书名Mathematica by Example, Fourth Edition

• by Martha L. Abell, James P. Braselton
• Publisher: Academic Press
• Year: 2008
• Paperback: 576 pages
• Publisher: Academic Press; 4 edition (September 23, 2008)
• Language: English
• ISBN-10: 0123743184
• ISBN-13: 978-0123743183
• Product Dimensions: 9 x 7.4 x 1.3 inches
• Based on: Versio6

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Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
CHAPTER 1 Getting Started 1
1.1 Introduction to Mathematica . . . . . . . . . . . . . . . . . . . . . 1
A Note Regarding Different Versions of
Mathematica . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Getting Started with Mathematica . . . . . . . . . . . . . . 3
Preview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Five Basic Rules of Mathematica Syntax . . . . . . . . . . . . . . 13
1.2 Loading Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2.1 Packages Included with Older Versions of
Mathematica . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2.2 Loading New Packages . . . . . . . . . . . . . . . . . . . . 15
1.3 Getting Help from Mathematica . . . . . . . . . . . . . . . . . . . 17
Mathematica Help . . . . . . . . . . . . . . . . . . . . . . 24
1.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
CHAPTER 2 Basic Operations on Numbers,
Expressions, and Functions 31
2.1 Numerical Calculations and Built-in Functions . . . . . . . . . . . 31
A Word of Caution . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2 Expressions and Functions: Elementary Algebra . . . . . . . . . . 39
Graphing Equations . . . . . . . . . . . . . . . . . . . . . . 71
2.3.4 Parametric Curves and Surfaces in Space . . . . . . . . . . 82
2.3.5 Miscellaneous Comments . . . . . . . . . . . . . . . . . . . 94
2.4 Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.4.1 Exact Solutions of Equations . . . . . . . . . . . . . . . . . 100
2.4.2 Approximate Solutions of Equations . . . . . . . . . . . . 110
2.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
CHAPTER 3 Calculus 117
3.1 Limits and Continuity . . . . . . . . . . . . . . . . . . . . . . . . . 117
3.1.1 Using Graphs and Tables to Predict Limits . . . . . . . . . 117
3.1.2 Computing Limits . . . . . . . . . . . . . . . . . . . . . . . 121
3.1.3 One-Sided Limits . . . . . . . . . . . . . . . . . . . . . . . . 123
3.1.4 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
3.2 Differential Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Derivative Test . . . . . . . . . . . . . . . . . . . . . . . . . 148
3.2.6 Applied Max/Min Problems . . . . . . . . . . . . . . . . . . 156
3.2.7 Antidifferentiation . . . . . . . . . . . . . . . . . . . . . . . 164
3.3 Integral Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
3.4 Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
3.5 Multivariable Calculus . . . . . . . . . . . . . . . . . . . . . . . . . 221
3.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
CHAPTER 4 Introduction to Lists and Tables 251
4.1 Lists and List Operations . . . . . . . . . . . . . . . . . . . . . . . 251
4.2 Manipulating Lists: More on Part and Map . . . . . . . . . . . . . 269
Using Graphics Primitives . . . . . . . . . . . . . . . . . . 277
4.2.2 Miscellaneous List Operations . . . . . . . . . . . . . . . . 283
4.3 Other Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 283
4.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
CHAPTER 5 Matrices and Vectors: Topics from
Linear Algebra and Vector Calculus 317
5.1 Nested Lists: Introduction to Matrices, Vectors, and
Matrix Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
5.1.1 Defining Nested Lists, Matrices, and Vectors . . . . . . . . 317
5.2 Linear Systems of Equations . . . . . . . . . . . . . . . . . . . . . 337
Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
5.3 Selected Topics from Linear Algebra . . . . . . . . . . . . . . . . 349
5.3.1 Fundamental Subspaces Associated withMatrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
5.3.2 The Gram–Schmidt Process . . . . . . . . . . . . . . . . . 351
5.3.3 Linear Transformations . . . . . . . . . . . . . . . . . . . . 355
5.3.4 Eigenvalues and Eigenvectors . . . . . . . . . . . . . . . . 358
5.3.5 Jordan Canonical Form . . . . . . . . . . . . . . . . . . . . 361
5.3.6 The QR Method . . . . . . . . . . . . . . . . . . . . . . . . 364
5.4 Maxima and Minima Using Linear Programming . . . . . . . . . . 366
5.4.1 The Standard Form of a Linear Programming
Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
5.4.2 The Dual Problem . . . . . . . . . . . . . . . . . . . . . . . 368
5.5 Selected Topics from Vector Calculus . . . . . . . . . . . . . . . . 374
5.6 Matrices and Graphics . . . . . . . . . . . . . . . . . . . . . . . . 415
5.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
CHAPTER 6 Applications Related to Ordinary and
Partial Differential Equations 435
6.1 First-Order Differential Equations . . . . . . . . . . . . . . . . . . 435
6.2 Second-Order Linear Equations . . . . . . . . . . . . . . . . . . . 457
6.2.1 Basic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 457
6.2.2 Constant Coefficients . . . . . . . . . . . . . . . . . . . . . 458
6.2.3 Undetermined Coefficients . . . . . . . . . . . . . . . . . . 464
6.2.4 Variation of Parameters . . . . . . . . . . . . . . . . . . . . 470
6.3 Higher-Order Linear Equations . . . . . . . . . . . . . . . . . . . . 472
6.3.4 Laplace Transform Methods . . . . . . . . . . . . . . . . . 481
6.3.5 Nonlinear Higher-Order Equations . . . . . . . . . . . . . . 492
6.4 Systems of Equations . . . . . . . . . . . . . . . . . . . . . . . . . 492
6.4.1 Linear Systems . . . . . . . . . . . . . . . . . . . . . . . . . 492
6.4.2 Nonhomogeneous Linear Systems . . . . . . . . . . . . . . 505
6.4.3 Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . 511
6.5 Some Partial Differential Equations . . . . . . . . . . . . . . . . . 532
6.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550
References 557
Index 559
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