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Abell M.L., Braselton J.P. — Mathematica by Example
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Название: Mathematica by ExampleАвторы: Abell M.L., Braselton J.P. Аннотация: Updated to be completely compatible with Mathematica version 3.0; designed for Mathematica beginners: a valuable addition to ANY Mathematica user's library; new applications from a variety of fields, especially biology, physics, and engineering, are included throughout the text; additional examples, especially in chapters one through six, should make this edition even more useful to instructors, students, business people, engineers, and other professionals using Mathematica on a variety of platforms; Step-by-step instructions for all Mathematica implementations; and CD-ROM Enclosed! All Mathematica input that appears in the book is included on the enclosed CD-ROM, which will operate on Macintosh, Windows 3.1.1 and 95, and UNIX machines with Mathematica 3.0 installed.
Язык: Рубрика: Руководства по программному обеспечению /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: revised editionГод издания: 1994Количество страниц: 523Добавлена в каталог: 11.12.2005Операции: Положить на полку |
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! (Factorial) 6 109 177 178 190 $DisplayFunction 58 61 62 80 325 438 445 446 449 454 457 460 469 475 483 484 486 487 489 492 494 496 502 508 $Version 2 $VersionNumber 2 % (Out) 150 266 270 271 && (And) 194 270 412 ' (Derivative) 110 111 113 119 (*...*) 319 (...) 4 25 26 43 84 103 * (Times) 4 11 24 40 41 + (plus) 24 305 ++ (Increment) 270 - (Minus) 24 305 -> (Rule) 42 43 44 49 51 52 135 137 144 182 211 218 234 361 431 434 437 439 444 446 458—460 477 . (dot) 304—310 312 319 322 325 329 330 362 / (Divide) 24 41 43 84 319 352 397 / . (ReplaceAll) 42 43 44 49 51 52 135 137 144 182 183 190 193 195—197 211 213 218 234 238 284 361 368 371 374 376 378 386 390 400 402 412 415 417 420 422 431 434 437 439 444 446 452—457 458 459 477 // (function application) 26—28 34 36 38 53 88 89 138 154 156 176 179 181 182 190 202 240 251 253 255 257 259 260 263 265 267 269 305 308 317 320 322 334 335 337 346 366 380 382 393 396 403 420 422 431 452 453 456 463 472—474 479 488 489 /; (Condition) 62—64 122 125 286 428 430 436 /@ (Map) 251 := (SetDelayed) 46 52 55 63 64 122 125 151 153 190 198 199 232 247 249 253 263 270 273 276 286 288 290 291 304 307 319 320 325 336 375 377 389 408 423 424 428 430 436 442 444 454 457 460 463 466—468 471—475 <= (LessEqual) 62—64 286 338—340 345 428 430 = (Set) 42 43 45 46 48 50 53 56 58 61 65 66 68 73 82 169 202 232 469 == (Equal) 84—89 92—96 116 120 127 128 135 137 138 140 142 145 146 163 164 173 181 183 210 217 224 225 310—312 329 365 370 372 378 386 393 400 406 412 416 422 445 447 453—457 493 >= (GreaterEqual) 62—64 122 340 345 436 >> (Put) 466 ? 8 11 12 46 56 180 220 ?? (Information) 10 67 70 75 @@ (Apply) 251 252 Abbreviated output (Short) 95 240 241 374 377 395 399 504 abs 29 Absolute value (Abs) 29 Absolute value (Abs), complex number 29 AccountingForm 267 268 Adding elements to lists 251 325 Algebra see SymbolicSum see Trigonometry Amortization 259 Animation 133 273 276 292 461 464 469 502 507 508 Annuity due 255 Apart 41 44 367 APPEND 251 AppendRows 314 appendto 251 320 325 Applied maxima and minima 134—141 Apply (@@) 250—252 Approximating arc length 166 Approximating area 149—156 162—166 Approximating double 219 220 Approximating eigenvalues 330 Approximating eigenvectors 330 Approximating integrals (NIntegrate) 161 162 Approximating numbers (N) 25—27 Approximating QR Method 336 337 Approximating solutions of a polynomial equation (NRoots) 88 89 90 91 Approximating solutions of a system of equations (FindRoot) 92 Approximating solutions of an equation (FindRoot) 88—99 Approximating solutions of an ordinary differential equation (NDSolve) 375—377 406—410 Approximating solutions to a system of differential equations (NDSolve) 451—457 Approximating triple 226 Approximating volume of solid of revolution 167—172 Arc length 166 ArcCos 28 34 35 ArcCosh 34 38 39 arccot 28 34 ArcCoth 34 arccsc 28 34 ArcLengthFactor 348 arcsec 28 ArcSech 34 arcsin 28 34 35 ArcSinh 34 38 arctan 28 34 35 180 ArcTanh 34 38 Area 162—164 Area, approximating 149—156 162—166 Area, polar coordinates 487—489 Arithmetic calculations 23—26 Array 230 231 Arrays 229—235 Arrays, computations with 304—308 arrays, defining 230 296—300 Arrays, extracting elements of (Part) 236—240 300—304 AspectRatio 59 60 62 64 497 498 Associated matrix of a linear transformation 322 Augmented matrix 313 AUTOMATIC 60 64 149 153 428 430 Autonomous system 450 Auxiliary equation 391 401 402 axes 59 71 73 87 93 143 146 149 153 201 215 216 223 243 351 365 369 460 475 AxesLabel 59 AxesOrigin 60 71 73 87 93 143 146 149 188 201 215 216 223 365 369 Bar charts 490 491 495 BarChart, BarLabels 490 BarChart, BarStyle 490 BarChart3D 495 496 BarLabels 490 BarStyle 490 Bessel function of the first kind (BesselJ) 472—474 Bessel function of the first kind (BesselJ), graphing 465 Bessel function of the first kind (BesselJ), zeros of 236 466—468 471 besselj 465 466 468 472—474 Bipolar 348 BOXED 351 475 501 502 505 508 BoxRatios 67 475 Calculus see DiracDelta see see see see cancel 41 44 334 367 403 433 cartesian 348 351 CartesianMap 482—484 Catalan 27 Cauchy-Euler equation 401 Cauchy-Euler equation, auxiliary equation 401 402 Center 444 450 Chain rule 112 Characteristic equation 326 391 Characteristic matrix 326 Characteristic polynomial 326 327 333 334 Characteristic value 326 CharacteristicPolynomial 326 327 Charts bar 490 491 495 Charts pie 491 492 Chop 331 448 472 473 Circumscribed rectangles 149 153 clear 45 46 63—65 ClipFill 479 Coefficient matrix 308 313 COLLECT 367 Column space 316 317 Column vector 299 300 CombinatorialSimplification Factorial (!) 6 109 177 178 190 compile 474 475 Compiled 449 453 454 456 457 CompiledFunction 475 Complete Selection 13 Complex conjugate 392 Complex-valued function image 482—484 ComplexExpand 54 180 393 ComplexMap, CartesianMap 482—484 ComplexMap, PolarMap 482—484 composition 52—54 Composition of functions, Composition 52—54 Composition of functions, Nest 52 54 55 Compound interest 252—254 Concave, down 119 Concave, up 119 Condition (/.) 62—64 122 125 286 428 430 436 Conic sections, circle 61 64 493 Conic sections, ellipse 494 495 Conic sections, graphing 61 64 493—495 Conic sections, hyperbola 493—495 Conic sections, parabola 494 495 Conjugate transpose 334 Conservative vector field 347 Conservative vector field, potential function 347 Constants, Catalan 27 Constants, E 27 Constants, EulerGamma 27 Constants, GoldenRatio 27 Constants, I 27 Constants, Infinity 6 27 101 108 154 156 174—179 181 183 Constants, Pi 27 ConstrainedMax 338 340 ConstrainedMin 338 339 341 345 ContourPlot, Axes 71 73 143 146 149 201 216 223 365 369 ContourPlot, AxesOrigin 71 73 143 146 149 201 216 223 365 369 ContourPlot, Contours 71 73 87 93 143 146 149 216 223 369 371 ContourPlot, ContourShading 71 72 73 87 93 143 146 149 201 216 223 365 369 371 ContourPlot, DisplayFunction 73 87 93 201 216 ContourPlot, Frame 71 73 143 146 149 216 223 365 369 ContourPlot, options 70 ContourPlot, PlotPoints 71 73 87 93 143 146 149 216 223 369 371 ContourPlot, PlotRange 73 216 371 contourplot3d 485 486 ContourPlot3D, ContourPlot3D 485 486 ContourPlot3D, Contours 485 contours 71 72 87 93 143 146 149 216 223 369 371 485 ContourShading 71 72 74 87 93 143 146 149 201 216 223 365 369 371 Convolution integral 435 Convolution theorem 435 CoordinatesFromCartesian 348 CoordinatesToCartesian 348 cos 12 28 31—33 248 cosh 36 37 Coslntegral 158 cot 28 COUNT 240 Critical points 116 210 Critical points, classification 209 237 238 Critical points, degenerate 209 211 Critical points, maximum 209 211 Critical points, minimum 209 211 Critical points, saddle 209 211 CrossProduct 348 Csc 28 cube 500 Curl 347 349 350 Curve-fitting 277—285 Cyclotomic 232 233 Cyclotomic polynomials 232 cylindrical 348 D 110—113 138 147 190 193 204—208 210 211 213 217 234 247 370 388 389 394 396 Dashing 55 58 60 106 108 124 125 127 163 164 166 188 191 192 Decreasing 119 Deferred annuity 258 259 defining arrays 296—300 Defining functions of a single variable 45—47 Defining functions of two variables 48 Defining functions, piecewise-defined 62—64 122 125 286 428 430 Defining functions, recursively defined 63 64 198 199 232 286 336 423 424 428 430 Defining functions, vector-valued 49 50 Defining functions, which remember the values computed 198 199 232 290 320 336 423 424 468 472—474 Defining lists 229—233 Defining matrices 296—300 Defining tables 296—300 Defining vectors 300 Degenerate critical point 209 Delayed evaluation (:=) 46 52 55 63 64 122 125 151 153 190 198 199 232 247 249 253 263 270 273 276 286 288 290 291 304 307 319 320 325 336 375 377 389 408 423 424 428 430 436 442 444 454 457 460 463 466—468 471—475 Denominator 42 44 104 Derivative 206—209 Derivative, applied maxima and minima 134—141 Derivative, calculating 110—112 Derivative, chain rule 112 Derivative, critical point 116 209—211 Derivative, definition 105 106 272 Derivative, graphing 123—125 131—134 Derivative, higher-order 112 113 Derivative, horizontal 115 126 127 Derivative, implicit function 142—147 Derivative, implicit function, tangent line 144 Derivative, inflection point 116 Derivative, Mean-Value theorem 128 Derivative, partial 203 204 207 Derivative, partial, higher-order 205 206 208 Derivative, product rule 112 Derivative, quotient rule 112 Derivative, Rolle's theorem 128 Derivative, tangent line 113 114 DET 304 305 327 389 396 Determinant 304 DiagonalMatrix 19 20 Difference quotient 105 106 272 Differential equations, Cauchy — Euler 401 Differential equations, constant coefficients 387 391 Differential equations, constant coefficients, characteristic equation 391 Differential equations, first-order, exact 369 Differential equations, first-order, homogeneous 366 Differential equations, first-order, linear 371 Differential equations, first-order, separable 364 Differential equations, fundamental set of solutions 390 Differential equations, general solution 391 Differential equations, homogeneous 387 390 391 394 Differential equations, Laplace transform 426—440 458—461 Differential equations, linear 371 387 Differential equations, nonhomogeneous 387 396 Differential equations, numerical solution (NDSolve) 375—377 406—410 451—457 Differential equations, partial 289—293 461—464 467—479 Differential equations, power series solution 192—198 411—426 Differential equations, second-order, constant coefficients 192 391—393 Differential equations, system 441—461 Differential equations, system, autonomous 450 Differential equations, system, numerical solution (NDSolve) 451—457 Differential equations, system, variation of parameters 446—449 Differential equations, variation of parameters 396—401 Dirac delta function 438 DiracDelta 438 439 DiracDelta, DiracDelta 438 439 DiracDelta, UnitStep 439 Direction 108 DiscreteMath see CombinatorialSimplification see DisplayFunction 58 61 62 65 73 76 78—80 87 93 114 120 125 131 132 133 144 188 201 216 273 276 278 280—282 284 288 293 325 380 438 443 445 446 449 454 455 457 460 464 465 469 475 483 484 486 487 489 494 496 502 508 Displaying several graphs 58 60—62 65 66 73 74 106 114 123—125 144 145 272—277 325 326 484 485 489 494 495 501—503 505 507 508 Distance formula 138 div 347 349 350 357 Divergence 347 Divergence theorem 356 DO 133 273 276 292 320 469 502 507 508 dodecahedron 500—502 dot (.) 304—310 312 319 322 325 329 330 362 Dot product 305 306 DotProduct 348 Double integral 218—220 Double integral, approximating (NIntegrate) 219 220 Double integral, polar coordinates 360—362 Double integral, volume 221—226 Double pendulum 458—461 Drop 251 320 431 DSOLVE 196 373 374 378 385 386 392—394 400 402 405 406 441 445 447 477 478 Dual problem 339 340 e 6 27 Eigensystem 326 329 330 442 444 Eigenvalues 326—331 334—337 442 444 452 453 456 Eigenvalues, approximating 329 330 Eigenvalues, QR method 334—337 Eigenvectors 326 329 330 Eigenvectors, approximating 330 ellipse 494 495 Ellipsoid 81 82 Elliptic 348 EllipticCylinder 348 Enter 2 24 Equations, approximating solutions of 88—99; see Differential equations
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