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Author Creutzig, Christopher. author MuPAD Tutorial [electronic resource] / by Christopher Creutzig, Walter Oevel Berlin, Heidelberg : Springer Berlin Heidelberg, 2004 Second Edition http://dx.doi.org/10.1007/978-3-642-59304-8 XIII, 415 p. 39 illus. online resource

SUMMARY

This book explains the basic use of the software package called MuPAD and gives an insight into the power of the system. MuPAD is a so-called comยญ puter algebra system, which is developed mainly by Sciface Software and the MuPAD Research Group of the University of Paderborn in Germany. This introduction addresses mathematicians, engineers, computer scientists, natural scientists and, more generally, all those in need of mathematical comยญ putations for their education or their profession. Generally speaking, this book addresses anybody who wants to use the power of a modern computer algebra package. There are two ways to use a computer algebra system. On the one hand, you may use the mathematical knowledge it incorporates by calling system functions interactively. For example, you can compute symbolic integrals or generate and invert matrices by calling appropriate functions. They comprise the system's mathematical intelligence and may implement sophisticated alยญ gorithms. Chapters 2 through 15 discuss this way of using MuPAD. On the other hand, with the help of MuPAD's programming language, you can easily add functionality to the system by implementing your own algorithms as MuPAD procedures. This is useful for special purpose applications if no apยญ propriate system functions exist. Chapters 16 through 18 are an introduction to programming in MuPAD

CONTENT

1. Introduction -- 1.1 Numerical Computations -- 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 fops -- 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 Interval Arithmetic -- 4.18 Null Objects: null (), NIL, FAIL, 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 and Inequalities -- 8.3 Differential Equations -- 8.4 Recurrence Equations -- 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 Introduction -- 11.2 Easy Plotting: Graphs of Functions -- 11.3 Advanced Plotting: Principles and First Examples -- 11.4 The Full Picture: Graphical Trees -- 11.5 Viewer, Browser, and Inspector: Interactive Manipulation -- 11.6 Primitives -- 11.7 Attributes -- 11.8 Colors -- 11.9 Animations -- 11.10 Groups of Primitives -- 11.11 Transformations -- 11.12 Legends -- 11.13 Fonts -- 11.14 Saving and Exporting Pictures -- 11.15 Importing Pictures -- 11.16 Cameras in 3D -- 11.17 Strange Effects in 3D? Accelerated OpenGL? -- 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 Scope of Variables -- 18.7 Type Declaration -- 18.8 Procedures with a Variable Number of Arguments -- 18.9 Options: the Remember Table -- 18.10 Input Parameters -- 18.11 Evaluation Within Procedures -- 18.12 Function Environments -- 18.13 A Programming Example: Differentiation -- 18.14 Programming Exercises -- A. Solutions to Exercises -- B. Documentation and References -- C. Graphics Gallery -- D. Comments on the Graphics Gallery

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