Mathematica, Second Edition

1.1 Notation and Conventions
1.2 The Kernel and the Front End
1.3 Mathematica Quirks
1.4 Mathematica Gives Exact Answers
1.5 Mathematica Basics
1.6 Cells
1.7 Getting Help
1.8 Packages
1.9 A Preview of What Is to Come
CHAPTER 2 Basic Concepts 22
2.1 Constants
2.2 “Built-In” Functions
2.3 Basic Arithmetic Operations
2.4 Strings
2.5 Assignment and Replacement
2.6 Logical Relations
2.7 Sums and Products
2.8 Loops
2.9 Introduction to Graphing
2.10 User-Defined Functions
2.11 Operations on Functions
CHAPTER 3 Lists 60
3.1 Introduction
3.2 Generating Lists
3.3 List Manipulation
3.4 Set Theory
3.5 Tables and Matrices
CHAPTER 4 Two-Dimensional Graphics 91
4.1 Plotting Functions of a Single Variable
4.2 Additional Graphics Commands
4.3 Special Two-Dimensional Plots
4.4 Animation
CHAPTER 5 Three-Dimensional Graphics 133
5.1 Plotting Functions of Two Variables
5.2 Other Graphics Commands
5.3 Special Three-Dimensional Plots
5.4 Standard Shapes—3D Graphics Primitives
CHAPTER 6 Equations 169
6.1 Solving Algebraic Equations
6.2 Solving Transcendental Equations
CHAPTER 7 Algebra and Trigonometry 186
7.1 Polynomials
7.2 Rational and Algebraic Functions
7.3 Trigonometric Functions
7.4 The Art of Simplification

CHAPTER 8 Differential Calculus 202
8.1 Limits
8.2 Derivatives
8.3 Maximum and Minimum Values
8.4 Power Series
CHAPTER 9 Integral Calculus 226
9.1 Antiderivatives
9.2 Definite Integrals
9.3 Functions Defined by
Integrals 9.4 Riemann Sums
CHAPTER 10 Multivariate Calculus 245
10.1 Partial Derivatives
10.2 Maximum and Minimum Values
10.3 The Total Differential
10.4 Multiple Integrals
CHAPTER 11 Ordinary Differential Equations 266
11.1 Analytical Solutions
11.2 Numerical Solutions
11.3 Laplace Transforms
CHAPTER 12 Linear Algebra 293
12.1 Vectors and Matrices
12.2 Matrix Operations
12.3 Matrix Manipulation
12.4 Linear Systems of Equations
12.5 Orthogonality
12.6 Eigenvalues and Eigenvectors
12.7 Diagonalization and Jordan Canonical Form
Appendix
A.1 Pure Functions
A.2 Patterns
A.3 Contexts
A.4 Modules 332
A.5 Commands Used in This Book
Index 353

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