Abell / Braselton Mathematica by Example

4. Auflage 2008
ISBN: 978-0-08-092169-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 577 Seiten, Web PDF

Mathematica by Example, 4e is designed to introduce the Mathematica programming language to a wide audience. This is the ideal text for all scientific students, researchers, and programmers wishing to learn or deepen their understanding of Mathematica. The program is used to help professionals, researchers, scientists, students and instructors solve complex problems in a variety of fields, including biology, physics, and engineering.

- Clear organization, complete topic coverage, and accessible exposition for novices
- Fully compatible with Mathematica 6.0
- New applications, exercises and examples from a variety of fields including biology, physics and engineering
- Includes a CD-ROM with all Mathematica input appearing in the book, useful to students so they do not have to type in code and commands

Autoren/Hrsg.

Abell, Martha L.

Braselton, James P.

Inhaltsverzeichnis

1;Front Cover;1
2;Mathematica by Example;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;10
6;Chapter 1. Getting Started;14
6.1;1.1 Introduction to Mathematica;14
6.1.1;A Note Regarding Different Versions of Mathematica;15
6.1.2;1.1.1 Getting Started with Mathematica;16
6.1.2.1;Preview;26
6.1.3;Five Basic Rules of Mathematica Syntax;26
6.2;1.2 Loading Packages;26
6.2.1;1.2.1 Packages Included wi.th Older Versions of Mathematica;27
6.2.2;1.2.2 Loading New Packages;28
6.3;1.3 Getting Help from Mathematica;30
6.3.1;Mathematica Help;37
6.4;1.4 Exercises;41
7;Chapter 2. Basic Operations on Numbers, Expressions, and Functions;44
7.1;2.1 Numerical Calculations and Built-in Functions;44
7.1.1;2.1.1 Numerical Calculations;44
7.1.2;2.1.2 Built-in Constants;47
7.1.3;2.1.3 Built-in Functions;48
7.1.4;A Word of Caution;51
7.2;2.2 Expressions and Functions: Elementary Algebra;52
7.2.1;2.2.1 Basic Algebraic Operations on Expressions;52
7.2.2;2.2.2 Naming and Evaluating Expressions;57
7.2.3;2.2.3 Defining and Evaluating Functions;60
7.3;2.3 Graphing Functions, Expressions, and Equations;65
7.3.1;2.3.1 Functions of a Single Variable;65
7.3.2;2.3.2 Parametric and Polar Plots in Two Dimensions;78
7.3.3;2.3.3 Three-Dimensional and Contour Plots: Graphing Equations;84
7.3.4;2.3.4 Parametric Curves and Surfaces in Space;95
7.3.5;2.3.5 Miscellaneous Comments;107
7.4;2.4 Solving Equations;113
7.4.1;2.4.1 Exact Solutions of Equations;113
7.4.2;2.4.2 Approximate Solutions of Equations;123
7.5;2.5 Exercises;128
8;Chapter 3. Calculus;130
8.1;3.1 Limits and Continuity;130
8.1.1;3.1.1 Using Graphs and Tables to Predict Limits;130
8.1.2;3.1.2 Computing Limits;134
8.1.3;3.1.3 One-Sided Limits;136
8.1.4;3.1.4 Continuity;137
8.2;3.2 Differential Calculus;141
8.2.1;3.2.1 Definition of the Derivative;141
8.2.2;3.2.2 Calculating Derivatives;148
8.2.3;3.2.3 Implicit Differentiation;151
8.2.4;3.2.4 Tangent Lines;152
8.2.5;3.2.5 The First Derivative Test and Second Derivative Test;161
8.2.6;3.2.6 Applied Max/Min Problems;169
8.2.7;3.2.7 Antidifferentiation;177
8.3;3.3 Integral Calculus;181
8.3.1;3.3.1 Area;181
8.3.2;3.3.2 The Definite Integral;187
8.3.3;3.3.3 Approximating Definite Integrals;192
8.3.4;3.3.4 Area;193
8.3.5;3.3.5 Arc Length;199
8.3.6;3.3.6 Solids of Revolution;203
8.4;3.4 Series;214
8.4.1;3.4.1 Introduction to Sequences and Series;214
8.4.2;3.4.2 Convergence Tests;218
8.4.3;3.4.3 Alternating Series;222
8.4.4;3.4.4 Power Series;223
8.4.5;3.4.5 Taylor and Maclaurin Series;226
8.4.6;3.4.6 Taylor’s Theorem;230
8.4.7;3.4.7 Other Series;233
8.5;3.5 Multivariable Calculus;234
8.5.1;3.5.1 Limits of Functions of Two Variables;235
8.5.2;3.5.2 Partial and Directional Derivatives;237
8.5.3;3.5.3 Iterated Integrals;251
8.6;3.6 Exercises;259
9;Chapter 4. Introduction to Lists and Tables;264
9.1;4.1 Lists and List Operations;264
9.1.1;4.1.1 Defining Lists;264
9.1.2;4.1.2 Plotting Lists of Points;271
9.2;4.2 Manipulating Lists: More on Part and Map;282
9.2.1;4.2.1 More on Graphing Lists: Graphing Lists of Points Using Graphics Primitives;290
9.2.2;4.2.2 Miscellaneous List Operations;296
9.3;4.3 Other Applications;296
9.3.1;4.3.1 Approximating Lists with Functions;296
9.3.2;4.3.2 Introduction to Fourier Series;300
9.3.3;4.3.3 The Mandelbrot Set and Julia Sets;312
9.4;4.4 Exercises;324
10;Chapter 5. Matrices and Vectors: Topics from Linear Algebra and Vector Calculus;330
10.1;5.1 Nested Lists: Introduction to Matrices, Vectors, and Matrix Operations;330
10.1.1;5.1.1 Defining Nested Lists, Matrices, and Vectors;330
10.1.2;5.1.2 Extracting Elements of Matrices;335
10.1.3;5.1.3 Basic Computations with Matrices;338
10.1.4;5.1.4 Basic Computations with Vectors;342
10.2;5.2 Linear Systems of Equations;350
10.2.1;5.2.1 Calculating Solutions of Linear Systems of Equations;350
10.2.2;5.2.2 Gauss–Jordan Elimination;355
10.3;5.3 Selected Topics from Linear Algebra;362
10.3.1;5.3.1 Fundamental Subspaces Associated with Matrices;362
10.3.2;5.3.2 The Gram–Schmidt Process;364
10.3.3;5.3.3 Linear Transformations;368
10.3.4;5.3.4 Eigenvalues and Eigenvectors;371
10.3.5;5.3.5 Jordan Canonical Form;374
10.3.6;5.3.6 The QR Method;377
10.4;5.4 Maxima and Minima Using Linear Programming;379
10.4.1;5.4.1 The Standard Form of a Linear Programming Problem;379
10.4.2;5.4.2 The Dual Problem;381
10.5;5.5 Selected Topics from Vector Calculus;387
10.5.1;5.5.1 Vector-Valued Functions;387
10.5.2;5.5.2 Line Integrals;397
10.5.3;5.5.3 Surface Integrals;400
10.5.4;5.5.4 A Note on Nonorientability;404
10.5.5;5.5.5 More on Tangents, Normals, and Curvature in R3;417
10.6;5.6 Matrices and Graphics;428
10.7;5.7 Exercises;443
11;Chapter 6. Applications Related to Ordinary and Partial Differential Equations;448
11.1;6.1 First-Order Differential Equations;448
11.1.1;6.1.1 Separable Equations;448
11.1.2;6.1.2 Linear Equations;455
11.1.3;6.1.3 Nonlinear Equations;463
11.1.4;6.1.4 Numerical Methods;466
11.2;6.2 Second-Order Linear Equations;470
11.2.1;6.2.1 Basic Theory;470
11.2.2;6.2.2 Constant Coefficients;471
11.2.3;6.2.3 Undetermined Coefficients;477
11.2.4;6.2.4 Variation of Parameters;483
11.3;6.3 Higher-Order Linear Equations;485
11.3.1;6.3.1 Basic Theory;485
11.3.2;6.3.2 Constant Coefficients;486
11.3.3;6.3.3 Undetermined Coefficients;488
11.3.4;6.3.4 Laplace Transform Methods;494
11.3.5;6.3.5 Nonlinear Higher-Order Equations;505
11.4;6.4 Systems of Equations;505
11.4.1;6.4.1 Linear Systems;505
11.4.2;6.4.2 Nonhomogeneous Linear Systems;518
11.4.3;6.4.3 Nonlinear Systems;524
11.5;6.5 Some Partial Differential Equations;545
11.5.1;6.5.1 The One-Dimensional Wave Equation;545
11.5.2;6.5.2 The Two-Dimensional Wave Equation;550
11.5.3;6.5.3 Other Partial Differential Equations;560
11.6;6.6 Exercises;563
12;References;570
13;Index;572