# Mastering Mathematica®

## 1st Edition

### Programming Methods and Applications

**Authors:**John Gray

**eBook ISBN:**9781483214030

**Imprint:**Academic Press

**Published Date:**18th March 1994

**Page Count:**666

## Description

Mastering Mathematica®: Programming Methods and Applications presents the mathematical results and turn them into precise algorithmic procedures that can be executed by a computer. This book provides insight into more complex situations that can be investigated by hand.

Organized into four parts, this book begins with an overview of the use of a pocket calculator. This text then looks in more detail at numerical calculations and solving equations, both algebraic and differential equations. Other parts consider the built-in graphics and show how to make pictures without programming. This book discusses as well the four styles of programming, namely, functional programming, imperative programming, rewrite programing, and object oriented programming. The reader is also introduced to differentiable mapping to show the analysis of critical points of functions and the developments in differential geometry that are required to study minimal surfaces.

This book is a valuable resource for graduate students in mathematics, mathematics education, engineering, and the sciences.

## Table of Contents

Preface

How to Use the Disk

Part I: Mastering Mathematica as a Symbolic Pocket Calculator

Chapter 1: A Quick Trip Through Elementary Mathematics

1 Opening Remarks

2 Grade School Arithmetic

3 High School Algebra and Trigonometry

4 College Calculus, Differential Equations and Linear Algebra

5 Graduate School

6 Practice

7 Exercises

Chapter 2: Interacting with Mathematica

1 The Different Aspects of Mathematica

2 Interacting with the Kernel

3 Interacting with the Front-End

4 Using Packages

5 Saving Work to be Reused

6 Practice

7 Exercises

Chapter 3: More About Numbers and Equations

1 Introduction

2 Numbers

3 Solving Algebraic Equations

4 Solving Ordinary Differential Equations

5 Practice

6 Exercises.

Chapter 4: Built-in Graphics

1 Plotting Commands and Optional Arguments

2 Two-Dimensional Graphics

3 Three-Dimensional Graphics

4 Animation

5 Sound

6 Practice

7 Exercises

Part II: Mastering Mathematica as a Programming Language

Chapter 5: The Mathematica Language

1 Everything Is an Expression

2 Lists, Arrays, Intervals, and Sets

3 Thread, Inner and Outer

4 Other Aspects

5 Practice

6 Exercises

Chapter 6: Functional Programming

1 Some Functional Aspects of Mathematica

2 Functional Programs

3 Practice

4 Exercises

Chapter 7: Rule Based Programming

1 Introduction

2 Rewrite Rules in Mathematica

3 Pattern Matching

4 Using Patterns in Rules

5 Restricting Pattern Matching with Predicates

6 Examples of Restricted Rewrite Rules

7 Practice

8 Exercises

Chapter 8: Procedural Programming

1 Introduction

2 Basic Operations

3 Modules, Blocks and With

4 Examples

5 Practice

6 Exercises

Chapter 9: Object-Oriented Programming

1 Introduction

2 The Duality Between Functions and Data

3 Object-Oriented Programming in Mathematica

4 The Hierarchy of Point Classes

5 Exercises

6 Implementation

Chapter 10: Graphics Programming

1 Introduction to Graphics Primitives

2 Two-Dimensional Graphics Objects, Graphics Modifiers and Options

3 Combining Built-in Graphics with Graphics Primitives

4 Graphics Arrays and Graphics Rectangles

5 Examples of Two-Dimensional Graphics

6 Three-Dimensional Graphics Primitives

7 Exercises

Chapter 11: Some Finer Points

1 Introduction

2 Packages

3 Attributes

4 Named Optional Arguments

5 Evaluation

6 Unbounded Search

7 Substitution and the Lambda Calculus

8 Exercises

Part III: Mastering Knowledge Representation in Mathematica

Chapter 12: Polya's Pattern Analysis

1 Introduction

2 Construction of Some Permutation Groups

3 The Geometric Approach

4 The Algebraic Approach

5 Implementation

Chapter 13: Object-Oriented Graph Theory

1 Introduction

2 Representations of Graphs

3 Products

4 Other Constructions in the Class Graph

5 Some Graph Algorithms

6 Exercises

7 Implementation

Chapter 14: Differentiable Mappings

1 Introduction

2 Differentiable Mappings

3 Making Plots of Differentiable Mappings

4 Examples

5 Dimension[domain] == 1: Curves

6 Implementation

Chapter 15: Critical Points and Minimal Surfaces

1 Introduction

2 Critical Points

3 Minimal Surfaces

4 Implementation

Part IV: Answers

Chapter 1: Answers

Chapter 3: Answers

Chapter 5: Answers

Chapter 6: Answers

Chapter 7: Answers

Chapter 8: Answers

References

Index

## Details

- No. of pages:
- 666

- Language:
- English

- Copyright:
- © Academic Press 1994

- Published:
- 18th March 1994

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483214030

## About the Author

### John Gray

John Gray is a professor of mathematics and computer science at University of Illinois in Urbana. He was responsible for establishing a course on mathematical software at U. of I. where they have used Mathematica since its inception. This course has empowered numerous mathematicians, engineers, scientists, teachers and students with the ability to use Mathematica as a programming language, and has also contributed to the development of this book.

### Affiliations and Expertise

University of Illinois, Urbana, U.S.A.