Mastering Mathematica®

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