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＜電子ブック＞
Introduction to Maple / by Andre HECK

版	2nd ed. 1996.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	1996
本文言語	英語
大きさ	online resource
著者標目	*HECK, Andre author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Mathematical analysis LCSH:Chemistry, Physical and theoretical LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Computer graphics LCSH:Mathematical physics FREE:Algebra FREE:Analysis FREE:Theoretical Chemistry FREE:Symbolic and Algebraic Manipulation FREE:Computer Graphics FREE:Mathematical Methods in Physics
一般注記	1 Introduction to Computer Algebra -- 1.1 What is Computer Algebra? -- 1.2 Computer Algebra Systems -- 1.3 Some Properties of Computer Algebra Systems -- 1.4 Advantages of Computer Algebra -- 1.5 Limitations of Computer Algebra -- 1.6 Design of Maple -- 2 The First Steps: Calculus on Numbers -- 2.1 Getting Started -- 2.2 Getting Help -- 2.3 Integers and Rational Numbers -- 2.4 Irrational Numbers and Floating-Point Numbers -- 2.5 Algebraic Numbers -- 2.6 Complex Numbers -- 2.7 Exercises -- 3 Variables and Names -- 3.1 Assignment and Unassignment -- 3.2 Evaluation -- 3.3 Names of Variables -- 3.4 Basic Data Types -- 3.5 Attributes -- 3.6 Properties -- 3.7 Exercises -- 4 Getting Around with Maple -- 4.1 Maple Input and Output -- 4.2 The Maple Library -- 4.3 Reading and Writing Files -- 4.4 Importing and Exporting Numerical Data -- 4.5 Low-Level I/O -- 4.6 Code Generation -- 4.7 Changing Maple to Your Own Taste -- 4.8 Exercises -- 5 Polynomials and Rational Functions -- 5.1 Univariate Polynomials -- 5.2 Multivariate Polynomials -- 5.3 Rational Functions -- 5.4 Conversions -- 5.5 Exercises -- 6 Internal Data Representation and Substitution -- 6.1 Internal Representation of Polynomials -- 6.2 Generalized Rational Expressions -- 6.3 Substitution -- 6.4 Exercises -- 7 Manipulation of Polynomials and Rational Expressions -- 7.1 Expansion -- 7.2 Factorization -- 7.3 Canonical Form and Normal Form -- 7.4 Normalization -- 7.5 Collection -- 7.6 Sorting -- 7.7 Exercises -- 8 Functions -- 8.1 Mathematical Functions -- 8.2 Arrow Operators -- 8.3 Piecewise Defined Functions -- 8.4 Maple Procedures -- 8.5 Recursive Procedure Definitions -- 8.6 unapply -- 8.7 Operations on Functions -- 8.8 Anonymous Functions -- 8.9 Exercises -- 9 Differentiation -- 9.1 Symbolic Differentiation -- 9.2 Automatic Differentiation -- 9.3 Exercises -- 10 Integration and Summation -- 10.1 Indefinite Integration -- 10.2 Definite Integration -- 10.3 Numerical Integration -- 10.4 Integral Transforms -- 10.5 Assisting Maple’s Integrator -- 10.6 Summation -- 10.7 Exercises -- 11 Series, Approximation, and Limits -- 11.1 Truncated Series -- 11.2 Approximation of Functions -- 11.3 Power Series -- 11.4 Limits -- 11.5 Exercises -- 12 Composite Data Types -- 12.1 Sequence -- 12.2 Set -- 12.3 List -- 12.4 Array -- 12.5 Table -- 12.6 Last Name Evaluation -- 12.7 Function Call -- 12.8 Conversion Between Composite Data Types -- 12.9 Exercises -- 13 The Assume Facility -- 13.1 The Need for an Assume Facility -- 13.2 Basics of assume -- 13.3 An Algebra of Properties -- 13.4 Implementation of assume -- 13.5 Exercises -- 13.6 Hierarchy of Properties -- 14 Simplification -- 14.1 Automatic Simplification -- 14.2 expand -- 14.3 combine -- 14.4 simplify -- 14.5 convert -- 14.6 Trigonometric Simplification -- 14.7 Simplification w.r.t. Side Relations -- 14.8 Control Over Simplification -- 14.9 Defining Your Own Simplification Routines -- 14.10 Exercises -- 14.11 Simplification Chart -- 15 Graphics -- 15.1 Some Basic Two-Dimensional Plots -- 15.2 Options of plot -- 15.3 The Structure of Two-Dimensional Graphics -- 15.4 The plottools Package -- 15.5 Special Two-Dimensional Plots -- 15.6 Two-Dimensional Geometry -- 15.7 Plot Aliasing -- 15.8 A Common Mistake -- 15.9 Some Basic Three-Dimensional Plots -- 15.10 Options of plot3d -- 15.11 The Structure of Three-Dimensional Graphics -- 15.12 Special Three-Dimensional Plots -- 15.13 Data Plotting -- 15.14 Animation -- 15.15 List of Plot Options -- 15.16 Exercises -- 16 Solving Equations -- 16.1 Equations in One Unknown -- 16.2 Abbreviations in solve -- 16.3 Some Difficulties -- 16.4 Systems of Equations -- 16.5 The Gröbner Basis Method -- 16.6 Inequalities -- 16.7 NumericalSolvers -- 16.8 Other Solvers in Maple -- 16.9 Exercises -- 17 Differential Equations -- 17.1 First Glance at ODEs -- 17.2 Analytic Solutions -- 17.3 Taylor Series Method -- 17.4 Power Series Method -- 17.5 Numerical Solutions -- 17.6 DEtools -- 17.7 Perturbation Methods -- 17.8 Partial Differential Equations -- 17.9 Lie Point Symmetries of PDEs -- 17.10 Exercises -- 18 Linear Algebra: The linalg Package -- 18.1 Loading the linalg Package -- 18.2 Creating New Vectors and Matrices -- 18.3 Vector and Matrix Arithmetic -- 18.4 Basic Matrix Functions -- 18.5 Structural Operations -- 18.6 Vector Operations -- 18.7 Standard Forms of Matrices -- 18.8 Exercises -- 19 Linear Algebra: Applications -- 19.1 Kinematics of the Stanford Manipulator -- 19.2 A Three-Compartment Model of Cadmium Transfer -- 19.3 Molecular-Orbital Hückel Theory -- 19.4 Vector Analysis -- 19.5 Moore-Penrose Inverse -- 19.6 Exercises -- References The first edition of this book has been very well received by the community. The new version 4 of Maple V contains so many new mathematical features and improvements in the user interface that Waterloo Maple Inc. markets it as "the Power Edition. " These two facts have made it necessary to write a second edition within a short period of the first. I corrected typographical errors, rephrased text, updated and improved many examples, and added much new material. Hardly any chapter has been left untouched. Substan­ tially changed or added sections and chapters address the assume facility, I/O, approximation theory, integration, composite data types, simplifica­ tion, graphics, differential equations, and matrix algebra. Tables summa­ rize features, command options, etc. , and constitute a quick reference. The enlarged index of the book has been carefully compiled to make locating search items quick and easy. Many new examples have been included show­ ing how to use Maple as a problem solver, how to assist the system during computations, and how to extend its built-in facilities. About the Maple Version Used The second edition of this book is fully revised and updated to Maple V Release 4. More precisely, the second edition of this book was produced with Maple V Release 4, beta 3 on a SUN SPARCstation 20, Model 71. There should be hardly any difference between this beta version and the final release; only minor differences in the user interface are not excluded HTTP:URL=https://doi.org/10.1007/978-1-4684-0484-5

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