Mathematica® by Example

Mathematica® by Example

2nd Edition - February 17, 1994

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  • Authors: Martha L Abell, James P. Braselton
  • eBook ISBN: 9781483213903

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Description

Mathematica by Example, Revised Edition 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 7 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. Chapter 7 discusses some of the more frequently used commands contained in various graphics packages available with Mathematica. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

Table of Contents


  • Preface

    1 Getting Started

    1.1 Introduction to Mathematica

    1.2 Getting Started with Mathematica

    1.3 Loading Packages

    Two Words of Caution

    1.4 Getting Help from Mathematica

    Help Commands

    Mathematica Help

    2 Mathematical Operations on Numbers, Expressions, and Functions

    2.1 Numerical Calculations and Built-in Functions

    Numerical Calculations

    Built-In Constants

    Built-In Functions

    The Absolute Value, Exponential and Logarithmic Functions

    Trigonometric Functions

    Inverse Trigonometric Functions

    A Word of Caution

    2.2 Expressions and Functions

    Basic Algebraic Operations on Expressions

    Naming and Evaluating Expressions

    A Word of Caution

    Defining and Evaluating Functions

    Additional Ways to Evaluate Functions and Expressions

    Composition of Functions

    A Word of Caution

    2.3 Graphing Functions, Expressions, and Equations

    Graphing Functions of a Single Variable

    Graphing Several Functions

    Piecewise-Defined Functions

    Graphs of Parametric Functions in Two Dimensions

    Three-Dimensional Graphics

    Graphing Level Curves of Functions of Two Variables

    Graphing Parametric Curves and Surfaces in Space

    A Word of Caution

    2.4 Exact and Approximate Solutions of Equations

    Exact Solutions of Equations

    Numerical Approximation of Solutions of Equations

    Application: Intersection Points of Graphs of Functions

    3 Calculus

    3.1 Computing Limits

    Computing Limits

    One-Sided Limits

    A Word of Caution

    3.2 Differential Calculus

    Calculating Derivatives of Functions and Expressions

    Tangent Lines

    Locating Critical Points and Inflection Points

    Using Derivatives to Graph Functions

    Graphing Functions and Derivatives

    Approximations with FindRoot

    Application: Rolle's Theorem and The Mean-Value Theorem

    Application: Graphing Functions and Tangent Lines

    Application: Maxima and Minima

    3.3 Implicit Differentiation

    Computing Derivatives of Implicit Functions

    Other Methods to Compute Derivatives of Implicit Functions

    Other Methods to Graph Equations

    3.4 Integral Calculus

    Estimating Areas

    Computing Definite and Indefinite Integrals

    Approximating Definite Integrals

    Application: Area Between Curves

    Application: Arc Length

    Application: Volume of Solids of Revolution

    Application: The Mean-Value Theorem for Integrals

    A Word of Caution

    3.5 Series

    Introduction to Series

    Determining the Interval of Convergence of a Power Series

    Computing Power Series

    Application: Approximating the Remainder

    Application: Series Solutions to Differential Equations

    Other Series

    3.6 Multivariable Calculus

    Limits of Functions of Two Variables

    Partial Differentiation

    Other Methods of Computing Derivatives

    Application: Classifying Critical Points

    Application: Tangent Planes

    Application: The Method of Lagrange Multipliers

    Double Integrals

    Application: Volume

    Triple Integrals

    Higher-Order Integrals

    4 Introduction to Lists and Tables

    4.1 Defining Lists

    A Word of Caution

    4.2 Operations on Lists

    Extracting Elements of Lists

    Graphing Lists of Points and Lists of Functions

    Evaluation of Lists by Functions

    Evaluation of Parts of Lists by Functions

    Other List Operations

    Alternative Way to Evaluate Lists by Functions

    4.3 Mathematics of Finance

    Application: Compound Interest

    Application: Future Value

    Application: Annuity Due

    Application: Present Value

    Application: Deferred Annuities

    Application: Amortization

    Application: Financial Planning

    4.4 Other Applications

    Application: Secant Lines, Tangent Lines, and Animations

    Application: Approximating Lists with Functions

    Application: Introduction to Fourier Series

    Application: The One-Dimensional Heat Equation

    5 Nested Lists: Matrices and Vectors

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

    Defining Nested Lists: 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

    Gauss-Jordan Elimination

    5.3 Selected Topics from Linear Algebra

    Fundamental Subspaces Associated with Matrices

    The Gram-Schmidt Process

    Linear Transformations

    Application: Rotations

    Eigenvalues and Eigenvectors

    Jordan Canonical Form

    The QR Method

    5.4 Maxima and Minima Using Linear Programming

    The Standard Form of a Linear Programming Problem

    The Dual Problem

    Application: A Transportation Problem

    5.5 Vector Calculus

    Definitions and Notation

    Application: Green's Theorem

    Application: The Divergence Theorem

    Application: Stoke's Theorem

    6 Applications Related to Ordinary and Partial Differential Equations

    6.1 First-Order Ordinary Differential Equations

    Separable Differential Equations

    Homogeneous Differential Equations

    Exact Equations

    Linear Equations

    Numerical Solutions of First-Order Ordinary Differential Equations

    Application: Population Growth and the Logistic Equation

    Application: Newton's Law of Cooling

    Application: Free-Falling Bodies

    6.2 Higher-Order Ordinary Differential Equations

    The Homogeneous Second-Order Equation with Constant Coefficients

    Nonhomogeneous Equations with Constant Coefficients Variation of Parameters

    Cauchy-Euler Equations

    Application: Harmonic Motion

    Numerical Solutions of Higher-Order Ordinary Differential Equations

    Application: The Simple Pendulum

    6.3 Power Series Solutions of Ordinary Differential Equations

    Power Series Solutions about Ordinary Points

    Power Series Solutions about Regular Singular Points

    6.4 Using the Laplace Transform to Solve Ordinary Differential Equations

    Definition of the Laplace Transform

    Solving Ordinary Differential Equations with the Laplace Transform

    Application: The Convolution Theorem

    Application: The Dirac Delta Function

    6.5 Systems of Ordinary Differential Equations

    Homogeneous Linear Systems with Constant Coefficients

    Variation of Parameters

    Nonlinear Systems, Linearization, and Classification of Equilibrium Points

    Numerical Solutions of Systems of Ordinary Differential Equations

    Application: Predator-Prey

    Application: The Double Pendulum

    6.6 Some Partial Differential Equations

    The One-Dimensional Wave Equation

    Application: Zeros of the Bessel Functions

    Application: The Two-Dimensional Wave Equation

    7 Some Graphics Packages

    7.1 ComplexMap

    7.2 ContourPlot3D

    7.3 Graphics

    Graphing in Polar Coordinates

    Creating Charts

    7.4 ImplicitPlot

    7.5 MultipleListPlot and Graphics3D

    7.6 PlotField and PlotField3D

    7.7 Polyhedra and Shapes

    Selected References

    Index

Product details

  • No. of pages: 536
  • Language: English
  • Copyright: © Academic Press 1994
  • Published: February 17, 1994
  • Imprint: Academic Press
  • eBook ISBN: 9781483213903

About the Authors

Martha L Abell

James P. Braselton

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