Mathematica by example

Introduction to Mathematica

A Note Regarding Different Versions of Mathematica

1.1.1. Getting Started with Mathematica

Five Basic Rules of Mathematica Syntax

1.2. Loading Packages

1.2.1. Packages Included with Older Versions of Mathematica

1.2.2. Loading New Packages

1.3. Getting Help from Mathematica

Mathematica Help

1.4. Exercises

Chapter 2. Basic Operations on Numbers, Expressions, and Functions

2.1. Numerical Calculations and Built-in Functions

2.1.1. Numerical Calculations

2.1.2. Built-in Constants

2.1.3. Built-in Functions

A Word of Caution

2.2. Expressions and Functions: Elementary Algebra

2.2.1. Basic Algebraic Operations on Expressions

2.2.2. Naming and Evaluating Expressions

2.2.3. Defining and Evaluating Functions

2.3. Graphing Functions, Expressions, and Equations

2.3.1. Functions of a Single Variable

2.3.2. Parametric and Polar Plots in Two Dimensions

2.3.3. Three-Dimensional and Contour Plots: Graphing Equations

2.3.4. Parametric Curves and Surfaces in Space

2.3.5. Miscellaneous Comments

2.4. Solving Equations

2.4.1. Exact Solutions of Equations

2.4.2. Approximate Solutions of Equations

2.5. Exercises

Chapter 3. Calculus

3.1. Limits and Continuity

3.1.1. Using Graphs and Tables to Predict Limits

3.1.2. Computing Limits

3.1.3. One-Sided Limits

3.1.4. Continuity

3.2. Differential Calculus

3.2.1. Definition of the Derivative

3.2.2. Calculating Derivatives

3.2.3. Implicit Differentiation

3.2.4. Tangent Lines

3.2.5. The First Derivative Test and Second Derivative Test

3.2.6. Applied Max/Min Problems

3.2.7. Antidifferentiation

3.3. Integral Calculus

3.3.1. Area

3.3.2. The Definite Integral

3.3.3. Approximating Definite Integrals

3.3.4. Area

3.3.5. Arc Length

3.3.6. Solids of Revolution

3.4. Series

3.4.1. Introduction to Sequences and Series

3.4.2. Convergence Tests

3.4.3. Alternating Series

3.4.4. Power Series

3.4.5. Taylor and Maclaurin Series

3.4.6. Taylor's Theorem

3.4.7. Other Series

3.5. Multivariable Calculus

3.5.1. Limits of Functions of Two Variables

3.5.2. Partial and Directional Derivatives

3.5.3. Iterated Integrals

3.6. Exercises

Chapter 4. Introduction to Lists and Tables

4.1. Lists and List Operations

4.1.1. Defining Lists

4.1.2. Plotting Lists of Points

4.2. Manipulating Lists: More on Part and Map

4.2.1. More on Graphing Lists: Graphing Lists of Points Using Graphics Primitives

4.2.2. Miscellaneous List Operations

4.3. Other Applications

4.3.1. Approximating Lists with Functions

4.3.2. Introduction to Fourier Series

4.3.3. The Mandelbrot Set and Julia Sets

4.4. Exercises

Chapter 5. Matrices and Vectors: Topics from Linear Algebra and Vector Calculus

5.1. Nested Lists: Introduction to Matrices, Vectors, and Matrix Operations

5.1.1. Defining Nested Lists, Matrices, and Vectors

5.1.2. Extracting Elements of Matrices

5.1.3. Basic Computations with Matrices

5.1.4. Basic Computations with Vectors

5.2. Linear Systems of Equations

5.2.1. Calculating Solutions of Linear Systems of Equations

5.2.2. Gauss-Jordan Elimination

5.3. Selected Topics from Linear Algebra

5.3.1. Fundamental Subspaces Associated with Matrices

5.3.2. The Gram-Schmidt Process

5.3.3. Linear Transformations

5.3.4. Eigenvalues and Eigenvectors

5.3.5. Jordan Canonical Form

5.3.6. The QR Method

5.4. Maxima and Minima Using Linear Programming

5.4.1. The Standard Form of a Linear Programming Problem

5.4.2. The Dual Problem

5.5. Selected Topics from Vector Calculus

5.5.1. Vector-Valued Functions

5.5.2. Line Integrals

5.5.3. Surface Integrals

5.5.4. A Note on Nonorientability

5.5.5. More on Tangents, Normals, and Curvature in R[superscript 3]

5.6. Matrices and Graphics

5.7. Exercises

Chapter 6. Applications Related to Ordinary and Partial Differential Equations

6.1. First-Order Differential Equations

6.1.1. Separable Equations

6.1.2. Linear Equations

6.1.3. Nonlinear Equations

6.1.4. Numerical Methods

6.2. Second-Order Linear Equations

6.2.1. Basic Theory

6.2.2. Constant Coefficients

6.2.3. Undetermined Coefficients

6.2.4. Variation of Parameters

6.3. Higher-Order Linear Equations

6.3.1. Basic Theory

6.3.2. Constant Coefficients

6.3.3. Undetermined Coefficients

6.3.4. Laplace Transform Methods

6.3.5. Nonlinear Higher-Order Equations

6.4. Systems of Equations

6.4.1. Linear Systems

6.4.2. Nonhomogeneous Linear Systems

6.4.3. Nonlinear Systems

6.5. Some Partial Differential Equations

6.5.1. The One-Dimensional Wave Equation

6.5.2. The Two-Dimensional Wave Equation

6.5.3. Other Partial Differential Equations.