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Index

AC circuit, 124 acceleration

due to gravity (g), 93 radial, 384 tangential, 384

Adams, Henry, 78, 318 adenosine diphosphate, 522 advertising, 106 air resistance, 21 Ali, Muhammad, 461, 715 aliasing, 623 Alice: an economics student, 119 Allen, Woody, 86 alpha decay, 250 Alvarez, A., 647 Anderson-May model, 512 angle of incidence, 145 angle of refraction, 145 Angstrom (A), 27, 481 anharmonic force, 318 annulus, 659 antikink, 7 40 Antonius, Marcus Aurelius, 284 area integral, 158 Arendt, Hannah, 588 Aristotle, 144 arms expenditures, 503 arms race model, 504 associative law, 170 Astronomer Royal, 350 atomic layer, 256 attractor, 445

butterfly, 604 San Marco, 591 strange, 602

Aussie barbecue, 651 autonomout> ODE, 263, 280 autonomous system

three-dimensional, 322

average unit cost, 138 Avogadro's number, 198

estimate of, 199

baby Justine, 13 backward Euler method, 526 Bacon, Francis, 9 Bacon, Roger, 144 bactericide, 80 bad bird, 402 badminton bird, 21 baleen whale, 520 band-width theorem, 699 bandwidth limited, 623 bargaining models, 117 Barnsley's fern, 583 beats, 56 Benny Boffo: realtor, 104, 107, 437 BEP, 138 Bergman, Ingrid, 532 Bernoulli brothers, 54 7 Bernoulli equation, 400 Bernoulli trial, 237, 251 Bernoulli, Daniel, 376, 474 Bernoulli, Jacob, 237 Bernoulli, John, 474 Bessel equation, 370 Bessel function, 375, 378

first kind, 371, 661, 682 modified, 387 second kind, 371, 661, 682 second-order, 684

Bessel zeros, 371 best-fit straight line, 59 Beveridge, William, 391 Bhagavad Gita, 659 bifurcation, 628

pitchfork, 630 tangent, 630

754

bifurcation diagram, 628 Big Bad Bog, 461 bikinis, 81 binomial coefficient, 237, 251 binomial distribution, 238, 251, 255 binomial function, 46 binomial probability function, 237 bipolar coordinates, 646 Black Friday, 90 black soliton, 711 Bloch wall, 707 Bloch, Felix, 708 blood alcohol level, 80 blood C02 , 4 73 Blowin' in the wind, 205 blue whales, 413 board foot, 36 Boffo Trucking Company, 107 Bogart, Humphrey, 532 Boltzmann constant, 198 bombs versus schools, 114 bone marrow, 4 71 bone strength, 40 Bouguer, Pierre, 414 bouncing ball, 502 boundary condition, 648, 652, 661,

666,669,676,684,692,693 Boussinesq's equation, 711, 719 Brachiosaurus, 71

heart rate, 76 brachistochrone, 54 7 brain teaser, 179 brain weight, 93 break-even point, 136 bridge design

minimizing costs, 139 bright soliton, 710 British Open, 437 Brobdingnag, 39 Brown, Robert, 197 Brownian motion, 197 BS model, 117 bumble bee, 178 bungee cord, 376 bungee jumping, 376 Burger's equation, 711, 722 butterfly effect, 602

INDEX

C02 molecular vibrations, 483 Calhoun, Charles, 624 calorie, 154 Camus, Albert, 730 Cantor set, 581, 620

middle-half, 583 middle-third, 583

capacitor, 124 charging a, 338

capacity dimension, 579 Capp, Al, 552 car prices, 106 Carroll, Lewis, 38, 61, 121, 325, 369,

438, 503, 636, 724 Carroll, Lewis , 261 carrying capacity, 487 Cartesian coordinates, 181 Carthage, 548 CAS, 1 Casablanca, 532, 672 Cassini gap, 592 Castle, Helen, 156 catenary, 551 cellular automata, 608 center, 267 center of gravity, 129 center of mass, 156, 160, 233

of charge distribution, 166 of semicircular plate, 165 of solid tetrahedron, 166 of triangular plate, 165

centripetal force, 391 chain reaction, 659 Chandrasekhar, S., 520 chaos, 323, 494, 627 chaotic attractor, 635 characteristic directions, 738, 7 40 characteristic matrix, 4 78 charge density, 182 charge distribution

center of mass, 166 Chebyshev polynomials, 469 chemical reaction, 525 Cheops (Khufu), 150 Chesterton, G. K., 414 chi-square, 63, 83, 101 chimpanzee

brain size, 33

INDEX

brain volume, 76 Chinese proverb, 209 Christie, Agatha, 231 Churchill, Winston, 4 71 Cioran, E. M., 734 circuit

tunnel diode oscillator, 445 circulation, 188 Cleveland's population, 90 closed path, 188 closed volume, 191 cloverleaf orbits, 358 cobweb diagram, 494 Colleen's restaurant job, 19 Colleen: MBA graduate/artist, 14,

19, 70, 81, 179, 236, 243, 376, 432

column vector, 476 competition

for food, 292 interspecific, 484 intraspecific, 484

compound interest, 28 computer algebra, 1, 113 Comte de Buffon, 229 concatenation operator, 157, 177, 192,

210,241,246,252,286,287, 289,290,312,486,496,507, 578, 618, 740

Confucius, 527 conservative field, 181, 187, 646 consumer prices, 14 consumption matrix, 46 continuity equation, 537 control parameter, 618 control rods, 659 coordinates

bipolar, 646 bispherical, 646 Cartesian, 669 cylindrical, 646 elliptic, 646 non-Cartesian, 643 orthogonal, 646 paraboloidal, 646 plane polar, 383 prolate spheroidal, 646 spherical, 646

spherical polar, 666 corn output, 61 Corn Palace, 61 corn yield, 69 Coulomb potential, 13 Coulomb's law, 132, 180 count number, 257 Cowper, William, 212

755

CPU time, 202, 203, 207, 210, 213, 222,227,228,230,236,242, 255,259,516-518,524,574, 577,585,590,600,605,627, 630, 635, 726

Crichton, Michael, 407 critical condition, 659 critical damping, 278 critical mass, 664 critical reflection, 149 cross product, 166, 169 crossed fields, 362 cubic map, 631 cubit, 157 cumulative density function, 241 cumulative probability, 240 cumulative probability distribution,

247 cumulative sales, 81 curl, 181, 646 cyclosorus fern, 587 cylinder

temperature distribution in, 666 cylindrical coordinates, 189

da Vinci, Leonardo, 292 damped SHO equation, 27 4 dart method, 250 Darwin, Charles, 484 data, 13 data storage matrices, 46 DC circuit, 121, 127 De Morgan, Augustus, 576 de Vries, G., 716 deer antlers, 62, 69 Delsaux, 197 Descartes, Rene, 144 devotion, 503 diamond-shaped mesh, 738 difference approximation

756

backward, 515 central, 515, 727, 734 finite, 513 forward, 515, 724, 732 fourth derivative, 516 second derivative, 516

difference equation first-order, 460 homogeneous, 460 inhomogeneous, 460 linear, 459 second order, 475 second-order, 460 third-order, 470

differential cross section, 96 diffusion, 199 diffusion coefficient, 648 diffusion equation, 641

modified, 692 dimension

capacity, 579 fractal, 579, 587

dimensional scaling, 36 dimensionless variable, 293 dinosaur, 71 Diogenes, 243 dipole field, 646 dipole-dipole interaction, 424 Dirty Bird, 128 discrete cumulative probability, 238 discrete Fourier transform, 623

inverse, 624 disease

periodic cycles of, 512 Disneyland, 414 dispersion, 703 display, 496 disposable income, 65 divergence, 181, 646 divergence theorem, 191 domain wall, 719 dot product, 166 Dot Product: Vectoria's mother, 166 Douady's rabbit, 590 double integral, 157, 190 double-well potential, 319 Dow Jones Index, 86 Doyle, Arthur Conan, 332

drug concentration, 118 drumhead

circular, 685 Duffing's equation, 618, 625

hard spring, 317 inverted, 317 soft spring, 317

Dumas, Alexander, 445 Dylan, Bob, 205

eardrum

INDEX

tympanic membrane, 418 vibrating, 431

eardrum equation, 300 eardrum model, 422 Earl of Chesterfield, 527 earthquake

Richter scale, 119 San Francisco, 119

eccentricity, 356 ecology, 484 economic health, 28 Eddington, Arthur, 398 Edelstein-Keshet, Leah, 471 effectiveness index, 116 eh, 114 eigenfrequencies, 58, 379, 394, 475 eigenfunction, 369 eigenvalue, 369, 476 eigenvectors, 483 Einstein equation, 198, 199 Einstein, Albert, 43, 47, 197, 229,

250, 402, 606, 686 electric dipole, 646 electric dipole potential, 52 electric field, 52 electric field vector, 181 electric force, 180, 362 electric potential, 13, 655

Coulomb, 13 Lennard-.Jones, 13, 424

electric quadrupole potential, 52 electrocardiograph, 358 electron volts, 27 electrostatic potential, 45, 181 ellipse, 356 elliptic cylinder

temperature distribution in, 666

INDEX

elliptic function amplitude of, 430 Jacobian, 420, 430

elliptic integral complete, 423 incomplete, 429

elliptic sine function, 430 Ellis, Havelock, 608 Emerson, Ralph Waldo, 712 envelope of safety, 140, 141 enzyme reaction, 414 epileptic seizures, 498 equation

baleen whale, 520 Boussinesq's, 711, 719 chemical reaction, 525 differential-difference, 4 75 diffusion, 641 Einstein, 198 Euler-Lagrange, 541, 548, 553 fish harvesting, 524 forced glycolytic, 628 Gompertz's, 413 heat diffusion, 648 Klein-Gordon, 733 Laplace's, 641, 651, 667 Malthus's, 407 Michaelis-Menton, 414 modified diffusion, 692 Navier-Stokes, 601 neutron diffusion, 660 PDE

general second-order, 738 Poisson's, 641 rabbits-foxes, 516 Schrodinger, 540, 641 Sel'kov model, 522 sine-Gordon, 738 Sturm-Liouville, 369 Vander Pol, 520 von Bertalanffy, 414 wave, 641, 672 white dwarf, 520 wire, 696

equation of state Van der Waals, 53

equipartition of energy, 199 equipotential surface, 183

equipotentials, 670 Erehwon, 543

aardwolves, 279 dress design, 541 eh, 114 Enon on the hill, 51 gnats, 461 gnus, 466 gnus and sung, 308

757

harvesting bandicoots, 466 Institute of Technology, 268, 655 military problem, 144 swamp fever, 463 tourists, 28 Trebla Nietsnie, 114

Erlenmeyer flask, 407 erosion, 56 error function, 160, 687 Euler algorithm, 517 Euler-Lagrange equation, 541, 548,

553 Excalibur, 647, 724 excitation

parametric, 444 explicit scheme, 724, 732

diffusion equation, 725 exponential function, 4 7 exponential model, 78, 80

Faraday, Michael, 701 fast Fourier transform (FFT), 624 Feigenbaum constant, 498 Ferdinand, Archduke Francis, 503 Fermat's principle, 33, 148, 547 Fermi, Enrico, 474 Fermi-Pasta-Ulam, 474 fern

Black Spleenwort, 583 cyclosorus, 587 fishbone, 587

ferromagnet, 703, 719 ferromagnetic domain, 707 Fibonacci, 467 Fick's law, 338, 692 fields, crossed, 362 finite difference approximation, 513,

514 fir tree yield, 36

758

first iterate map, 495 fish harvesting, 524 fishbone fern, 587 fixed point, 265

stable, 507 unstable, 508

Flamsteed, John, 350 floating point number, 66, 72, 78 flu epidemic, 413, 470 fluid velocity vector, 666 focal/spiral point, 267, 275 Fourier cosine series, 560, 569 Fourier series, 55, 359, 532, 559, 649 Fourier sine series, 560, 568 Fourier sine transform, 686, 689 Fourier sum, 650 Fourier transform, 622, 697

inverse, 697 fractal, 579, 590 fractal dimension, 579, 587, 604, 620

box counting, 584 Sierpinski's gasket, 582

fractal fern, Barnsley's, 585 Frank N. Stein, 358 free body diagram, 129, 433 free edges, 680 free space, 182 Freeman Dyson, 655 frequency

Nyquist, 622 sampling, 622

friction, 384 Friedman, Milton, 107 Frobenius series, 370 fructose-6-phosphate, 522 Fry, Christopher, 93 fundamental numbers

evaluation of, 250 fur catches, 291

Gabor, ZsaZsa, 738 Galilei, Galileo, 166 Gardner, Ed, 562 Gardner, John, 181 Gause, 409 Gauss's law, 182, 193 Gauss's theorem, 187 Gauss, Karl Friedrich, 548, 688

INDEX

Gaussian probability distribution, 240, 253

geodesic, 547 geometric similarity, 36, 39 Gibbs phenomena, 564, 565 Gilbert, William S. , 261 Glitz department store, 14, 81, 97,

236 glycolysis, 522 gnats, 461 GNP, 65, 503 gnus, 329 gnus and sung, 308 Golden Fleece, 414 golf ball

drag on, 432 lift on, 432 spin, 433

golf ball model, 432 Gompertz's law, 413 Gore, Al, 696 Gouy, M., 197 gradient, 181 gradient operator, 666

symbol for, 48 Grammy Awards, 205 Graphical Command

II, 157, 177, 192, 210, 241, 246, 252,286,287,289,290,312, 486,496,507,578,618,740

animate, 54, 381, 395, 530, 535, 650,675,694,699,718,721

animate3d, 57, 665, 680, 684 circle, 457, 599 contourplot3d, 161 coordplot, 644 DEplot, 297, 305, 342 DEplot3d, 315, 713 dfieldplot, 269 display, 67, 73, 79, 88, 96, 103,

161,241,275,277,296,299, 304,320,329,334,342,344, 371,385,389,412,436,443, 450,457,482,496,530,534, 539,563,574,576,579,585, 600,604,606,619,629,658, 670, 707, 727, 730, 737

fieldplot, 189, 367, 670

INDEX

fieldplot3d, 184, 191 implicitplot, 309, 546, 658, 670 implicitplot3d, 184 listcontplot, 45 listcontplot3d, 45 listdensityplot, 45, 614 loglogplot, 34 matrixplot, 44 odeplot,368,436,443,519,524,

603, 604, 606 phaseportrait, 270, 275, 276, 288,

312,319,411,449,450,705, 709

plot, 66, 72, 79, 83, 86, 95, 117, 135, 137, 142, 151, 157, 159, 204,220,225,241,246,254, 286,296,303,305,311,318, 328,334,344,361,371,373, 400,410,417,424,426,430, 472,496,530,534,539,545, 550,557,562,570,578,586, 626,634,637,726,729,733, 735, 741

plot3d, 103, 182, 192, 590, 654 PLOT3D(POLYGONS), 192 pointplot, 208, 389, 481, 496,

574, 576, 584 pointplot3d, 103, 210, 213, 502,

507, 518, 603 polarplot, 178, 357, 385 polygonplot, 208, 578, 585 REplot, 462, 465, 468, 486 scatterplot, 15, 62, 82, 95, 204,

238,239,246,247,258,480, 493

spacecurve, 116, 174, 346, 364, 489, 509, 511, 523

sphereplot, 443 textplot, 136, 137, 157, 161, 188,

277,290,303,313,371,373, 496, 706, 710

textplot3d, 162, 192, 211, 213 graphs

functions of, 11 the pictures of science, 11

gravitational constant, 93 Great Bear Lake, 691 great circle, 547

Great flu epidemic, 19, 85 Great pyramid, 150 Greg's quarter-pounder, 349 ground state energy, 120 grounded, 655 Gulliver's Travels, 39

half-wave rectifier, 565 Halley's comet, 350 Halley, Edmund, 350 Hammerstein II, Oscar, 144 Hancock, Tony, 615 hard spring, 300 hard spring equation, 265 harmonics, 627 Harriet Beacher Stowe, 672 harvesting

blue whales, 413 Hathaway, 452 heart, modeling the, 358 heat diffusion, 648 heat diffusion equation, 528 heat loss, 39

759

Heather: pre-Med student, 33, 71, 128,134,407,432,464,473

heating oil consumption, 70 helix, 175 Heller, Joseph, 65 Helmholtz, Heinrich, 418 Heraclitus, 186 Herbert, George, 220 Herodotus, 150 Herschel, John F. W. , 261 Hexagonium chip, 220 higher-order singular point, 282, 301 HilArious Nerd, 543 histogram, 44 histogram bins, 255 hole in one, 437 Holtz, Lou, 301 homogeneous ODE, 326 Hooke's law, 419, 426, 474 Horace, 629 Hubbard, Elbert, 643 Hudson's Bay Company, 291 Hudson, Rock, 666 Hugo: eccentric scientist, 358, 659,

666

760

human surface area, 42 Hungry Heifer Steak House, 19, 104,

107 Huxley, Thomas, 11, 611 hydrogen atom motion, 27 hyperbolic function, 22 hypersphere, volume of, 231

ice wine, 243 ideal gas constant, 198 ideal gas law, 12 impedance, 124 implicit Euler method, 526 implicit method, 526 implicit solution, 429 importance sampling, 224, 228 imported cars, 91 impressionism, 587 Inca ruins, 150 inclined plane, 133 inductance, 124 inert gas crystals, 424 infectious disease, 301, 338 inflation, 65

correcting for, 13 inflection point, 29, 152 inhomogeneous ODE, 326 initial condition, 67 4, 676, 684 initialization, 735, 740 integral, mass, 233 integration

Glenshaw-Curtis quadrature, 216 double, 234 double integral, 157 error, 216 Monte Carlo, 215, 223, 228 Monte Carlo error, 216 multidimensional, 215 rectangular rule, 215 Simpson's rule, 215 trapezoidal rule, 215 triple integral, 157

Intel chips, 81 Internet, 90 interspecific competition, 484 intraspecific competition, 484 inverse cube law, 358 inverse Fourier transform, 622

inverse square law, 350 iron core inductor, 291 iron sphere

INDEX

temperature distribution in, 672 irrotational field, 185

Jacobian elliptic function, 420, 430 James, William, 268 Jaws 2, 341 Jeans, Sir James, 20 Jemez Mountain Bike Challenge, 382 Jennifer: applied mathematician, 38,

314,318,391,432,473,573 Johnson, Samuel, 536, 651, 704 Jolly Roger, 414 Jonathan Swift, 39 Julia set, 588 Julia, Gaston, 588 Jupiter, 356

KdV equation, 702, 716, 734 Kelvin, Lord, 548 Kepler's third law, 13, 76, 597 Kerr medium, 703 Keynes, John Maynard, 134 Khrushchev's secret purge, 80 kink, 719, 740 Kipling, Rudyard, 150, 499 Kirchhoff's current rule, 446 Kirchhoff's potential rule, 274, 291 Kirchhoff's rules, 122 Kirchhoff, Gustav Robert, 121 Klein-Gordon equation, 731 knuckleball, 20 Koch curve, 582 Kodak, 326 Koestler, Arthur, 71 Kop, 200 Koran, 56 Korteweg, D. J., 716 Kruskal, Martin, 734 Kundera, Milan, 513

lace, great grandma's, 614 Lacroix, Christian, 541 ladder problem, 129 Lagrange's equations, 438 Lagrangian, 438

rotating pendulum, 444

INDEX

Lake Ogopogo, 406 Lao-tzu, 516 Laplace transform, 329

inverse, 695 Laplace transform method, 692 Laplace's equation, 641, 651, 667 Laplace, P. S., 583 Laplacian operator, 187, 641, 677 laser beam competition, 402 lattice, rectangular, 209 Lawrence, T. E., 492 lead poisoning, 339 least average unit cost, 137 least squares, 59, 64, 83, 101 left-handed, 243 Legendre equation, 373 Legendre function, 667

associated, 667 Legendre polynomials, 373, 470 Lennard-Jones potential, 13, 424 Leonardo of Pisa, 467 lifetime, 76 Lilliput, 39 limit cycle, 445, 458

stable, 446 Lin, Herbert, 75 linear algebra package, 181, 201 linear correlation

coefficient, 60, 70, 109 negative, 60 positive, 60

linear ODE, 264, 280, 326 linear pursuit, 414 Linnaeus, Carl, 128 Liverpool, 200 local variables, 588 log-log plot, 34, 72 logistic curve, 82, 85, 150, 236 logistic equation, 409, 413 logistic map, 492, 629, 633 long-distance running, 77 longitudinal vibrations, 481 Loren, Sophia, 81 Lorenz equations, 601 Lorenz force law, 362 Lorenz, Edward, 601 Los Alamos, 382, 474 Los Alamos National Laboratory, 527

Louie the Louse, 332 love affair, 280 low-pass filter, 623 LRC circuit

periodically driven, 568 Lucas, George, 362 lung cancer death rates, 92 lung disease, 243 Lyapunov exponent, 632, 633 Lyapunov, Alexander M., 632

Machu Pichu, 43, 483 magnetic bottle, 365 magnetic force, 362 magnetic sensor, 382 magnetic spin, 708 Malthus's equation, 407 Malthus's law, 407 Malthus, Thomas, 467 Manchester United, 200 Mandelbrot map, 588 Mandelbrot set, 590 Mandelbrot, Benoit, 588 Maniac I, 474 manufacturing plant, 137 map

cubic, 631 first iterate, 495 fixed point, 490, 495

stability, 495 logistic, 492, 629, 633 Mandelbrot, 588 one-dimensional, 490, 636 quartic, 631 Saturn's rings, 596 second iterate, 495 sine, 631, 635 standard, 501 tent, 631, 635 third iterate, 495

761

trajectory, 490 two-dimensional, 576, 588 two-dimensional piecewise, 583

map function, 173 Maple

animation, 53 how to start, 54

assigned values, 15

762

case sensitive, 25 command line, 14 comment, 15, 65 definite integral, 27 ditto operator, 25 gradient operator, 47 Help, 17, 21, 27, 164 indefinite integral, 27 integration, 153 internal memory, 15 library, 15 linear algebra package, 43, 47 list, 15, 21, 34, 62, 95, 167 networks package, 29 plottools package, 156, 232 protected symbols

time, 21 root of, 130 set, 18 statistics package, 15, 66, 222,

252 string, 16, 24 student package, 156, 215, 232 symbolic computation, 113 system, 14 Topic Search, 17 worksheet, 14

Maple 6, 2 Maple Command

- >, 34, 41, 66, 72, 74, 78, 83, 86, 333, 493, 522

#, 15 &*, 477, 726, 732 II, 157, 177, 192, 210, 241, 246,

252,286,287,289,290,312, 486,496,507,578,618,740

*,17,476 /, 17 %, 25, 152 _Env AllSolutions, 295 about, 342 abs, 366, 574, 634, 708 adaptive=false, 385 add, 55, 84, 88, 90 addvertex, 30 algsubs, 656 alias, 30, 315, 376, 383, 391,

543, 553, 624

align, 161 align=LEFT, 192 align=RIGHT, 157 allpairs, 31 allvalues, 130, 603

INDEX

alpha, 318, 384, 454, 694, 716 angle, 168 animate, 54, 55, 381, 395, 530,

535,650,675,688,690,694, 699, 718, 721

animate3d, 57, 665, 680, 684 arc, 188 arcsin, 147 arctan, 721, 740 array, 44, 625, 726, 729, 732 array(identity), 476 array(sparse), 477 arrow, 157, 170, 188 arrow operator, 288 arrows=MEDIUM, 269, 275, 289,

305,319,342,670,705,709 arrows=THICK, 49, 184, 189,

367 assign, 123, 125, 130, 177, 182,

272,286,295,303,305,310, 328,352,354,364,392,454, 471,529,538,545,550,555, 566, 603, 619, 625, 657

assume, 27, 125, 168, 173, 342, 350,378,383,391,415,429, 548,553,566,667,673,677, 689, 692, 697, 708, 716

augment, 98 axes=boxed, 44, 103, 177, 184,

208,213,232,315,489,511, 654, 657, 670

axes=framed, 41, 47, 57, 162, 546, 665, 718, 721

axes=NONE, 192 axes=normal, 116, 170, 174, 232,

275,289,346,368,436,523, 705, 709

band, 725, 729, 732 BesselJ, 371, 661, 684 BesselJZeros, 371, 662, 682, 684 BesselY, 372, 661, 682 beta, 318, 359, 625, 712 binomial, 46

INDEX

binomiald, 238, 240 boundary condition, 656 cdf, 241 changevar, 225 charmat, 478 circle, 457, 599 coeff, 73, 79, 84, 334, 352, 384,

426,587,649,653,656,661, 674, 678

collect, 168, 303, 352, 359, 378, 384,392,416,441,447,448, 492,529,538,645,656,705, 720

colon, 15 color, 15, 21, 24, 34, 41, 49, 62,

66, 67, 74, 82, 83, 86-88, 95, 96, 103, 135, 137, 142, 157,161,170,177,204,208, 211,220,225,238,246,254, 258, 286, 328, 590, 740

color=COLOR(RGB), 208 combine, 544, 698

symbolic, 115 trig, 173, 454, 555

conjugate, 538 connect, 30 contourplot, 49 contourplot3d, 161 contours, 45, 47, 49, 57, 182,

654, 657 convert

exp, 697 list, 4 77 matrix, 477 piecewise,. 567 polynom, 25, 115, 419, 425,

514, 595 trig, 385, 404, 544, 652, 673

coordplot, 644 coords=cylindrical, 189, 660 coords=polar, 385, 644, 656, 681 coords=spherical, 187, 667 cos, 47, 57, 95, 130, 140, 173,

186,213,454,562,648,720 cosh, 366, 652, 718, 721 crossprod, 169, 363 curl, 182, 187, 189, 192 dcdf, 247

763

dchange, 274,294,399,448,490, 705, 713, 716, 720

delete, 32 delta, 53 DEplot, 297, 305, 306, 342 DEplot3d, 315, 713 describe[linearcorrelation], 62, 66,

108 describe[range], 253 det, 478 DEtools[expsols], 693 dfieldplot, 269 diag, 729 diff, 24, 33, 36, 117, 138, 141,

146, 151,153,173,177,269, 272,274,285,288,293,294, 302,304,310,315,319,327, 332,337,341,346,359,362, 384,411,415,424,439,447, 454,518,528,533,543,549, 553,566,602,648,660,673, 681,686,689,692,697,705, 708, 712, 716, 720, 735, 740

Dig~s,23,72,78,501,517,624,

633, 740 Dirac, 689 dirgrid, 269, 270, 275, 305, 342,

705, 709 display, 15, 18, 24, 35, 41, 49,

67, 73, 74, 79, 83, 84, 88, 96, 103, 136, 137, 142, 143, 161,170,177, 184,189, 192, 204,208,211,214,220,226, 241,246,254,258,275,277, 287,290,296,304,311,315, 320,329,334,342,361,371, 389,412,430,436,443,472, 482,530,534,557,574,576, 585,600,604,619,670,707, 710, 727, 730, 733, 737

diverge, 182, 192 division, 17 dotprod, 168, 169, 173 Doubleint, 158, 190, 234 draw, 31 dsolve, 277, 327, 333, 335, 336,

343,345,354,359,364,371, 378,400,420,426,544,549,

764

554,566,687,690,697,717, 720

numeric, 368, 435, 457, 519, 603, 606, 618, 625

edges, 30 eigenvalues, 478 end, 109, 590 epsilon, 350, 576 eval, 556, 649 evalc, 125, 343, 538, 678, 698 evalf, 25, 62, 66, 90, 94, 95, 131,

132, 147, 152, 160, 164, 168, 175,190,203,207,212,216, 220,226,230,234,252,253, 423,426,429,435,465,479-481,530,588,590,598,655, 664, 726, 729, 732, 735, 740

evalm, 46, 433, 476, 477, 726, 729, 732

eweight, 31 exp,47,57, 73, 79,84, 151,158,

191,220,225,536,649,661, 740

expand, 123,138,141,187,275, 293,294,378,384,385,392, 399,404,434,441,447,448, 500,563,571,644,661,667, 681, 698, 709

factor, 14 7, 448 FFT, 625 fieldplot, 49, 189, 367, 670 fieldplot3d, 184, 191 filled=true, 45, 157, 161, 220,

225, 654 fit[leastsquare], 67, 72, 79, 83,

87, 95, 103, 109, 334, 586 fnormal, 226 font, 232, 392, 626 for .. .from ... by ... to ... while .. do ... od,

88 for. .. from ... to ... do ... od, 99, 142,

202,210,212,221,227,230, 235,238,252,257,297,320, 436,457,461,477,488,493, 507,517,523,574,576,578, 599,612,618,625,629,633, 658,670,712,726,729,732, 735, 740

fourier, 697 fouriercos, 689 fouriersin, 687 frac, 501

INDEX

frames, 54, 55, 530, 535, 650, 675,688,690,694,718,721

frequency, 258 fsolve, 118, 138, 147, 151, 177,

310,373,379,385,388,465, 494,495,508,545,557,596

fsolve(avoid), 490 function composition operator,

494 function operator, 68, 72, 288,

505, 726, 729, 732 gamma,273,292,318,471,618,

660, 712 global, 108 grad, 48, 187, 670 grid, 49, 184, 189, 309, 590, 644,

654, 657, 658, 665, 670 histogram, 254 I, 536, 708 if...then ... fi, 203, 207, 230, 584,

589,599,613,634,729,733, 740

implicitplot, 309, 546, 658, 670 implicitplot3d, 184 infinity, 272, 563, 568, 569, 675 infolevel, 400 insequence=true, 482, 665, 727,

730, 733, 737 Int, 25, 152, 175, 225, 391, 663 int, 25, 152, 175, 189, 220, 302,

318,391,423,546,558,567, 570,649,653,663,675,679, 684, 717, 721

integrand, 225 interface(showassumed=O), 173 invfourier, 698 invlaplace, 694 irem, 729 isolate, 596, 717 kappa, 478 labelfont, 23, 67, 88, 95, 258 labelling=true, 644 labels, 15, 23, 35, 41, 44, 66, 67,

73, 74, 79, 82, 86, 88, 95,

INDEX

96, 103, 115-117, 135, 137, 151,162,170,174,182,189, 204,208,210,213,220,226, 232,238,246,258,277,290, 320,334,361,424,462,576, 626, 688, 710, 721, 740

lambda, 694 laplace, 692, 693 laplacian, 187, 644, 651, 656,

660, 667, 677, 681 left quotes, 168 lhs, 146, 392, 549, 717 lightmodel=light1, 684 lightmodel=light2, 57, 161 lightmodel=light3, 46, 590, 654 lightmodel=light4, 47 limit, 272, 664 limit(right), 555 linalg[matrix], 275 line_int, 183 linecolor, 270, 275, 305, 315, 342,

705 linestyle, 246 linestyle=2, 95 linestyle=3, 241, 303, 328, 530 listcontplot, 45 listcontplot3d, 45 listdensityplot, 45, 609, 614 ln, 72, 78, 83, 115 local, 108 loglogplot, 34, 41 logplot, 37 map, 173, 203, 333, 351, 362,

578 matrix, 46, 98, 612 matrixplot, 44, 46 max, 481 maxfun=-1, 603, 606, 618, 625 mean, 222, 227, 253 method=classical[foreuler], 519 method=classical[rk4], 524 mod, 740 mod 2, 609 mu, 129, 661 multiplication, 17 new, 30 nops, 102, 108, 252, 257 norm, 174,175,351,433

normald, 241 nu, 391, 661

765

numer, 544, 549, 554 numpoints, 54, 55, 174, 287, 361,

606, 690, 699, 718 odeplot,368,436,443,519,524,

603, 606 omega, 124, 173, 278, 318 op, 17, 83, 103, 125, 210, 213,

343,393,426,478,481,697 orientation, 44, 46, 47, 57, 103,

116,162,170,182,191,232, 315,346,436,489,511,546, 590, 654, 665, 684, 714

output=listprocedure, 368, 618 P(n,u), 373 pdetest, 533, 718, 721 pdsolve

HINT, 644 HINT,INTEGRATE, 644 HINT,INTEGRATE,build, 645,

651, 656, 673, 677, 681 INTEGRATE,build, 648, 667

phaseportrait, 270, 275, 276, 288, 312,319,320,411,450,705, 709

phi, 145, 186, 350, 454, 712 Pi, 55, 95, 131, 168, 177, 188,

212,230,232,350,389,435, 530, 562, 625, 648

piecewise, 151, 366, 534, 562, 566, 657, 670, 684

plot, 23, 24, 35, 66, 67, 72, 73, 79, 83, 84, 86-88, 95, 115, 117,135,137, 142,151, 157, 161,177,204,220,225,241, 246,254,286,296,303,305, 311,318,328,334,335,344, 361,379,388,392,400,410, 417,424,430,457,472,496, 530,534,539,545,550,557, 562,570,586,619,626,634, 637,670,726,729,733,735, 740

plot3d, 47, 103, 182, 192, 590, 654

PLOT3D(POLYGONS), 192 plots[display], 232

766

plottools[rotate], 574 pointplot, 208, 389, 481, 496,

574, 576, 584, 599 pointplot3d, 103, 210, 213, 502,

507, 518, 603 polar, 125 polarplot, 357, 385 polygonplot, 208, 578, 585 proc, 108, 588 psi, 378, 533, 67 4, 705, 716 radnormal, 125, 468, 479, 481 radsimp, 343, 555 rand, 98, 203, 207, 210, 213,

230,235,252,257,576,584 randmatrix, 98 randomize(), 98, 202, 206, 210,

212,221,226,229,234,252, 257, 576, 584

read, 637 REplot, 462, 465, 468, 486 restart, 21 rho, 233, 454 rhs, 68, 73, 79, 83, 84, 88, 90,

95, 103, 109, 142, 146, 246, 269,334,343,346,352,361, 378,404,426,545,546,550, 587,599,603,645,656,661, 663,668,673,687,690,694, 717, 721

rotate, 381 rsolve, 462, 464, 467, 471, 479,

485, 488 scale, 578 scaling=constrained, 47, 57, 189,

192,208,211,214,232,357, 367,457,550,557,574,599, 644, 657, 658, 670

scatterplot, 15, 21, 62, 82, 95, 204,238,239,246,258,480, 493

scene, 275, 289, 306, 313, 315, 321, 412, 705, 709

sech, 735 semicolon, 15 semitorus, 232 seq, 17, 46, 72, 78, 83, 84, 90,

99, 103,109, 142,157, 177, 203,208,222,227,238,239,

INDEX

244,252,257,275,287,290, 311,333,357,371,373,389, 472,476,493,502,518,574, 576,578,600,609,625,634, 658, 726, 729, 732, 740

setattribute, 476 shading=xyz, 46, 57 shading=z, 162, 368, 604, 606 shading=zgreyscale, 47, 184 shading=zhue, 44, 184, 590, 654,

665, 680, 684 shortpathtree, 31 signum, 574 simplify, 130, 131, 174, 175, 278,

351,384,403,439,454,529, 537,538,544,549,553,656, 661, 678, 684, 693, 717

sqrt,symbolic, 721 simplify(symbolic), 168, 356, 648,

668, 677, 681, 687, 698 simpson, 216 sin, 53, 130, 140, 145, 173, 186,

213,234,294,315,454,562, 649,661,684,720,732,740

sinh, 653, 721 sixsphere, 646 sol[], 139, 141, 310, 355, 416,

420, 544, 603, 625 solve, 123, 125, 130, 131, 136,

138-141, 146, 147, 176, 182, 266,269,271,286,294,295, 303,304,336,352,384,386, 415,416,421,422,424,428, 430,441,454,478,529,537, 550,555,567,571,603,650, 657,669,675,679,684,687, 690, 693, 721

sort, 257, 479 spacecurve, 116, 17 4, 177, 346,

489, 509, 511, 523 sphereplot, 443 sqrt,90, 103,105,125,173,188,

203,213,216,233,241,287, 293,341,366,448,479,528, 543,548,553,645,652,656, 669,673,678,718,721,735, 740

stackmatrix, 609

INDEX

standarddeviation, 223, 227, 253 statevalf, 244, 258 statevalf[pdf,normald], 254 stats[statevalf], 238, 240 statsort, 257 step~ze,270,275,289,305,315,

319, 411, 705, 709 style=hidden, 184 style=line, 208, 210, 213, 254,

287, 344, 564 style=patch, 44, 46, 208, 232 style=patchcontour, 47, 57, 182,

184, 546, 684 style=patchnogrid, 103, 192, 590,

665 style=point, 34, 41, 67, 72, 74,

79, 83, 86, 87, 103, 161, 204,238,286,305,334,462, 570

style=wireframe, 443 subs, 25, 84, 90, 94, 103, 109,

115, 140, 141, 146, 152, 182, 189,274,275,294,303,319, 336,343,352,378,399,403, 416,425,439,447,454,492, 500,507,537,544,549,550, 553,566,570,598,645,648, 649,652,655,656,661,669, 673,678,684,687,690,693, 697,705,708,713,717,720

subsop, 609 Sum, 245, 563, 568, 569, 650,

653, 675 sum,99, 103,203,238,359,533,

563,570,571,650,653,664, 675, 680, 684

symbol=box, 15, 34, 41, 67, 74, 79, 82, 88, 286

symbol=circle, 21, 62, 66, 67, 83, 86, 95, 103, 161, 238, 246,258,296,305,462,570

symbol=cross, 87, 204 symbol=diamond, 576 symbolsize, 286, 305, 334 tally, 257 tan, 141 tanh, 718 tau, 274, 293, 705, 712, 716

767

taylor, 25, 115, 418, 425, 514, 595

textplot, 136, 137, 157, 161, 188, 277,287,290,296,313,371, 373, 394, 706

textplot3d, 162, 177, 192, 211, 213

Theta, 177, 294 theta, 94, 130, 140, 145, 168,

177,188,293,350,656,669 thickness, 67, 184, 188, 246, 287,

361, 688, 721, 740 thickness=2, 95, 142, 157, 177,

220,225,241,344,371,379, 385, 489, 530

thickness=3, 254, 309 tickmarks, 15, 23, 35, 41, 62,

66, 73, 74, 79, 82, 88, 96, 103, 115-117, 137,151, 162, 170,174,177,189,204,208, 210,213,220,226,246,254, 258,275,309,315,320,329, 361,424,462,545,576,654, 688, 690, 707, 740

time(), 202, 212, 221, 227, 517, 518,524,574,576,584,588, 598,602,606,612,618,624, 629, 633, 740

title, 24, 96, 135, 289 to ... while ... do ... od, 589 transform, 257 transform[scaleweight], 253 transform[tally], 252 transform[tallyinto], 253 translate, 578 transpose,44,46,609, 726,729,

732 trapezoid, 216 Tripleint, 162, 193 trunc, 496, 576, 733 unapply, 68 unassign, 131, 142, 297, 305,

311,336,410,454,461,465, 468, 507, 534, 603, 619

unprotect, 21,273,292,318,333, 471,584,612,618,660,712

value, 158, 163, 191, 193, 234, 386, 566

768

vector, 48, 351, 362, 365 view, 15, 35, 41, 62, 66, 67, 72,

73, 79, 83, 86, 88, 96, 137, 142,162,189,208,232,329, 361,389,511,545,727,737, 740

weights, 30 while ... do ... od, 207 with(combinat,fibonacci), 469 with(describe), 222, 227, 252 with(DEtools), 181, 186, 269,

273,288,292,301,309,315, 318,341,410,446,705,708, 712

with(inttrans), 330, 686, 689, 692, 697

with(linalg), 43, 4 7, 166, 173, 181,186,201,350,362,433, 476,609,612,644,651,655, 660,667,677,681,725,729, 732

with(linalg,randmatrix), 98 with(LREtools), 462, 464, 467,

476, 485 with(networks), 30 with( orthopoly), 373 with(PDEtools), 273, 292, 399,

446, 705, 712, 716, 720 with(plots), 15, 21, 34, 41, 43,

46, 47, 53, 54, 57, 65, 72, 78, 82, 86, 93, 102, 115, 135, 137,140,156, 166, 176, 181,201,205,212,220,225, 237,244,252,256,273,285, 288,292,301,309,315,318, 334,341,345,350,362,383, 407,424,433,446,471,476, 485,492,517,528,534,536, 543,548,553,562,569,574, 576,584,598,609,612,618, 624,629,643,648,651,655, 660,667,673,677,681,686, 689,692,697,705,708,712, 716, 720, 725, 729, 732, 735, 740

with(plottools), 156, 166, 186, 232,379,383,457,574,598

with(statplots), 15, 62, 82, 93,

INDEX

201, 244, 256, 480 with(stats), 15, 62, 66, 72, 78,

82, 86, 93, 102, 108, 201, 222,227,237,244,252,256, 334, 480, 584

with(stats[statplots]), 21, 222, 227, 237, 252, 492

with(student), 156, 186, 216, 225, 232

zip, 34, 41, 66, 72, 74, 78, 83, 86, 333, 586

Maple Help inifcns, 37 4

Maple procedure, 109 Mary Shelley, 358 mass integral, 159, 163 matrix

characteristic, 478 column, 726 determinant of, 483 diagonal, 4 77 identity, 4 76 inverse, 483 row, 726 sparse, 477 square, 476 tridiagonal, 477, 729, 732

matrix multiplication, 726 maxima, 48 maximum sustained yield, 413 Maxwell, James Clerk, 113 May, Robert, 397, 484, 492 Maynard-Smith/Slatkin model, 486 MCAT, 101 mean, 252 mean free path, 212 Mel: hardware head, 236 Merlin, 647 mesh, diamond-shaped, 738 method of characteristics, 738 Metropolis, 14

Amusement Park, 381 Country Club, 432, 437 Daily Bugle, 238 falling burger, 349 freeway, 244 Institute of Technology, 21 murder case, 332

INDEX

office buildings, 111 Stock Exchange, 552

Michaelis-Menton equation, 414 Michiavelli, Nicolo, 376 microbiology, 407 Microhard, 220 microton accelerator, 501 Mike and Vectoria, 175 Mike: mathematician/ archaeologist,

43, 150, 175, 181,231,301, 418,492,532,552,559,680

milk sales, 29 Mimas, 593 minima, 48 minimizing travel time, 29 minimum area, 546 mirage, 547 mode, allowed, 380 model

Anderson-May, 512 arms race, 503, 504 badminton bird, 402 baleen whale, 520 Barnsley's fern, 583 bilateral arms race, 505 bombs versus schools, 114 bouncing ball, 499 bungee cord, 376 butterfly attractor, 601 cellular automata, 611 circular membrane, 681 competition, 484, 516 computer, 220, 224 cooling law, 332 dating game, 97 diffusing perfume, 212 Douady's rabbit, 588 Dow Jones, 86 dress design, 541 drunkard's walk, 200 Duffing's equation, 318 eardrum, 418 economics, 134 electric circuit, 121 envelope of safety, 140 equipotential, 655 erosion, 56 Fibonacci, 467

fish harvesting, 524 fish population, 464 Fisher, 728 fluid flow, 666 glycolytic oscillator, 521 gnat, 461 gnus and sung, 308 golf ball, 432

769

gravitational acceleration, 93 Halley's comet, 350 heart rate, 71 heat diffusion, 64 7 heat flow, 527, 686, 688 human fly, 552 ice wine, 243 inclined ladder, 128 KdV soliton, 715 KdV soliton collision, 734 kink soliton, 719 Klein-Gordon, 730 Lennard-Janes, 424 logistic, 81, 492 magnetic bottle, 362 Maynard-Smith/Slatkin, 486 Monte Carlo, 229 neutron diffusion, 659 NLSE soliton, 708 nonlinear diode, 398 nonlinear pursuit, 414, 452 normal mode, 4 73 nuts and bolts, 236 opera singer, 562 Penelope Jitter Bug, 209 power law, 33 pursuit, 341 pyramid, 150 Queen Dido, 548 Rossler's, 606 rabbits and foxes, 284 radioactive contamination, 691 rainbow, 144 real estate, 102 rectangular membrane, 676 red blood cell, 4 71 ride, 438 RLC circuit, 273 rotating wheel, 382 safety envelope, 345

770

Saturn's rings, 592 senate renewal, 78 SGE soliton collision, 738 ship hull, 156 Sierpinski gasket, 576 simple pendulum, 292 ski hill, 47 solitary wave, 704 string, 565 tenure policy, 268 three piece string, 536 three wave, 712 tripolar arms race, 511 tunnel diode, 445 two-dimensional heat flow, 651 vapor deposition, 255 vector, 173, 181, 186 vibrating bar, 696 vibrating heart, 358 vibrating string, 532 wallpaper pattern, 574 wave equation, 672 weedeater, 391 wheel, 231 yeast, 407

model equation, 13, 59, 67, 71, 82, 85, 101

exponential, 59 functional, 59 linear, 59 logistic, 59 polynomial, 59 power law, 59

modes, normal, 391 modified Bessel equation, 387 modified Euler algorithm, 521 modulus, 125 moment of a force, 130 moment of inertia

of triangular plate, 165 Mona Lisa, 292 Monte Carlo, 195

dart method, 229, 250 estimate of 1r, 229 integration, 215

Monte Carlo method, 195 mouse

dragging the, 117

INDEX

mouse button clicking on, 17

Mr. X: the human fly, 552 multiple regression analysis, 101 multiplication factor, 659 Museum of Modern Art, 552 Musharif-UD-DIN, 29 musical notes, 685

National Geographic, 140, 249 natural gas prices, 91 Navier-Stokes equations, 601 negative resistance, 446 Nemerov, Howard, 382 Neptune, 356 neutron diffusion equation, 660 new home cost, 110 New South Wales, 651 Newton

law of gravitation, 93 law of resistance, 22 second law, 22, 93

Newton's law of cooling, 37, 332 Newton's method, 118 Newton's second law, 293, 362, 403,

418, 475 Newton, Isaac, 144, 350, 474 NLSE, 708 Noah's ark, 156 Noah: meteorologist, 156 nodal line, 684 nodal point, 267 nodes, 395 noise, 636 nonautonomous nonlinear ODE, 318 nonautonomous ODE, 263 nonlinear diode, 398 nonlinear drag, 406 nonlinear Klein-Gordon equation, 733 nonlinear models

first-order, 398 second-order, 414

nonlinear ODE, 264, 280 nonlinear PDE, 702 nonlinear relation, 72 nonlinear Schri:idinger equation, 702 nonlinear spring, 307 normal distribution, 240

INDEX

normal modes, 58, 376, 391, 474 nuclear explosion, 665 nuclear fission, 659 numerical mesh, 724

rectangular, 724 Nyquist frequency, 622 Nyquist, H., 623

octopus, 591 ODE

pth-order linear, 326 Bernoulli, 400 Bessel, 370 constant coefficient, 326 Duffing's, 618, 625 Gompertz's, 413 homogeneous, 326 inhomogeneous, 326 Legendre, 373 linear system, 328 logistic, 409 Michaelis-Menton, 414 modified Bessel, 387 rabbits-foxes, 516 Riccati, 403 Vander Pol, 448 von Bertalanffy, 414

Ohm's law, 122, 124, 447 Ohm, George Simon, 122 Olympic 100 meter times, 77 Olympic games, 36 one out of eight rule, 611 open surface, 188 Operophtera brumata, 490 optical path length, 148 ordinary point, 265, 281 orthogonality, 649, 662 oscillator

glycolytic, 521 forced, 628

tunnel diode, 445 Oster, G. F., 484 outbreak of war, 503 outward flux, 191 overdamped SHO, 276

p-q diagram, 296, 311 Palace of the Governors, 527

parabolic cylinder, 192 parabolic trajectory, 141 paraboloid, 161 parallelepiped

volume of, 169, 172 parametric excitation, 444, 445 Paris gun, 348 Parseval's theorem, 622, 624 partial derivative, 48 particular solution, 327 Pat: forensic scientist, 332 patterns, wallpaper, 574 PDE

linear, 641 nonlinear, 701

pendulum, rotating, 444 Penelope Jitter Bug, 209 perihelion, 356 period doubling, 318, 323 period eight, 323 period four, 323, 494, 627 period one, 323, 494 period two, 323, 494, 617, 627 permittivity, 132, 182 Perrin, Jean, 199 Peter, Paul, and Mary, 205 phase, 500 phase angle, 125 phase plane, 264 phase space, 602

771

phase-plane diagram, 305 phase-plane portrait, 264, 274, 312,

320 phase-plane trajectory, 264 Physics of Sports, 20 piano string, struck, 568 piecewise function, 150 Pirates of the Caribbean, 414 pitchfork bifuraction, 630 plane wave, 536 plate, semicircular, 665 Plato, 350, 452 Pluto, 356 Poincare section, 617 Poincare's theorem, 284, 288 point

fixed, 265 focal/spiral, 267, 275, 283

772

higher-order singular, 282, 301 nodal, 267, 282 ordinary, 265, 281 saddle, 267, 283, 319 saddle-vortex, 306 simple singular, 281 simple stationary, 266 singular, 281 stable equilibrium, 267 stable focal, 267, 311 stable nodal, 267, 283 stationary or singular, 281 unstable focal, 267 unstable nodal, 267 vortex, 267, 275, 302, 319

Poisson distribution, 243, 255 Poisson's equation, 641 polar form, 125 polar plot, 178 polio epidemic, 85 polynomial fit, 59 polynomial force law, 302 population growth

with emigration, 339 with immigration, 338

Port Radium, 692 potential

alternating surface, 659 split, 671 velocity, 666

potential energy, 439 Pound, Roscoe, 314 power law, 22, 33, 36, 38, 41,76 power spectrum, 622

chaotic, 627 Prandtl number, 601 predator-prey interaction, 284, 332 price and supply, 340 projectile motion, 26 puffin explosion, 463 pulsating sphere, 531 purchasing power, 14, 15, 63 pursuit problem, 452 pyramid

cone-shaped, 155 fiat, 155 Great, 150

INDEX

quarter cylinder temperature distribution in, 665

quartic map, 631 Queen Dido, 548 quote

A good scientist is, 655 A great many people, 268 A journey of, 516 A person employed on, 643 A picture may, 263 A product of the untalented, 552 A professor can, 128 A sleeping presence is, 64 7 A study of very simple, 484 A tool knows, 513 A traveler without, 29 Ain't she sweet?, 173 All for one, 445 All is flux, 186 All science is dominated, 424 All the effects, 583 An archaeologist is, 231 An effective human being, 569 And if you take, 325 Angling may be said, 464 Appetite comes with , 9 Are five nights warmer, 724 Aristotle could have avoided, 59 Art is the imposing of, 573 As for life, 284 Astronomy compels the soul, 350 Begin at the beginning, 7 Chaos often breeds, 318 Climb ev'ry mountain, 144 Does the flap, 601 Either that wallpaper goes, 574 Elementary my dear Watson, 332 Everyone lives by selling, 102 Everything you see, 81 Float like a butterfly, 461 For nothing on earth, 712 For the sake of persons, 113 Give me another horse, 521 God does not care, 606 God does not play, 229 Great fleas have, 576 Harp not, 565 Haute Couture should be , 541

INDEX

He was a self-made man, 65 He who does not mind, 651 How can you tell, 696 How many times, 205 Humor is emotional chaos, 618 Humpty Dumpty sat, 636 I beheld the wretch, 358 I believe that, 33 I cannot talk, 212 I evidently knew more, 134 I have never let, 114 I have nothing to offer, 471 I never hated a man, 738 I never learn anything, 301 I shall use the phrase, 398 I was observing, 715 I would advise you, 536 I wouldn't say, 4 73 I'm notorious for, 666 If all economists, 13 If Noah had been, 156 If the radiance, 659 If you are idle, 704 If you know it, 633 Ignorance is an evil weed, 391 Imagination is more, 4 7 Income Tax has made, 432 It is here, 608 It is marvelous indeed, 592 It is not knowledge, 688 It is nothing short, 686 It is written, 166 It isn't so much , 261 It's food too fine , 615 It's just a job, 715 It's pretty, 499 It's red hot , 615 Just when you thought, 341 Learning without thought, 527 Let no one ignorant , 452 Let's fight till six, 503 Life is a wave, 53 Logical consequences are, 611 Man can believe, 195 Man your ships, 362 Masterpieces are not, 719 Mastery is not something, 181 Mathematics is the queen, 548

773

Mechanics is the paradise, 140 Money is better, 86 Not everything that can, 250 Now this is not the end, 745 Nowadays people know, 224 Of all the thirty-six, 209 Oh yes, there is, 681 One ring to rule them all, 445 Opera is when a guy, 562 Opinion is like, 292 Part of the secret, 9 Physics tries to discover, 20 Population, when unchecked, 467 Practical politics consists, 78 Praise without end, 382 Predictions of the future, 588 Rumor is not, 728 Science is a collection, 3 Science is the knowledge , 261 Shake, rattle and roll, 624 Simulated disorder, 724 Some books are, 9 Some people think, 200 Something deeply hidden, 43 Statistical thinking will, 236 Sweet food of, 9 Take some more tea , 261 That's a great deal, 369 The buyer needs, 220 The desire of knowledge, 273 The elegant body of, 397 The fundamental cause, 676 The great tragedy, 11 The knowledge of the world, 527 The law must be stable, 314 The map appears, 492 The mathematics of , 407 The most incomprehensible, 402 The photographer is like, 345 The progress of science, 71 The purpose of, 1 The rule is, 121 The unexamined life is not, 691 The world is never quiet, 730 There is no better, 701 There is no means, 734 There is no such thing, 107 These are the voyages, 308

774

They [atoms] move, 255 Thieves respect property, 414 Thou seest the mountains, 56 Though you drive away, 629 Thus grew the tale, 7 45 To gyre is to go around, 438 We called him Tortoise, 672 We will now discuss, 484 We're all of us sentenced, 708 What is the use, 38 When asked what wine, 243 When our results, 602 Where in this, 93 Who did you pass, 61 Who shall doubt, 150 Wisdom consists in being, 376 You can't learn, 8 You have so many, 97 You just pick a chord, 532 You may be disappointed, 418 You press the button, 326

Rabelais, Fran<;ois , 9 radian, 293, 435 radioactive chain, 339 radioactive contamination, 691 radioactive gas, 692 rain cloud, 205 rainbow

primary, 144 secondary, 144

Rainbow County, 144, 205, 243, 284, 376

raindrop, 145 random number generator, 195, 210,

219, 251, 576, 584, 636 random number seed, 252 random walk, 195, 197, 201

of perfume molecule, 212 three-dimensional, 209

range, 348 ray diagram, 148 Rayleigh number, 601 Rayleigh's criterion, 375 reaction-diffusion equation, 728 real estate appraisal, 102 rectangular barrier, 540 recurrence relation, 3 7 4

INDEX

red blood cells, 471 reflection coefficient, 536 refractive index, 145 regression analysis, 63, 101 relativity, general theory, 358 resistance, 124

negative, 446 Stokes's law, 345

revenue curve, 140 Riccati equation, 403 Richter scale, 119 rk4 method, 522 rkf45 method, 513, 603 RLC circuit, 273

equation, 265 Rob the unicyclist, 361 Roche limit, 594 Roche, Edouard, 594 rocket flight, 155 Rocky Mountain, 437 Roddenberry, Gene, 308 Rogers, Will, 432 Rolf, Ida P., 569 Romeo and Juliet, 280 root mean square deviation, 245 root mean square distance, 201, 204 roots, coalescence of, 303 rotation of earth, 94 rotational equilibrium, 130 round-off error, 517 route to chaos, 318 row vector, 4 76 rowing times, 36 Rowland, Helen, 681 rug design, 608 rule of 72, 121 Russell, Bertrand, 59, 424, 676 Russell, John Scott, 715 Russell: engineer/sportsman, 29, 144,

205,341,446,527,647,724

Saccharomyces cerevisiae, 409 saddle point, 267, 288, 319, 706 saddle-vortex point, 306 Sagan, Carl, 633 sales price, 137 sampling frequency, 622, 625 sampling theorem, 622

INDEX

San Marco attractor, 591 Sante Fe, 527 Saperstein, Alvin, 503 Sarah's dive, 349 saturable refractive index, 711 Saturn, 356

moons, 593 rings of, 592

scalar field, 641 scaling, 38, 71 Schizosaccharomyces kephir, 409 Schopenhauer, Arthur, 292 Schri:idinger equation, 540, 641 Scott Russell, John, 715 second iterate map, 495 seismic surveying, 148 semi-log plot, 78 semi-major axis, 356 semicircular plate

center of mass, 165 semitorus, 231 Senator Strom Thurmond, 78 sensitivity to initial conditions, 605 separation constant, 652, 656, 668,

673, 677 separation of variables, 643 separatrix, 268, 704, 710 seq, 496 sequoias, 42 set, Cantor, 581 sewage treatment plant, 135 Shakespeare, William, 521, 565 Shankly, Bill, 200 Shannon, C. E., 623 Shaw, George Bernard, 13, 345 Sheelo: photographer/ entrepreneur,

140, 243, 345, 432 Shelley, Mary, 358 SHO, 267 Sidney, Sir Philip, 9 siege tower, 231 Sierpinski's carpet, 582 Sierpinski's gasket, 576 signal processing, 623 signum function, 343 Sills, Beverly, 418 Simon Legree, 672 simple harmonic oscillator, 264

simple interest, 28 simple pendulum equation, 265 simple plane pendulum, 292 simple singularity, 281

condition for, 282 simple stationary point, 266 Simplicius, 255 Simpson's rule, 216 sine map, 631, 635

775

sine-Gordon equation, 702, 720, 739 single-valuedness, 685 singular point, 281 SIR model, 301 skeletal bone weight, 41 ski hill, 47 smart parrot, 242 Snell's law, 33, 145 Snide Lee Lizard, 209 soccer, 200, 201 Socrates, 691 soft spring, 300 solid tetrahedron

center of mass, 166 mass, 166 volume, 166

solitary wave, 703 antikink, 703 black, 703 bright, 703, 708 kink, 703 nontopological, 703 three-wave, 712 topological, 703

solitary waves, 702 soliton, 702, 734

analytic solution, 715 antikink, 7 40 black, 711 bright, 710 kink, 740 stationary, 711

soliton collision, 7 40 solution

implicit, 429 steady-state, 360 transient, 360

sound waves, 148 special functions, 330, 369

776

spherical polar coordinates, 186, 212 spleen, 471 Spuzzum, 413 square membrane, 680 stability, 161 stable focal point, 267, 311 stable nodal point, 267 standard deviation, 64, 89, 101, 110,

222, 252, 253 standard map, 501 standard pressure, 212 standard temperature, 212 static equilibrium, 129 static friction, coefficient of, 129 stationary points, 265, 294, 309

classification of, 282 Statistical Abstract of the U.S., 14 statistical floating point evaluation,

238 steady-state, 490, 651 steady-state solution, 360 Stegobium panaceum, 490 stellerator, 501 Sterne, Laurence, 273 Stevenson, Robert Louis, 102 stiff ODE, 525 stiffness, 696 stochastic, 576 stochastic motion, 197 stock market, 86 stock market crash, 87 Stokes's law, 345 Stokes's theorem, 187, 188 Story Character

Alice: an economics student, 119 Benny Boffo: realtor, 104, 107,

437 Colleen: MBA graduate/artist,

14, 19, 70, 81, 179, 236, 243, 376, 432

Dot Product: Vectoria's mother, 166

Frank N. Stein: human replica, 358

GregArious Nerd: Erehwon math­ematician, 542, 655

Heather: pre-Med student, 33, 71,128,134,407,432,464,

INDEX

473 Hugo: eccentric scientist, 358,

659, 666 Jennifer: applied mathematician,

38,314,318,391,432,473, 573

Jerry: Noah's neighbor, 156 Louie the Louse: murder sus­

pect, 332 Mel: hardware head, 236 Mike: mathematician/ archaeologist,

43,150,175,181,231,301, 418,492,532,552,559,680

Mr. X: the human fly, 552 Noah: meteorologist, 156 Pat: forensic scientist, 332 Richard: lonely bachelor, 97 Russell: engineer/ sportsman, 29,

144,205,341,446,527,647, 724

Sheela: photographer/ entrepreneur, 140, 243, 345, 432

Syd Boffo: realtor, 102, 104, 107, 437

Trebla Nietsnie: administrator, 114

Tsigo Loib: conservationist, 308 Vectoria: physicist/Mike's girl­

friend, 21, 166, 175, 181, 255,273,301,362,402,532, 536,558,559,565,569,672, 676, 681

strange attractor, 602, 618 Rossler's, 606

string, 672 5-piece, 540 piano, 532, 566 plucked, 535, 676 struck, 568 struck piano, 675

Strogatz, Steven, 280 StruveH function, 684 Sturm-Liouville equation, 369 substrate, 256 Sun Tzu, 724 supercritical condition, 659 superposition

linear, 645, 662, 675, 679, 684

INDEX

surface integral, 188 suspension bridge, 132 Syd Boffo: realtor, 102, 104, 107,

437 symbolic computation

algebraic models, 114

Tacitus, 728 tangent bifurcation, 630 tangent field, 265, 269, 289, 299, 305 Tappert, Fred, 718 Taylor expansion, 26, 281, 377, 418,

514 Taylor, Edward , 615 Telluride, Colorado, 382 tension, 376 tent map, 631, 635 tenure, 268 terminal velocity, 22, 403 testdatl.m files, 637 textplot, 496 Theodore Roosevelt Lake, 341 Theodoric of Freiburg, 144 theorem

Parseval's, 622, 624 Poincare, 284 sampling, 622

thermonuclear fusion, 365 third iterate map, 495 Thurber, James, 618 tidal force, 594 time of flight, 348 Tolkien, J. R. R., 445 toroid, 231, 233 total cost, 135 total revenue, 137 trading records

Hudson's Bay Company, 291 transcendental equation, 118, 120 transcendental function, 295 transform

discrete Fourier, 623 fast Fourier (FFT), 624 Fourier, 622

transient, 622 transmission coefficient, 536, 540 trapezoidal rule, 216 Trebla Nietsnie: administrator, 114

trial number, 201 triangular plate

center of mass, 165

777

moment of inertia, 165 Tribolium castaneum, 490 Tribolium confusum, 490 tridiagonal matrix, 477, 725, 729,

732 triple integral, 157, 162 tripolar arms race, 511 Tsigo Loib, 308 tumor, cancerous, 413 tunnel diode oscillator, 300 tunneling

quantum, 540 Turgeniev, Ivan, 263 turning points, 422 Twain, Mark, 33, 114 Twain, Mark , 9 two-soliton solution, 718 Tyndall, John, 53 typographical errors, 249

U.S. Senate, 78 Ulam, Stan, 608 uncertainty principle, 699 Uncle Tom's Cabin, 672 underdamped SHO, 275 unequal probabilities, 205 unequal step sizes, 205 unit vectors, 48, 166

Cartesian, 352, 433 spherical polar, 352

unstable focal point, 267 unstable nodal point, 267 Uranus, 356 utility function, 119, 120

Van der Pol equation, 265, 300, 448 Van der Waals

equation of state, 53 Vander Waals interaction, 424 vapor deposition, 256 vector

acceleration, 17 4 and trig identity, 172 angle between two, 167, 171, 172 column, 4 76

778

identity, 172 manipulations, 171 position, 17 4 resultant, 167 row, 476 sum, 170 velocity, 17 4

vector calculus, 181 vector field, 641 Vectoria: physicist/Mike's girlfriend,

21,166, 175, 181,255,273, 301,362,402,532,536,558, 559,565,569,672,676,681

velocity field, 188 velocity potential, 666 Verhulst, 409 Verhulst equations, 307 vibrating cylinder, 685 vibrating wire, 696 Vicious, Syd, 532 Vidal, Gore, 592 viewing box, rotation of, 4 7 Vinci, Leonardo da, 140 visible spectrum, 147 visual hallucination patterns, 45 volcanic eruption, 140 volume integral, 162 Von Neumann, John, 608 vortex point, 267, 275, 284, 302, 319

Walesa, Lech, 97 Walton, Isaac, 464 water skier, 341 water wave, 715 wave

beats, 56 dispersive, 55 longitudinal, 53 nondispersive, 55 plane, 536 standing, 54 transverse, 53 traveling, 54

wave equation, 532, 641, 672 wave phenomena, 53 weather forecasting, 601 weedeater, 391 weight function, 369

well depth, calculating, 348 Wells, H. G., 236

INDEX

white dwarf stars, 520 Whitehead, Alfred North, 573 Whitehorn, Katherine, 473 Whittaker function, 164 widget production, 139 Wilde, Oscar, 195, 224, 574 Williams, Tennessee, 708 wire equation, 696 Wolfram, Stephen, 608 Woods, Tiger, 436 Woolf, Virginia, 719

yeast, 410 yeast growth, 332 Yellen, Jack, 173

Zabusky, Norman, 734 zero circulation, 183 zeroth law of thermodynamics, 4 7 4 zoological scaling, 75 zoologists, 41