UID:
almahu_9947362945402882
Format:
XIII, 497p. 84 illus.
,
online resource.
ISBN:
9781468405194
Content:
In symbolic computation on computers, also known as computer algebra, keyboard and display replace the traditional pencil and paper in doing mathematical computations. Interactive computer programs, which are called computer algebra systems, allow their users to compute not only with numbers, but also with symbols, formulae, equations, and so on. Many mathematical computations such as differentiation, integration, and series expansion of functions, and inversion of matrices with symbolic entries, can be carried out quickly, with emphasis on exactness of results, and without much human effort. Computer algebra systems are powerful tools for mathematicians, physicists, chemists, engineers, technicians, psychologists, sociologists, ... , in short, for anybody who needs to do mathematical computations. Com puter algebra systems are indispensable in modern pure and applied scien tific research and education. This book is a gentle introduction to one of the modern computer algebra systems, viz., Maple. Primary emphasis is on learning what can be done with Maple and how it can be used to solve (applied) mathematical problems. To this end, the book contains many examples and exercises, both elementary and more sophisticated. They stimulate you to use Maple and encourage you to find your way through the system. An advice: read this book in conjunction with the Maple system, try the examples, make variations of them, and try to solve the exercises.
Note:
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 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 Evaluation -- 3.2 Unassignment -- 3.3 Full Evaluation -- 3.4 Names of Variables -- 3.5 Basic Data Types -- 3.6 Exercises -- 4 Getting Around with Maple -- 4.1 Input and Output -- 4.2 The Maple Library -- 4.3 Reading and Writing Files -- 4.4 Formatted I/O -- 4.5 Code Generation -- 4.6 Changing Maple to your own Taste -- 4.7 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 Maple Procedures -- 8.4 Recursive Procedure Definitions -- 8.5 unapply -- 8.6 Operations on Functions -- 8.7 Anonymous Functions -- 8.8 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 Truncated Series Expansions, Power Series, and Limits -- 11.1 Truncated Series Expansions -- 11.2 Power Series -- 11.3 Limits -- 11.4 Exercises -- 12 Composite Data Types -- 12.1 Sequence -- 12.2 Set -- 12.3 List -- 12.4 Array -- 12.5 convert and map -- 12.6 Exercises -- 13 Simplification -- 13.1 Automatic Simplification -- 13.2 expand -- 13.3 combine -- 13.4 simplify -- 13.5 convert -- 13.6 Trigonometric Simplification -- 13.7 Simplification w.r.t. Side Relations -- 13.8 Exercises -- 14 Graphics -- 14.1 Some Basic Two-Dimensional Plots -- 14.2 Options of plot -- 14.3 The Structure of Two-Dimensional Graphics -- 14.4 Special Two-Dimensional Plots -- 14.5 Plot Aliasing -- 14.6 A Common Mistake -- 14.7 Some Basic Three-Dimensional Plots -- 14.8 Options of plot3d -- 14.9 The Structure of Three-Dimensional Graphics -- 14.10 Special Three-Dimensional Plots -- 14.11 Animation -- 14.12 Exercises -- 15 Solving Equations -- 15.1 Equations in One Unknown -- 15.2 Abbreviations in solve -- 15.3 Some Difficulties -- 15.4 Systems of Equations -- 15.5 The Gröbner Basis Method -- 15.6 Numerical Solvers -- 15.7 Other Solvers in Maple -- 15.8 Exercises -- 16 Differential Equations -- 16.1 First Glance at ODEs -- 16.2 Analytic Solutions -- 16.3 Taylor Series Method -- 16.4 Power Series Method -- 16.5 Numerical Solutions -- 16.6 Perturbation Methods -- 16.7 Liesymm -- 16.8 Exercises -- 17 Linear Algebra: Basics -- 17.1 Basic Operations on Matrices -- 17.2 Last Name Evaluation -- 17.3 The Linear Algebra Package -- 17.4 Exercises -- 18 Linear Algebra: Applications -- 18.1 Kinematics of the Stanford Manipulator -- 18.2 A 3-Compartment Model of Cadmium Transfer -- 18.3 Molecular-orbital Hückel Theory -- 18.4 Prolate Spheroidal Coordinates -- 18.5 Moore-Penrose Inverse -- 18.6 Exercises.
In:
Springer eBooks
Additional Edition:
Printed edition: ISBN 9781468405217
Language:
English
DOI:
10.1007/978-1-4684-0519-4
URL:
http://dx.doi.org/10.1007/978-1-4684-0519-4
