL, FAIL, and undefined.- 5 Evaluation and Simplification.- 5.1 Identifiers and Their Values.- 5.2 Complete, Incomplete, and Enforced Evaluation.- 5.3 Automatic Simplification.- 6 Substitution: subs, subsex, and subsop.- 7 Differentiation and Integration.- 7.1 Differentiation.- 7.2 Integration.- 8 Solving Equations: solve.- 8.1 Polynomial Equations.- 8.2 General Equations.- 8.3 Differential and Recurrence Equations.- 8.4 solve in MuPAD Versions Beyond 1.4.- 9 Manipulating Expressions.- 9.1 Transforming Expressions.- 9.2 Simplifying Expressions.- 9.3 Assumptions About Symbolic Identifiers.- 10 Chance and Probability.- 11 Graphics.- 11.1 Graphs of Functions.- 11.2 Graphical Scenes.- 11.3 Curves.- 11.4 Surfaces.- 11.5 Further Possibilities.- 11.6 Printing and Saving Graphics.- 12 The History Mechanism.- 13 Input and Output.- 13.1 Output of Expressions.- 13.2 Reading and Writing Files.- 14 Utilities.- 14.1 User-Defined Preferences.- 14.2 Information on MuPAD Algorithms.- 14.3 Restarting a MuPAD Session.- 14.4 Executing Commands of the Operating System.- 15 Type Specifiers.- 15.1 The Functions type and testtype.- 15.2 Comfortable Type Checking: the Type Library.- 16 Loops.- 17 Branching: if-then-else and case.- 18 MuPAD Procedures.- 18.1 Defining Procedures.- 18.2 The Return Value of a Procedure.- 18.3 Returning Symbolic Function Calls.- 18.4 Local and Global Variables.- 18.5 Subprocedures.- 18.6 Type Declaration.- 18.7 Procedures with a Variable Number of Arguments.- 18.8 Options: the Remember Table.- 18.9 Input Parameters.- 18.10 Evaluation Within Procedures.- 18.11 Function Environments.- 18.12 A Programming Example: Differentiation.- 18.13 Programming Exercises.- Solutions to Exercises.- Documentation and References.