Discovering mathematics with maple : an interactive exploration for mathematicians, engineers and econometricians使用MABLE发现数学

作者： R.J. Stroeker 著

出 版 社：

出版时间： 1999-6-1字数：版次： 1页数： 227印刷时间： 1999/06/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783764360917包装： 平装内容简介

This book introduces Maple in a rather special way; namely, it shows how a computer algebra system most naturally fits into a mathematically oriented work environment. The intended audience is the mixed group of mathematicians, econometricians, engineers and other scientists, principally those who in their chosen discipline need to work with mathematical ideas and techniques. The book distinguishes itself from existing ones in the following ways: - It instructs the reader about the use of Maple by posing problems of a strictly mathematical nature. - It is intended not as a mere introduction to Maple, but also to show how Maple - and other computer algebra systems - may enrich our knowledge and deepen our understanding of mathematics. In that respect it focusses on mathematics rather than on Maple. In doing this it tries to convince scientists who are not naturally inclined to incorporate the computer into their daily work routine that a computer algebra system may very well enhance their theoretical work.

目录

Preface

Plan of this Book

1A Tour of Maple V

1.1 Introduction

1.2 Maple's User Interface

1.3 Just a Maple Session

1.3.1 Numerical Calculations

1.3.2 Symbolic Calculations

1.4 Worksheets and Assignments

1.4.1 Worksheet la. Numbers

1.4.2 Assignments la. Numbers

1.4.3 Worksheet lb. Variables and Names

1.4.4 Assignments lb. Variables and Names

1.5 Exercises

1.6 Survey of Used Maple Expressions

2 Functions and Sequences

2.1 Introduction

2.2 Selected Concepts from Analysis

2.3 A Tricky Probability Function

2.3.1 Mathematical Functions

2.3.2 Investigating a Probability Function

2.3.3 Investigating a Strange Sequence

2.4 Workshects and Assignments

2.4.1 Worksheet 2a. Functions

2.4.2 Assignments 2a. Functions

2.4.3 Worksheet 2b. Sequences

2.4.4 Assignments 2b. Sequences

2.5 Exercises

2.6 Survey of Used Maple Expressions

3Matrices and Vectors

3.1 Introduction

3.2 Selected Concepts from Linear Algebra

3.3 A Least Squares Filter

3.3.1 Matrices and Vectors

3.3.2 Removing Noise from a Data Set

3.4 Worksheets and Assignments

3.4.1 Worksheet 3a. Matrices

3.4.2 Assignments 3a. Matrices

3.4.3 Worksheet 3b. Vectors

3.4.4 Assignments 3b. Vectors

3.5 Exercises

3.6 Survey of Used Maple Expressions

4 Counting and Summation

4.1 Introduction

4.2 Selected Concepts from Discrete Mathematics

4.3 Binomial Coefficients

4.3.1 Maple's binomial Function

4.3.2 Two Binomial Identities

4.3.3 The Binomial Series

4.3.4 The De Moivre-Laplace Limit Theorem

4.4 Worksheets and Assignments

4.4.1 Worksheet 4a. Symbolic Summation

4.4.2 Assignments 4a. Symbolic Summation

4.4.3 Worksheet 4b. Counting and Random Numbers

4.4.4 Assignments 4b. Counting and Random Numbers . . .

4.5 Exercises

4.6 Survey of Used Maple Expressions

5 Derivative and Integral

5.1 Introduction

5.2 Further Concepts from Analysis

5.3 Riemann's Non-differentiable Function

5.3.1 Investigating the Riemann Function

5.3.2 Finding a Primitive Function

5.4 Worksheets and Assignments

5.4.1 Worksheet 5a. Differentiation

5.4.2 Assignment 5a. Differentiation

……

6 Vector Spaces and Linear Mappings

A Exercises in Experimentation

B Hints and Answers

C Quick Guide to Selected Maple Commands

Bibliography

Index