Mathematica by Example

Preface

▩ Chapter 1 Getting Started

■ 1.1 Macintosh Basics

The Mathematica Folder

Opening Mathematica Files

■ 1.2 Introduction to the Basic Types of Cells, Cursor Shapes, and Evaluating Commands

Evaluating Mathematica Input

Converting Active Cells to Inactive Cells

Cursor Shapes

■ 1.3 Introduction to the Mathematica Menu

File

Edit

Style

Window

■ Preview

Five Basic Rules of Mathematica Syntax

▩ Chapter 2 Mathematical Operations on Numbers, Expressions and Functions

■ 2.1 Numerical Calculations and Built-In Functions

□ Numerical Calculations and Built-In Constants

□ Built-In Functions

■ 2.2 Expressions and Functions

□ Basic Algebraic Operations on Expressions

□ Naming and Evaluating Expressions

□ Defining and Evaluating Functions

□ Additional Ways to Evaluate Functions and Expressions

□ Retrieving Unnamed Output

□ Composition of Functions

■ 2.3 Mod Math

Mod

PolynomialMod

■ 2.4 Graphing Functions and Expressions Plot

□ Graphing Severla Functions Simultaneousyl

□ Graphing Options

○ Graphing Features and Options of Version 2.0

○ Displaying Several Graphs with Version 2.0

□ Labeling Graphs in Version 2.0

□ Piecewise Defined Functions

■ 2.5 Exact and Approximate Solutions of Equations

□ Exact Solutions of Equations

□ Exact Solutions of Systems of Equations

□ Numerical Approximation of Solutions of Equations

○ Approximating Solutions of Equations with Version 2.0

□ Application: Intersection Points of Graphs of Functions

▩ Chapter 3 Calculus

■ 3.1 Computing Limits

Limit

Computing Limits with Version 2.0

■ 3.2 Differential Calculus

□ Calculating Derivatives of Functions and Expressions

□ Graphing Functions and Derivatives

□ Computing Higher Order Derivatives

□ Locating Critical Points and Inflection Points

□ Application: Graphing Functions and Tangent Lines

□ Application: Maxima and Minima

□ Application: A Command that Graphs Functions and Derivatives on the Same Axes

■ 3.3 Implicit Differentiation with Mathematica

□ Computing Derivatives of Implicit Functions

□ Other Methods to Compute Derivatives of Implicit Functions

○ Graphing Implicit Functions with Version 2.0

■ 3.4 Integral Calculus

□ Computing Definite and Indefinite Integrals

□ Numerically Computing Definite Integrals

○ Definite Integration with Version 2.0

□ Application: Area Between Curves

□ Application: Arc Length

□ Application: Volumes of Solids of Revolution

■ 3.5 Series

□ Computing Power Series

□ Application: Approximating the Remainder

□ Application: Series Solutions to Differential Equations

■ 3.6 Multi-Variable Calculus

□ Elementary Three-Dimensional Graphics

□ ContourPlot and Version 2.0

□ Partial Differentiation

□ Other Methods of Computing Derivatives

□ Application: Classifying Critical Points

□ Application: Tangent Planes

□ Application: Lagrange Multipliers

□ Multiple Integrals

□ Application: Volume

□ Series in More than One Variable

▩ Chapter 4 Introduction to Lists and Tables

■ 4.1 Defining Lists

Table

Hermite PolynomialS

■ 4.2 Operations on Lists

□ Extracting Elements of Lists

□ Graphing Lists and Lists of Functions

□ Evaluation of Lists by Functions

□ Other List Operations

□ Alternative Ways to Evaluate Lists by Functions

■ 4.3 Applications

□ Application: Interest, Annuities, and Amortization

○ Additional Output Features of Version 2.0

□ Application: Graphing Parametric Equations with ListPlot and ParametricPlot

□ Application: Creating Tables of Derivatives of a Function

□ Application: Graphing Equations

□ Application: Tangent Lines and Animations

□ Application: Approximating Lists with Functions

□ Application: Introduction to Fourier Series

▩ Chapter 5 Introduction to Nested Lists: Matrices and Vectors

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

□ Defining Matrices and Vectors

□ Extracting Elements of Matrices

□ Basic Computations with Matrices and Vectors

■ 5.2 Linear Systems of Equations

□ Calculating Solutions of Linear Systems of Equations

□ Application: Characteristic and Minimal Polynomials

□ Application: Maxima and Minima Using Linear Programming

■ 5.3 Vector Calculus

□ Review of Definitions and Notation

□ Application: Green's Theorem

□ Application: The Divergence Theorem

□ Application: Stoke's Theorem

■ 5.4 Saving Results for Future Mathematica Sessions

□ Application: Constructing a Table of Zeros of Bessel Functions

□ An Alternative Method

□ Chapter 6 Applications Related to Ordinary and Partial Differential Equations

■ 6.1 Linear Equations

DSolve

□ Application: The Falling Body Problems

■ 6.2 Exact Differential Equations

■ 6.3 Undetermined Coefficients

■ 6.4 Linear n-th Order Differential Equations with Constant Coefficients

■ 6.5 The Cauchy-Euler Equation

■ 6.6 Variation of Parameters

■ 6.7 Capabilities of DSolve

Bessel's Equation, Legendre's Equation, and Airy's Equation

■ 6.8 Systems of Linear Differential Equations

□ Application: Spring Problems

□ Application: Classification of Equilibrium Points

■ 6.9 Series Solutions to Ordinary Differential Equations

■ 6.10 Series Solutions of Partial Differential Equations

□ Application: TWo-Dimensional Wave Equation in a Circular Region

• 6.11 Numerical Solutions of Differential Equations

○ Application: The Damped Pendulum Equation

• 6.12 Numerical Solutions of Systems of Differential Equations

○ Application: Van der Pol's Equation

□ Chapter 7 Introduction to Mathematica Packages

■ 7.1 Algebra

□ GosperSum.m

○ SymbolicSum.m

□ Relm.m

■ 7.2 Linear Algebra

○ Cholesky.m

○ Application: Quadratic Equations

□ CrossProduct.m

○ MatrixManipulation.m

○ Application: Computing the Adjacency Matrix of a Graph

○ Orthogonalization.m

○ Application: Distance

○ Tridiagonal.m

• 7.3 Version 2.0 Calculus

○ LaplaceTransform.m

○ Application: Solutions of Ordinary Differential Equations

O FourierTransform.m

■ 7.4 Discrete Math

□ CombinatorialFunctions.m

□ CombinatorialSimplification.m

□ Permutations.m

▩ Chapter 8 Some Graphics Packages

■ 8.1 Graphics.m

Graphing in Polar Coordinates

Creating Pie Charts and Bar Charts

■ 8.2 Polyhedra.m

■ 8.3 Shapes.m

■ 8.4 ParametricPlot3D.m

Graphing Functions in Space

Graphing Curves in Space

• 8.5 ImplicitPlot.m

Graphing Equations with Version 2.0

• 8.6 PlotField.m

Graphing Vector Fields in 2-Space

• 8.7 PlotField3D.m

Graphing Vector Fields in 3-Space

• 8.8 ComplexMap.m

▩ Chapter 9 Some Special Packages

• 9.1 Approximations.m

• 9.2 GaussianQuadrature.m

• 9.3 NLimit.m

• 9.4 PolynomialFit.m

■ 9.5 RungeKutta.m

■ 9.6 ContinuousDistributions.m and DescriptiveStatistics.m

• 9.7 HypothesisTests.m

• 9.8 ConfidenceIntervals.m

• 9.9 LinearRegression.m

▩ Chapter 10 Getting Help from Mathematica and Making Mathematica Do What You Want

■ 10.1 Getting Help From Mathematica

□ Help Commands

□ Mathematica Help

○ Version 2.0 and Kernel Help

■ 10.2 The init.m File

■ 10.3 Explanation of the Mathematica Menu

■ The Version 1.2 Menu

Edit

Startup Settings, Action Settings

Animation Settings

Cell

Action, Kernel Interrupt, Style

Window

• The Version 2.0 Menu

Short and Long Menus, Edit

○ Action Settings for Version 2.0

■ 10.4 Common Errors and Their Remedies

■ 10.5 Additional References

▩ Appendix: Introduction to Programming in Mathematica

Local Variables, Block and Module

If statements and Do Loops

Examples of Routines Used in this Book

▩ Index