Mathematica by Example 5 Edition

front-matter-2017......Page 1
copyright-2017......Page 4
Preface......Page 5
1.1 Introduction to Mathematica......Page 7
 A Note Regarding Different Versions of Mathematica......Page 8
1.1.1 Getting Started with Mathematica......Page 9
 Preview......Page 19
 Five Basic Rules of Mathematica Syntax......Page 20
1.2 Getting Help from Mathematica......Page 21
 Mathematica Help......Page 27
2.1.1 Numerical Calculations......Page 33
2.1.2 Built-In Constants......Page 35
2.1.3 Built-In Functions......Page 36
 A Word of Caution......Page 39
2.2.1 Basic Algebraic Operations on Expressions......Page 41
2.2.2 Naming and Evaluating Expressions......Page 45
2.2.3 Defining and Evaluating Functions......Page 47
2.3.1 Functions of a Single Variable......Page 53
2.3.2 Parametric and Polar Plots in Two Dimensions......Page 66
2.3.3 Three-Dimensional and Contour Plots; Graphing Equations......Page 74
2.3.4 Parametric Curves and Surfaces in Space......Page 84
2.3.5 Miscellaneous Comments......Page 96
2.4.1 Exact Solutions of Equations......Page 101
2.4.2 Approximate Solutions of Equations......Page 110
3.1.1 Using Graphs and Tables to Predict Limits......Page 115
3.1.2 Computing Limits......Page 118
3.1.3 One-Sided Limits......Page 120
3.1.4 Continuity......Page 122
3.2.1 Definition of the Derivative......Page 125
3.2.2 Calculating Derivatives......Page 131
3.2.3 Implicit Differentiation......Page 135
3.2.4 Tangent Lines......Page 137
 Tangent Lines of Implicit Functions......Page 139
 Parametric Equations and Polar Coordinates......Page 141
3.2.5 The First Derivative Test and Second Derivative Test......Page 147
3.2.6 Applied Max/Min Problems......Page 155
3.2.7.1 Antiderivatives......Page 165
 u-Substitutions......Page 166
3.3.1 Area......Page 168
3.3.2 The Definite Integral......Page 174
3.3.4 Area......Page 180
 Parametric Equations......Page 184
 Polar Coordinates......Page 185
3.3.5 Arc Length......Page 186
 Parametric Equations......Page 187
 Polar Coordinates......Page 190
 Volume......Page 191
 Surface Area......Page 202
3.4.1 Introduction to Sequences......Page 204
3.4.2 Introduction to Infinite Series......Page 208
3.4.3 Convergence Tests......Page 211
3.4.4 Alternating Series......Page 215
3.4.5 Power Series......Page 216
3.4.6 Taylor and Maclaurin Series......Page 220
3.4.7 Taylor's Theorem......Page 224
3.4.8 Other Series......Page 235
3.5.1 Limits of Functions of Two Variables......Page 237
3.5.2 Partial and Directional Derivatives......Page 239
 Classifying Critical Points......Page 246
 Tangent Planes......Page 249
 Lagrange Multipliers......Page 252
3.5.3 Iterated Integrals......Page 255
 Area, Volume, and Surface Area......Page 256
 Triple Iterated Integrals......Page 262
4.1.1 Defining Lists......Page 265
4.1.2 Plotting Lists of Points......Page 270
4.2 Manipulating Lists: More on Part and Map......Page 283
4.2.1 More on Graphing Lists; Graphing Lists of Points Using Graphics Primitives......Page 292
4.3 Other Applications......Page 300
4.3.1 Approximating Lists with Functions......Page 301
4.3.2 Introduction to Fourier Series......Page 305
 Application: The One-Dimensional Heat Equation......Page 309
 Application: The Wave Equation on a Circular Plate......Page 312
4.3.3 The Mandelbrot Set and Julia Sets......Page 316
5.1.1 Defining Nested Lists, Matrices, and Vectors......Page 331
5.1.2 Extracting Elements of Matrices......Page 338
5.1.3 Basic Computations with Matrices......Page 340
5.1.4.1 Basic Operations on Vectors......Page 345
5.1.4.2 Basic Operations on Vectors in 3-Space......Page 346
5.2.1 Calculating Solutions of Linear Systems of Equations......Page 353
5.2.2 Gauss-Jordan Elimination......Page 357
5.3.1 Fundamental Subspaces Associated with Matrices......Page 364
5.3.2 The Gram-Schmidt Process......Page 366
5.3.3 Linear Transformations......Page 370
 Application: Rotations......Page 371
5.3.4 Eigenvalues and Eigenvectors......Page 372
5.3.5 Jordan Canonical Form......Page 376
5.3.6 The QR Method......Page 379
5.4.1 The Standard Form of a Linear Programming Problem......Page 381
5.4.2 The Dual Problem......Page 383
 Application: A Transportation Problem......Page 386
5.5.1 Vector-Valued Functions......Page 389
5.5.2 Line Integrals......Page 400
5.5.3 Surface Integrals......Page 403
5.5.4 A Note on Nonorientability......Page 407
5.5.5 More on Tangents, Normals, and Curvature in R3......Page 420
5.6.1 Manipulating Photographs with Built-In Functions......Page 430
5.6.2 Manipulating Photographs by Viewing Them as a Matrix or Array......Page 433
6.1.1 Separable Equations......Page 445
6.1.2 Linear Equations......Page 452
6.1.2.1 Application: Free-Falling Bodies......Page 456
6.1.3 Nonlinear Equations......Page 459
6.1.4 Numerical Methods......Page 462
6.2.1 Basic Theory......Page 466
6.2.2 Constant Coefficients......Page 467
 Application: Harmonic Motion......Page 470
6.2.3 Undetermined Coefficients......Page 472
6.2.4 Variation of Parameters......Page 478
6.3.1 Basic Theory......Page 481
6.3.2 Constant Coefficients......Page 482
6.3.3 Undetermined Coefficients......Page 484
 Variation of Parameters......Page 488
6.3.4 Laplace Transform Methods......Page 490
 Application: The Convolution Theorem......Page 495
 Application: The Dirac Delta Function......Page 498
6.3.5 Nonlinear Higher-Order Equations......Page 500
 A(t) Constant......Page 501
 Application: The Double Pendulum......Page 509
6.4.2 Nonhomogeneous Linear Systems......Page 515
6.4.3 Nonlinear Systems......Page 519
 Linearization......Page 522
6.5.1 The One-Dimensional Wave Equation......Page 543
6.5.2 The Two-Dimensional Wave Equation......Page 549
6.5.3 Other Partial Differential Equations......Page 559
Bibliography......Page 563
Index......Page 564