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Computer Science with MATHEMATICA ®: Theory and Practice for Science, Mathematics, and Engineering [Pehme köide]

  • Formaat: Paperback / softback, 412 pages, kõrgus x laius x paksus: 245x188x20 mm, kaal: 713 g, 116 Line drawings, unspecified
  • Ilmumisaeg: 28-Feb-2000
  • Kirjastus: Cambridge University Press
  • ISBN-10: 0521663954
  • ISBN-13: 9780521663953
Teised raamatud teemal:
  • Formaat: Paperback / softback, 412 pages, kõrgus x laius x paksus: 245x188x20 mm, kaal: 713 g, 116 Line drawings, unspecified
  • Ilmumisaeg: 28-Feb-2000
  • Kirjastus: Cambridge University Press
  • ISBN-10: 0521663954
  • ISBN-13: 9780521663953
Teised raamatud teemal:
Computer algebra systems have revolutionized the use of computers within mathematics research, and are currently extending that revolution to the undergraduate mathematics curriculum. But the power of such systems goes beyond simple algebraic or numerical manipulation. In this practical resource Roman Maeder shows how computer-aided mathematics has reached a level where it can support effectively many of the computations in science and engineering. Besides treating traditional computer science topics, he demonstrates how scientists and engineers can use these computer-based tools to do scientific computations. A valuable text for computer science courses for scientists and engineers, this book will also prove useful to Mathematica users at all levels. Covering the latest release of Mathematica, the book includes useful tips and techniques to help even seasoned users.

This introductory course shows scientists and engineers how Mathematica can be used to do scientific computations.

Arvustused

'This is an excellent introductory textbook in computer science via Mathematica. I recommend it for use in computer science classes for science and engineering students.' T. E. Simos, Computing Reviews

Muu info

This introductory course shows scientists and engineers how Mathematica can be used to do scientific computations.
Preface ix
About This Book xiii
Computers and Science
From Problems to Programs
3(11)
Computers
14(4)
Programming Languages
18(5)
Computer Science
23(4)
Mathematica's Programming Language
Arithmetic and Logic
27(3)
Definitions
30(4)
Simple Program Structures
34(10)
Structure of Expressions
44(5)
Help with Problems
49(3)
Exercises
52(5)
Iteration and Recursion
The Greatest Common Divisor
57(3)
The 3x + 1 Problem
60(4)
Advanced Topic: Loop Invariants
64(5)
Application: Differential Equations
69(7)
Exercises
76(5)
Structure of Programs
Complex Parametric Lines
81(4)
The First Package
85(5)
Optional Arguments
90(4)
A Template Package
94(2)
Exercises
96(3)
Abstract Data Types
Definition of Abstract Data Types
99(3)
Example: Modular Numbers
102(4)
Design of Abstract Data Types
106(4)
Exercises
110(5)
Algorithms for Searching and Sorting
Searching Ordered Data
115(6)
Sorting Data
121(8)
Binary Trees
129(9)
Exercises
138(5)
Complexity of Algorithms
Complexity of Computations
143(4)
Example: Computing the nth Fibonacci Number
147(9)
Special Topic: Dynamic Programming
156(6)
Long-Integer Arithmetic and Fast Multiplication
162(5)
Exercises
167(4)
Operations on Vectors and Matrices
Vectors and Matrices
171(4)
Inner and Outer Products
175(10)
Linear Algebra
185(9)
Programs with Arrays
194(8)
Application: Aggregation
202(5)
Exercises
207(6)
List Processing and Recursion
Symbolic Expressions and Lists
213(4)
List Processing
217(6)
Exercises
223(4)
Rule-Based Programming
Pattern Matching
227(4)
Rules and Term Rewriting
231(4)
Simplification Rules and Normal Forms
235(6)
Application: Trigonometric Simplifications
241(7)
Exercises
248(7)
Functions
A Notation for Functions (λ Calculus)
255(5)
Functions as Values
260(6)
Example: Simulation of Shift Registers
266(2)
Exercises
268(5)
Theory of Computation
Computable Functions
273(7)
Models of Computation
280(2)
Turing Machines
282(11)
Recursive Functions Are Turing Computable
293(6)
Exercises
299(4)
Databases
Database Design
303(5)
Relational Databases
308(6)
Data Entry and Queries
314(5)
Commercial Databases
319(2)
Exercises
321(4)
Object-Oriented Programming
Introduction
325(2)
Example: Bank Accounts
327(3)
Principles of Object-Oriented Programming
330(2)
Application: Collections
332(9)
Exercises
341(4)
Appendix A Further Reading
A.1 A Guide to the Literature
345(2)
A.2 References
347(6)
Appendix B More Information About Mathematica
B.1 Computations You Can Do with Mathematica
353(11)
B.2 The Code for the Illustrations in this Book
364(4)
B.3 Mathematica's Evaluation Method
368(6)
B.4 Syntax of Operators
374(3)
Index 377