Cover
Half-title
Title
Copyright
Contents
Preface
1 Getting Started
1.1 Launching Mathematica
1.2 The Basic Technique for Using Mathematica
1.3 The First Computation
1.4 Commands for Basic Arithmetic
1.5 Input and Output
1.6 The BasicMathInput Palette
1.7 Decimal In, Decimal Out
1.8 Use Parentheses to Group Terms
1.9 Three Well-Known Constants
1.10 Typing Commands in Mathematica
Numerical Approximation and Scientific Notation
Trigonometric Functions
Logarithms
Factoring Integers
Factoring and Expanding Polynomials
Plotting Functions
Manipulate
Square Root Function
Real and Imaginary Parts of Complex Numbers
Extracting Digits from a Number
Programming
Naming Things
1.11 Saving Your Work and Quitting Mathematica
1.12 Frequently Asked Questions About Mathematica’s Syntax
Why Do All Mathematica Command Names Begin with Capital Letters?
Why Does My Input Appear in Color as I Type?
Why Are the Arguments of Commands Enclosed in Square Brackets?
What Happens If I Use Incorrect Syntax?
2 Working with Mathematica
2.1 Opening Saved Notebooks
2.2 Adding Text to Notebooks
Text Cells
Adding Mathematical Expressions to Text
Modifying the Stylesheet
2.3 Printing
2.4 Creating Slide Shows
2.5 Creating Web Pages
2.6 Converting a Notebook to Another Format
2.7 Mathematica’s Kernel
Numbering Input and Output
Reevaluating Previously Saved Notebooks
2.8 Tips for Working Effectively
Referring to Previous Output
Referring to Previous Input
Postfix Command Structure
Prefix Command Structure
Undoing Mistakes
Keyboard Shortcuts
Typesetting Input—More Shortcuts
Suppressing Output and Entering Sequences of Commands
2.9 Getting Help from Mathematica
Getting Information on a Command whose Name You Know
Command Completion
Command Templates
The Documentation Center
2.10 Loading Packages
2.11 Troubleshooting
Recognizing a Crash
Aborting Calculations and/or Recovering from a Crash
Mac OS Procedure
Windows Procedure
Running Efficiently: Preventing Crashes
3 Functions and Their Graphs
3.1 Defining a Function
Clearing a Function
3.2 Plotting a Function
3.3 Using Mathematica’s Plot Options
How to Get the Same Scaling on Both Axes
How to Get the Axes to Intersect at the Origin
How to Display Mesh Points
How to Add Color and Other Style Changes: Graphics Directives
How to Remove the Axes or Add a Frame
How to Place Arrowheads on the Axes
How to Add Grid Lines and Adjust Ticks on the Axes
How to Add Labels
Exclusions and Vertical Asymptotes
Putting a Logarithmic Scale on One or Both Axes
3.4 Investigating Functions with Manipulate
Other Dynamic Display Commands
3.5 Producing a Table of Values
Manipulating a Grid
3.6 Working with Piecewise Defined Functions
3.7 Plotting Implicitly Defined Functions
3.8 Combining Graphics
Superimposing Plots
Producing Filled Plots
Superimposing Graphics
Graphics Side-by-Side
Graphics in a Grid
3.9 Enhancing Your Graphics
Drawing Tools
Graphics Primitives
3.10 Working with Data
3.11 Managing Data—An Introduction to Lists
3.12 Importing Data
3.13 Working with Difference Equations
4 Algebra
4.1 Factoring and Expanding Polynomials
4.2 Finding Roots of Polynomials with Solve and NSolve
4.3 Solving Equations and Inequalities with Reduce
4.4 Understanding Complex Output
4.5 Working with Rational Functions
Solving Equations
Simplifying Rational Expressions
Formatting Output Using TraditionalForm
Vertical Asymptotes
Long Division of Polynomials
Partial Fractions
4.6 Working with Other Expressions
Simplifying Things
Manipulating Trigonometric Expressions
4.7 Solving General Equations
4.8 Solving Difference Equations
4.9 Solving Systems of Equations
5 Calculus
5.1 Computing Limits
5.2 Working with Difference Quotients
Producing and Simplifying Difference Quotients
Average Rate of Change
Instantaneous Rate of Change
5.3 The Derivative
5.4 Visualizing Derivatives
5.5 Higher Order Derivatives
5.6 Maxima and Minima
5.7 Inflection Points
5.8 Implicit Differentiation
5.9 Differential Equations
5.10 Integration
5.11 Definite and Improper Integrals
Computing Definite Integrals
Riemann Sums
Computing Improper Integrals
Defining Functions with Integrals
Some Integrals Are Bad
5.12 Numerical Integration
5.13 Surfaces of Revolution
5.14 Sequences and Series
6 Multivariable Calculus
6.1 Vectors
The Dot Product and the Norm
Rendering Vectors in the Plane
The Cross Product
6.2 Real-Valued Functions of Two or More Variables
Plotting Functions of Two Variables with Plot3D
Options for 3D Plotting Commands
Plotting Functions of Two Variables with ContourPlot
Plotting Level Surfaces with ContourPlot3D
Graphics3D Primitives
Differentiation of Functions of Two or More Variables
Optimization
Constrained Optimization
Integration of Functions of Two or More Variables
6.3 Parametric Curves and Surfaces
Parametric Curves in the Plane
Parametric Curves in Space
Parametric Surfaces in Space
6.4 Other Coordinate Systems
Polar Coordinates
Cylindrical and Spherical Coordinates
Integration in Other Coordinate Systems
6.5 Vector Fields
Defining a Vector Field
Plotting a Two-Dimensional Vector Field
Divergence and Curl of a Three-Dimensional Vector Field
6.6 Line Integrals and Surface Integrals
Line Integrals
Surface Integrals
7 Linear Algebra
7.1 Matrices
Entering Matrices
Editing Matrices
7.2 Performing Gaussian Elimination
Referring to Parts of Matrices
Gaussian Elimination
7.3 Matrix Operations
7.4 Minors and Cofactors
7.5 Working with Large Matrices
7.6 Solving Systems of Linear Equations
Nonhomogeneous Systems of Linear Equations
Homogeneous Systems of Equations
Using LinearSolve and NullSpace to Solve Nonhomogeneous Systems
7.7 Vector Spaces
Span and Linear Independence
Bases
Rank and Nullity
Orthonormal Bases and the Gram–Schmidt Process
QR-Decomposition
7.8 Eigenvalues and Eigenvectors
Finding Eigenvalues and Eigenvectors Automatically
Finding Eigenvalues and Eigenvectors Manually
Diagonalization
7.9 Visualizing Linear Transformations
8 Programming
8.1 Introduction
8.2 FullForm: What the Kernel Sees
8.3 Numbers
Types of Numbers: Integer, Rational, Real, and Complex
Displaying Numbers
Precision and Accuracy
8.4 Map and Function
Functional Programming
8.5 Control Structures and Looping
Predicates
Control Structures: If, Which, Piecewise
Looping with While and For
8.6 Scoping Constructs: With and Module
Scoping and Dynamic Elements
8.7 Iterations: Nest and Fold
8.8 Patterns
Index