# Mathematica by Example

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Mathematica by Example presents the commands and applications of Mathematica, a system for doing mathematics on a computer. This text serves as a guide to beginning users of Mathematica and users who do not intend to take advantage of the more specialized applications of Mathematica. The book combines symbolic manipulation, numerical mathematics, outstanding graphics, and a sophisticated programming language. It is comprised of 10 chapters. Chapter 1 gives a brief background of the software and how to install it in the computer. Chapter 2 introduces the essential commands of Mathematica. Basic operations on numbers, expressions, and functions are introduced and discussed. Chapter 3 provides Mathematica's built-in calculus commands. The fourth chapter presents elementary operations on lists and tables. This chapter is a prerequisite for Chapter 5 which discusses nested lists and tables in detail. The purpose of Chapter 6 is to illustrate various computations Mathematica can perform when solving differential equations. Chapters 7, 8, and 9 introduce Mathematica Packages that are not found in most Mathematica reference book. The final chapter covers the Mathematica Help feature. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

## Table of Contents

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

## Product details

- No. of pages: 670
- Language: English
- Copyright: © Academic Press 1992
- Published: January 28, 1992
- Imprint: Academic Press
- eBook ISBN: 9781483259284