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Mathematica® by Example
- 2nd Edition - February 17, 1994
- Authors: Martha L Abell, James P. Braselton
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 0 4 1 5 3 0 - 4
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 1 3 9 0 - 3
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… Read more
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Request a sales quoteMathematica 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.
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
- No. of pages: 536
- Language: English
- Edition: 2
- Published: February 17, 1994
- Imprint: Academic Press
- Paperback ISBN: 9780120415304
- eBook ISBN: 9781483213903