The MAPLE book

Frank Garvan1584882328, 9781584882329, 9781420035605

Maple is a very powerful computer algebra system used by students, educators, mathematicians, statisticians, scientists, and engineers for doing numerical and symbolic computations. Greatly expanded and updated from the author’s MAPLE V Primer, The MAPLE Book offers extensive coverage of the latest version of this outstanding software package, MAPLE 7.0The Maple Book serves both as an introduction to Maple and as a reference. Organized according to level and subject area of mathematics, it first covers the basics of high school algebra and graphing, continues with calculus and differential equations then moves on to more advanced topics, such as linear algebra, vector calculus, complex analysis, special functions, group theory, number theory and combinatorics. The Maple Book includes a tutorial for learning the Maple programming language. Once readers have learned how to program, they will appreciate the real power of Maple. The convenient format and straightforward style of The MAPLE Book let users proceed at their own pace, practice with the examples, experiment with graphics, and learn new functions as they need them. All of the Maple commands used in the book are available on the Internet, as are links to various other files referred to in the book. Whatever your level of expertise, you’ll want to keep The MAPLE Book next to your computer.

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Table of contents :
c2328fm……Page 1
The MAPLE BOOK……Page 2
PREFACE……Page 5
CONTENTS……Page 7
APPENDIX C: FURTHER READING……Page 0
1.1 Starting a MAPLE session……Page 15
1.3 Basic syntax……Page 17
1.5 Help……Page 19
1.6 A sample session and context menus……Page 21
1.7 Palettes……Page 24
1.8 Spreadsheets……Page 26
1.9 Quitting MAPLE……Page 28
2.1 Exact arithmetic and basic functions……Page 29
2.2 Floating-point arithmetic……Page 30
3.1.2 Expanding an expression……Page 32
3.1.3 Collecting like terms……Page 33
3.1.4 Simplifying an expression……Page 34
3.1.5 Simplifying radicals……Page 35
3.1.6 Working in the real domain……Page 36
3.1.7 Simplifying rational functions……Page 38
3.1.8 Degree and coefficients of a polynomial……Page 40
3.1.10 Restoring variable status……Page 41
3.2.1 Left- and right-hand sides……Page 42
3.2.3 Finding approximate solutions……Page 43
3.3.1 Complete integer factorization……Page 44
3.3.3 Gcd and lcm……Page 45
3.3.5 Integer solutions……Page 46
3.4 Unit conversion……Page 47
3.5.1 Degrees and radians……Page 49
3.5.2 Trigonometric functions……Page 50
3.5.3 Simplifying trigonometric functions……Page 51
4.1 Sequences……Page 53
4.2 Sets……Page 54
4.3 Lists……Page 55
4.5 Arrays……Page 56
4.6 Data conversions……Page 57
4.7 Other data types……Page 58
5.1 Defining functions……Page 59
5.3 Summation and product……Page 60
5.4 Limits……Page 62
5.5 Differentiation……Page 63
5.6 Extrema……Page 64
5.7 Integration……Page 66
5.7.1.1 Substitution……Page 68
5.7.1.3 Partial fractions……Page 69
5.9 The student package……Page 70
6.1 Two-dimensional plotting……Page 78
6.1.2 Parametric plots……Page 80
6.1.3 Multiple plots……Page 81
6.1.4 Polar plots……Page 82
6.1.5 Plotting implicit functions……Page 83
6.1.6 Plotting points……Page 84
6.1.7 Title and text in a plot……Page 85
6.1.8 Plotting options……Page 87
6.1.10 Other plot functions……Page 90
6.2 Three-dimensional plotting……Page 96
6.2.2 Multiple plots……Page 99
6.2.3 Space curves……Page 100
6.2.4 Contour plots……Page 101
6.2.5 Plotting surfaces defined implicitly……Page 102
6.2.7 Three-dimensional plotting options……Page 103
6.2.8 Other three-dimensional plot functions……Page 106
6.3 Animation……Page 110
7.1 The MAPLE procedure……Page 112
7.1.1 Local and global variables……Page 113
7.2 Conditional statements……Page 114
7.2.1 Boolean expressions……Page 116
7.3 The “for” loop……Page 118
7.4 Type declaration……Page 122
7.5 The “while” loop……Page 123
7.6 Recursive procedures……Page 126
7.7 Explicit return……Page 128
7.8 Error statement……Page 129
7.9 args and nargs……Page 133
7.10.1 Formatted output……Page 134
7.10.2 Interactive input……Page 136
7.10.4 Reading data from a file……Page 138
7.10.6 Writing and saving to a file……Page 140
7.11 Generating C and Fortran code……Page 142
7.13 The MAPLE interactive debugger……Page 143
7.14.1 Packages as tables……Page 146
7.14.2 Modules for packages……Page 148
7.15 Answers to programming exercises……Page 152
8.1 Solving ordinary differential equations……Page 157
8.1.2 Initial conditions……Page 159
8.2.1 odeadvisor……Page 161
8.2.2 Integrating factors……Page 164
8.2.3 Direction fields……Page 165
8.3 Numerical solutions……Page 167
8.4.2 Variation of parameters……Page 169
8.4.3 Reduction of order……Page 170
8.5 Series solutions……Page 171
8.5.1 The method of Frobenius……Page 172
8.6 The Laplace transform……Page 174
8.6.1 The Heaviside function……Page 175
8.6.2 The Dirac delta function……Page 178
8.7.1 DE plotting functions……Page 179
8.7.3 DE manipulation……Page 180
8.7.5 Differential operators……Page 181
8.7.7 Simplifying DEs and rifsimp……Page 182
9.1 Vectors, Arrays, and Matrices……Page 183
9.1.1 Matrix and Vector entry assignment……Page 185
9.1.2 The Matrix and Vector palettes……Page 187
9.1.3 Matrix operations……Page 188
9.1.4 Matrix and vector construction shortcuts……Page 190
9.1.5 Viewing large Matrices and Vectors……Page 192
9.2 Matrix context menu……Page 194
9.2.1 The Export As submenu……Page 195
9.2.4 The Solvers submenu……Page 196
9.2.5 The Conversions submenu……Page 197
9.2.6 The In-place Options submenu……Page 198
9.3 Elementary row and column operations……Page 199
9.4 Gaussian elimination……Page 201
9.5 Inverses, determinants, minors, and the adjoint……Page 202
9.6.2 Constant matrices and vectors……Page 203
9.6.3 Diagonal matrices……Page 204
9.6.6 Hilbert matrices……Page 205
9.6.8 Identity matrix……Page 206
9.6.10 Random matrices and vectors……Page 207
9.6.12 Vandermonde matrices……Page 210
9.7 Systems of linear equations……Page 211
9.8 Row space, column space, and nullspace……Page 215
9.9 Eigenvectors and diagonalization……Page 217
9.10 Jordan form……Page 218
9.11.1 The dot product and bilinear forms……Page 219
9.11.2 Vector norms……Page 220
9.11.3 Matrix norms……Page 221
9.12 Least squares problems……Page 222
9.13 QR-factorization and the Gram-Schmidt process……Page 224
9.14 LU-factorization……Page 226
9.15 Other LinearAlgebra functions……Page 228
9.16 The linalg package……Page 239
9.16.1 Matrices and vectors……Page 240
9.16.2 Conversion between linalg and LinearAlgebra……Page 241
9.16.3 Matrix operations in linalg……Page 243
9.16.4 The functions in the linalg package……Page 244
10.1.1 Vector operations……Page 247
10.1.2 Length, dot product, and cross product……Page 248
10.1.3 Plotting vectors……Page 249
10.2.1 Lines……Page 251
10.2.2 Planes……Page 252
10.3.1 Differentiation and integration of vector functions……Page 254
10.3.2 Space curves……Page 255
10.3.2 Tangents and normals to curves……Page 257
10.3.3 Curvature……Page 260
10.4 The gradient and directional derivatives……Page 261
10.5.1 Local extrema and saddle points……Page 262
10.5.2 Lagrange multipliers……Page 264
10.6.1 Double integrals……Page 266
10.6.2 Triple integrals……Page 267
10.6.3 The Jacobian……Page 268
10.7.2 Divergence and curl……Page 269
10.7.3 Potential functions……Page 270
10.8 Line integrals……Page 271
10.9 Green’s theorem……Page 272
10.10 Surface integrals……Page 273
10.10.1 Flux of a vector field……Page 275
10.10.2 Stoke’s theorem……Page 277
10.10.3 The divergence theorem……Page 278
11.1 Arithmetic of complex numbers……Page 280
11.2 Polar form……Page 282
11.3 nth roots……Page 283
11.4 The Cauchy-Riemann equations and harmonic functions……Page 284
11.5 Elementary functions……Page 286
11.6 Conformal mapping……Page 288
11.7 Taylor series and Laurent series……Page 291
11.8 Contour integrals……Page 295
11.9 Residues and poles……Page 296
12.1 Opening an existing worksheet……Page 298
12.2 Saving a worksheet……Page 299
12.3 Opening a MAPLE text file……Page 300
12.4 Exporting worksheets and LaTeX……Page 301
13.1 Adding text……Page 303
13.3 Adding titles and headings……Page 304
13.5 Cutting and pasting……Page 305
13.6 Bookmarks and hypertext……Page 306
14.1.1 Two-dimensional plot objects……Page 309
14.1.2 Three-dimensional plot objects……Page 313
14.1.3 Transformation of plots……Page 319
14.2 The geometry package……Page 326
14.3.1 Regular polyhedra……Page 328
14.3.2 Quasi-regular polyhedra……Page 331
14.3.3 The Archimedean solids……Page 332
15.1 Overview of mathematical functions……Page 336
15.2 Bessel functions……Page 339
15.3 The Gamma function……Page 340
15.4 Hypergeometric functions……Page 344
15.5 Elliptic integrals……Page 346
15.6 The AGM……Page 348
15.7 Jacobi’s theta functions……Page 349
15.8 Elliptic functions……Page 350
15.9 The Riemann zeta-function……Page 352
15.10 Orthogonal polynomials……Page 353
15.11.1 Fourier transforms……Page 354
15.11.2 Hilbert transform……Page 356
15.11.3 Mellin transform……Page 357
15.12 Fast Fourier transform……Page 358
15.13 Asymptotic expansion……Page 360
16.1 Introduction……Page 361
16.2 Data sets……Page 362
16.3.1 Describing the center of a data set……Page 363
16.3.2 Describing the dispersion of a data set……Page 365
16.3.3 Describing characteristics of a data set……Page 369
16.4 Transforming data……Page 374
16.5 Graphical methods for describing data……Page 378
16.5.1 Histogram……Page 380
16.5.2 Box plot……Page 382
16.5.3 Scatter plot……Page 384
16.7 ANOVA……Page 390
16.8.1 Evaluating distributions……Page 391
16.8.2 Generating random distributions……Page 393
CHAPTER 17: OVERVIEW OF OTHER PACKAGES……Page 394
17.1 Finite fields……Page 395
17.2 Polynomials……Page 398
17.3 Group theory……Page 401
Cartesian products……Page 406
Combinations……Page 407
Partitions and compositions……Page 408
Sets……Page 409
Other functions……Page 410
Undirected graphs……Page 412
Weighted graphs and flows……Page 414
17.4.3 The combstruct package……Page 415
Divisors and factors……Page 416
Primes……Page 417
mod n……Page 418
Continued fractions……Page 421
Other functions……Page 422
17.5.3 p-adic numbers……Page 424
17.6 Numerical approximation……Page 427
17.7.2 The codegen package……Page 428
17.7.3 The diffalg package……Page 429
17.7.6 The finance package……Page 430
17.7.8 The geometry package……Page 431
17.7.9 The geom3d package……Page 434
17.7.10 The Groebner package……Page 435
17.7.12 The LREtools package……Page 436
17.7.13 The Ore_algebra package……Page 437
17.7.15 The powseries package……Page 438
17.7.18 The Slode package……Page 439
17.7.21 The tensor package……Page 440
17.8.3 The LinearFunctionalSystems package……Page 442
17.8.5 The ListTools package……Page 443
17.8.8 The RandomTools package……Page 444
17.8.11 The Sockets package……Page 445
17.8.13 The StringTools package……Page 446
17.8.14 The Units package……Page 447
17.8.15 The XMLTools package……Page 448
The MAPLE Application Center……Page 450
Interesting URLs……Page 453
APPENDIX B: GLOSSARY OF COMMANDS……Page 455
APPENDIX C: FURTHER READING……Page 465
REFERENCES……Page 467