An Introduction to Maple V / by Jack-Michel Cornil, Philippe Testud
| データ種別 | 電子ブック |
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| 出版情報 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer , 2001 |
| 本文言語 | 英語 |
| 大きさ | XX, 470p. 105 illus : online resource |
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| 内容注記 | 1. What MAPLE Can Do for You 1.1 Arithmetic 1.2 Numerical Computations 1.3 Polynomials and Rational Functions 1.4 Trigonometry 1.5 Differentiation 1.6 Truncated Series Expansions 1.7 Differential Equations and Systems 1.8 Integration 1.9 Plot of Curves 1.10 Plot of Surfaces 1.11 Linear Algebra 2. Introduction 2.1 First Steps 2.2 Assignment and Evaluation 2.3.1 Fundamental Operations 2.4 First Approach to Functions 2.5 Simplification of Power Functions 3. Arithmetic 3.1 Divisibility 3.2 Diophantian Equations 4. Real Numbers, Complex Numbers 4.1 The Real Numbers 4.2 The Complex Numbers 5.1 Curves Defined by an Equation y = f (x) 5.2 The Environment of plot 5.3 Parametrized Curves in Cartesian Coordinates 5.4 Curves in Polar Coordinates 5.5 Curves Defined Implicitly 5.6 Polygonal Plots 5.7 Mixing Drawings 5.8 Animation 5.9 Using Logarithmic Scales 6. Equations and Inequations 6.1 Symbolic Solution: solve 6.2 Approximate Solution of Equations: fsolve 6.3 Solution of Recurrences: rsolve 7. Limits and Derivatives 7.1 Limits 7.2 Derivatives 8. Truncated Series Expansions 8.1 The Function series 8.2 Operations on Truncated Series Expansions 8.3 Series Expansion of an Implicit Function 9. Differential Equations 9.1 Methods for Solving Exactly 9.2 Methods for Approximate Solutions 9.3 Methods to Solve Graphically 10. Integration and Summation 10.1 Integration 10.2 Operations on Unevaluated Integrals 10.3 Discrete Summation 11. Three-Dimensional Graphics 11.1 Surfaces Defined by an Equation z = f (x, y) 11.2 The Environment of plot3d 11.3 Surface Patches Parametrized in Cartesian Coordinates 11.4 Surfaces Patches Parametrized in Cylindrical Coordinates 11.5 Surface Patches Parametrized in Spherical Coordinates 11.6 Parametrized Space Curves 11.7 Surfaces Defined Implicitly 11.8 Mixing Plots from Different Origins 12. Polynomials with Rational Coefficients 12.1 Writing Polynomials 12.2 Coefficients of a Polynomial 12.3 Divisibility 12.4 Computation of the g.c.d. and the I.c.m 12.5 Factorization 13. Polynomials with Irrational Coefficients 13.1 Algebraic Extensions of ? 13.2 Computation Over an Algebraic Extension 13.3 Polynomials with Coefficients in ?/p? 14. Rational Functions 14.1 Writing of the Rational Functions 14.2 Factorization of the Rational Functions 14.3 Partial Fraction Decomposition 14.4 Continued Fraction Series Expansions 15. Construction of Vectors and of Matrices 15.1 The linalg Library 15.2 Vectors 15.3 Matrices 15.4 Problems of Evaluation 15.5 Special Matrices 15.6 Random Vectors and Matrices 15.7 Functions to Extract Matrices 15.8 Constructors of Matrices 16. Vector Analysis and Matrix Calculus 16.1 Operations upon Vectors and Matrices 16.2 Basis of a Vector Subspace 17. Systems of Linear Equations 17.1 Solution of a Linear System 17.2 The Pivot’s Method 18. Normalization of Matrices 18.1 Determinant, Characteristic Polynomial 18.2 Eigenvalues and Eigenvectors of a Matrix 19. Orthogonality 19.1 Euclidean and Hermitean Vector Spaces 19.2 Orthogonal Polynomials 20. Vector Analysis 20.1 Jacobian Matrix, Divergence 20.2 Gradient, Laplacian, Curl 20.3 Scalar Potential, Vector Potential 21. The MAPLE Objects 21.1 Basic Expressions 21.2 Real and Complex Numerical Values 21.3 Expression Sequences 21.4 Ranges 21.5 Sets and Lists 21.6 Unevaluated Integrals 21.7 Polynomials 21.8 Truncated Series Expansions 21.9 Boolean Relations 21.10 Tables and Arrays 22. Working More Cleverly with the Subexpressions 22.1 The Substitution Functions 22.2 The Function map 23. Programming: Loops and Branches 23.1 Loops 23.2 Branches 24. Programming: Functions and Procedures 24.1 Functions 24.2 Procedures 24.3 About Passing Parameters 24.4 Follow-up of the Execution of a Procedure 24.5 Save and Reread a Procedure 25. The Mathematical Functions 25.1 Catalogue of Mathematical Functions 25.2 How Does a MAPLE Function Work? 26. Maple Environment in Windows -- 26.1 The MAPLE Worksheet -- 26.2 The File Menu -- 26.3 The Edit Menu -- 26.4 The View Menu -- 26.5 The Insert Menu -- 26.6 The Format Menu -- 26.7 The Options Menu -- 26.8 The Window Menu -- 26.9 On-line Help |
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| 一般注記 | MAPLE is a computer algebra system which, thanks to an extensive library of sophisticated functions, enables both numerical and formal computations to be performed. Until recently, such systems were only available to professional users with access to mainframe computers, but the rapid improvement in the performance of personal computers (speed, memory) now makes them accessible to the majority of users. The latest versions of MAPLE belong to this new generation of systems, allowing a growing audience of users to become familiar with computer algebra. This work does not set out to describe all the possibilities of MAPLE in an exhaustive manner; there is already a great deal of such documentation, including extensive online help. However, these technical manuals provide a mass of information which is not always of great help to a beginner in computer algebra who is looking for a quick solution to a problem in his own speciality: mathematics, physics, chemistry, etc. This book has been designed so that a scientist who wishes to use MAPLE can find the information he requires quickly. It is divided into chapters which are largely independent, each one being devoted to a separate subject (graphics, differential equations, integration, polynomials, linear algebra, ... ), enabling each user to concentrate on the functions he really needs. In each chapter, deliberately simple examples have been given in order to fully illustrate the syntax used |
| 著者標目 | *Cornil, Jack-Michel author Testud, Philippe author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Algorithms FREE:Mathematics FREE:Algorithms |
| 分 類 | DC23:518.1 |
| 巻冊次 | ISBN:9783642567292 
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| ISBN | 9783642567292 |
| URL | http://dx.doi.org/10.1007/978-3-642-56729-2 |
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※2021年9月12日以降