Bibliography

Application problems, 59-66, 178-189, 232-236, 343-347, 403-409, 513-522, 591-596, 672-675

Application software, 19 Approximations, 412, 450 A programming language (APL), 21 Archimedean spiral, 270 Archimedes, 193 Ardon, Jean Robert, 353 Area estimation, 599 Argument angle, 357 Arithmetic logic unit (ALU), 18, 36 Arithmetic operations, 523-524, 532-533 Array

in matrix, 67, 69, 76-77 operations, 79 three-dimensional (3-D), 141 two-dimensional (2-D), 141

Artifi cial intelligence, 13 ASCII (American Standard Code Information

Interchange) code representation, 527-528 fi les, 46-47, 604, 606 matrix creation, string commands,

115-116, 172 Assembler, functions of, 20 Assembly language, 19-20 Augmented matrix, 89 Automation, 8 Automobile industry, 2, 7 Average, 449 axis

performance analysis, 629, 634, 647 plotting, 260-261, 265-267, 269, 273, 276, 281,

285, 291, 294, 302-303, 350-351 polynomials, 473, 482

Azimuth, 292, 294

Backlash, 89 Bar graphs, 620 Batch fi les, 600 Beginners All-purpose Symbolic Instruction

Code (BASIC), 16, 20, 523 Berners-Lee, Tim, 2 bernoulli function, 484 Bernoulli, Daniel I, 353

Bernoulli, Jean, 353 Bernoulli, Jean, II, 353 Bernoulli, Nicolaus, III, 353 Bessel function, 484 Best fi t polynomial, 422 Beta, function, 484 Binary fi les, 47, 606 Bingaman, Jeff, 9 Binomial

characteristics of, 126 complex numbers, 356 defi ned, 414

Binomial function, 484 Biotechnology, 13 Blank spaces, 66 Block box system, 474 Bode plots, 426-427 Boeing, 7, 11 Boldface, 257, 260 Bombelli, Raffaele, 353 Bouncker, William, 193 Boundary conditions, 463-464, 466 Brackets, 67, 69, 114, 263, 367, 418, 614 Brain science, 13 Branching commands, 523-524 Briggs, Henry, 194 Burgi, Jobst, 194 Bus, defi ned, 18

C/C++ programming languages, 21-22, 598 Calculations, performance sequence, 43 Calculus, 412, 440 Capital-interest problem, 573-576,

599, 642-649 Cartesian coordinate points

implications of, 221-222, 243, 261, 376 2-D, 237 3-D, 376

Cartesian form, complex numbers, 356 Cartesian plane, 199, 246, 290 Cartesian plot, 269 Cartesian rectangular axes system, 349 Case sensitivity, 46, 196, 528 Cauchy form, 473 Cauchy matrix, 129 Cell architecture, 12 Cell arrays, 114 Cell phones, 11 Central processing unit (CPU), 17-20 Chain rule, 445 char, 113-116, 151

Character strings in matrix creation, 69-70 plotting, 240-241

Chebspec matrix, 129 Chebyshev function, 485 China, see Ancient history of mathematics,

China competition from, 6 educational attainment in, 8 research and development, 8

Ch’ung-Chih, 193 Circuit analysis, 14 Circular shifting, 132-133 Citigroup, 6 Climate change, 13 Cofunctions, 197 Cognitive science, 13 Colon, 45, 72-73, 99-100, 122-123 Color

coding, plotting, 251-253, 255-256 selection of, 598

Column(s) in matrix, 67, 69, 71-72, 74-76, 80-81, 83, 87,

91-113 vector, 71-72

Comma, 47, 67, 69, 71 Command(s), see Commands list

case sensitivity, 529 clearing, 43 entering, 43 format, 43, 46, 196 list of, 44 lowercase, 46, 196 multiple line, 73 partial, 541 special characters, 257 text control, 257 window, 24, 26-27

Commands list, see xlabel; ylabel; zlabel abs, 98, 371, 373, 597 addpath dir, 602 afl ip, 125 all, 535-536 alpha, 373 analyze, 611-613 AND, 530 angle, 373, 641 ans, 44, 149 any, 535-536 approx, 561-562 area, 100-101, 164, 280, 452-453, 581 arrows, 260 astroid, 270-272 autoexec.bat, 600

backspace, 242 bar, 272-273, 287-288 base2dec, 116-117 bath, 287 beep, 44, 56 beta, 268, 280, 427 bin2dec, 117 bitmax, 44, 55 bold, 303 box, 259, 303 box on/box off, 256 break, 553, 555 calendar, 127, 169 cardioid, 270 carriage return, 242 Casesen on/casesen off, 43, 196 check_age, 543-544 check_value_of_a, 542-543 circshift, 132-133 class, 473 clc, 43 clear, 43 clf, 281 clock, 44, 55, 623 close, 281 collect, 438 color, 256 comp_matr_op, 371-372 compass, 273-274, 373 complex, 356 Compmatop, 368-371 compose, 436 computer, 44, 55 cond, 87-88, 129, 166, 171 conj, 370 conjugate, 365-366 constant radius, 281-282 contour, 275, 292-294, 296, 301 conv, 421 copyfi le, 603 cos, 597 cputime, 44, 55, 599, 623 Ctrl key, with C key, 46 cumprod, 96-97, 164, 216 cumsum, 96, 164, 216 cumtrapz, 101-102, 453 cylinder, 290 Data, 294 date, 44, 55 datenum, 127-128 dec2base, 116-117 dec2bin, 117 dec2hex, 117 default, 253

delaunay, 299 den, 145-146, 216, 427, 624-626, 664 der, 452 deriv, 444 det, 83, 87-88, 109, 129, 147-149, 166-167, 459-460 detach, 278 diag, 98-99, 120-121, 149, 459-461 diary fi le, 604 diaryname, 604 dif, 455-456 difeq, 467, 471 diff, 100, 450-451, 507 differ, 451 diff_plots, 272-274 digit, 457-458 discrete, 379 disp

complex numbers, 351, 365-366 matrices, 150-151, 216-217 performance analysis, 620, 624, 630-632,

634, 638, 641, 643-644, 646, 648, 650, 653-654, 657, 659, 664, 667

plotting, 239-241, 266 polynomials, 486-487, 490-493, 502, 504,

507, 509 relational operations, 542-543, 546,

556-561, 564-568, 571, 574, 577, 580 disp_circle, 269-270 dist, 278, 288 div, 366 dlsim, 481 dot, 77-78, 97 double, 173, 456 dsolve, 413, 471, 473 dydx, 451 echo, 47, 614-615 eig, 108, 459-460 eigval, 108-110 eigvec, 108-110 elapse-time, 599 else, 566-567, 569, 586 elseif, 540, 542-543, 545 ellipsoid, 292 empty, 135 end, 72, 557, 564, 567, 569, 580, 583, 587, 620,

624, 650, 667-668 eps, 44, 55 erf, 484 erfc, 484 error, 553-554, 617 etime, 44, 623 eval, 173 exist, 535, 601, 609, 616, 635 exp, 44, 105, 216, 240

Commands list (contd.) expand, 439 expm, 105 expression, 59 expy, 439 eye, 133-134, 140-143, 154, 169, 281, 284 ezplot, 263-267, 269, 482, 499, 507, 509 ezpolar, 268 faceted, 292 factor, 214, 438 factorial, 438-439 feather, 273-275, 373-374 feed character, 242 fi gure, 280 fi ll, 279-280, 287-288, 292 fi lled, 253, 301 fi ltfi lt, 430 fi nd, 104-105, 167-168, 535, 537 fi ndstr, 173 fi ndsym, 433, 497 fi nish.m, 598 fi nite, 535 fi x, 156 fl agn, 553 fl at, 292 fl iplr, 104, 156 fl ipud, 104, 149 fl ops, 44, 55, 623-625 fmin, 483 fn, 619, 622-623 foh, 479 for-end, 85, 537, 545-546, 548-549,

552-553, 558 fplot, 262-263 fprint, 556, 650 fprintf, 241-242, 561, 565, 632, 638, 653-654,

657, 664-665, 668-669 freqs, 425 full, 142, 144, 146, 148-149 function, 47, 50-51, 53 gallery, 129 gcd, 195, 213 ginput, 261-262, 265-266 global, 614 grid, 281, 302 grid off, 256, 258-259 grid on

complex numbers, 350-351 performance analysis, 629, 634, 638, 644,

646-647 plotting, 256, 258-259, 266-267, 282, 285 polynomials, 420, 427-428, 469, 490, 493,

499-500, 505 relational operations, 571, 583

gtext, 257-258 help

help funfun, 614 help graph2D/help graph3D, 301 helpwin, 30-31

hex2dec, 117 hilb, 128-129, 169-170 hist, 276 hold on/hold off, 248, 267, 583 horner, 440 ieg, 151 imag, 370 imp_sum_x, 552-553 impz, 424-425 increment, 73 indexes, 141 indexmax, 92 indexmin, 92 inf, 44, 135 inmem, 603, 635 input

example of, 53n implications of, 44, 617, 619 matrix creation, 69-71

int, 455, 498 integ, 502 interp, 292 inv, 84, 131, 167, 171, 459-460 ischar, 535, 537 isempty, 136-138, 535-536 isequal, 134-135 isfi nite, 535, 537 isieee, 46, 148 Isim, 476 isimag, 535 isinf, 535, 537 isletter, 535 isnan, 535 isnumeric, 535-536 Ispar, 143 isprime(n), 214 isreal, 535 isspace, 535 issparse, 143, 148 keyboard, 617, 619 kron, 141-142 label, 257-259. See also xlabel; ylabel; z-label legend, 258-260, 271, 279, 303, 577, 581, 644 len, 172 length

implications of, 137, 140, 247, 450, 481 matrix creation, 71, 112 polynomials, 424-425

license, 44, 56

limit, 441-442 line, 248 line color, 268, 273, 476 linefeed, 242 line style, 248, 268, 273, 275, 476 linspace, 74-75, 244-246, 254, 258, 280,

290, 293 load, 47 log, 44, 105-106, 226-229 logm, 106, 136 logspace, 75 lookfor, 26, 29, 609, 616 ls, 602 mag, 641 magic, 123-125, 169, 281 matlabrc.m, 598 max, 91-92, 121-122, 168, 566, 597, 634 maxi, 121 mean, 94-95 median, 95, 163 mesh, 290-292, 294, 301 meshgrid, 140, 275, 290, 293, 299 mfun, 484 min, 91-92, 121-122, 163, 168, 556 mini, 121 mix, 147-149 mkdir, 602 mlock, 623 more, 46 nan, 44 Nbin, 277 [N/D], 214-215 nestpl, 497 new, 165 newstring, 530 nnz, 143-144 noise, 249 norm, 78, 97-98, 164 NOT, 530 now, 127-128, 169, 171 null, 111-112 num, 141, 426-427 numb, 116 numbase, 116 numden, 436 num_ele, 604 numsp, 439 nzmax, 143 ode, 413, 467-470, 506 ones, 133-134, 136-137, 139, 141, 144, 149, 154,

169, 643 options, 252-253, 274-275, 281 OR, 530 ort, 120-121

orthonormal, 85 part, 137-138 pascal, 123, 125, 169 pause, 44, 617, 619 pcode, 622-623 peaks, 294-295, 298-299 performance, 620-622 perm, 557 phase, 641 pi, 44 pie, 277-279, 287-289 plot

complex numbers, 350 performance analysis, 624, 629, 634, 644,

647, 658 plotting, 237-238, 243-244, 246-251,

254-255, 268, 271, 273, 281-285, 287, 298, 302

polynomials, 420, 426-428, 468-469, 473, 494

relational operations, 540, 542, 561, 574, 576, 581, 587

point transpose, 369 polar, 268, 273-275, 302, 373 poles, 424 poly, 107-108, 151, 497-498 polyfi t, 422 polyval, 419 polyvalm, 419 present, 171 pretty, 435, 497, 507 prewarp, 479-480 prime(n), 193, 195, 214 prod, 93, 163, 365-366, 420-422, 438 profi le, 619-620, 635-637, 658 psqr, 497 quad, 452-453 quiver, 275 rand, 110, 134-135, 169, 253, 301 randn, 131-132, 140, 169, 276 random, 131 randperm, 132 rank, 87, 89 rat(n), 214-215 rats, 84 rcond, 87-88 real, 370 realmax, 44, 55 realmin, 44, 55 refresh, 260 rem, 213 repmat, 139 reshape, 102-103 residue, 423-424

Commands list (contd.) result, 527 return, 553-554, 617 ribbon, 281 rmpath, 602 rms, 449 rotate, 294 roots, 351 rot90, 103 rpa, 457 rref, 87, 90 rrefmovie, 28, 90 scatter, 252-254, 301-302 semilog, 302 shading, 292-294 shg, 281 simple, 437-438 simplify, 437-438 size, 71, 112, 137, 298 sol, 468 solve, 461-462 sort, 93-94, 597 sortrows, 94 spallo, 143 sparse, 142-145, 147-149, 623-624 sphere, 291 spline, 422-423, 494-495 sprandn, 145-148 sprandsym, 145-146 sprintf, 241-242 spy, 143, 145-147, 149-150, 174-175, 624 sqrt, 44, 97, 106, 265, 275, 284, 293, 300, 355 sqrtm, 106 square, 163 stairs, 272-273, 287-288, 574 stand, 164 startup.m, 598 std, 96 stem, 272-273, 286-288, 430, 488,

493, 574, 668 stiff, 467 strcat, 173 strcmp, 528 string

implications of, 116-120, 257, 617 in matrix creation, 69-70, 115, 172 polynomials, 432 relational operations, 530

stringvec, 112, 115 strncmp, 528 subplot

complex numbers, 350 matrices, 145n, 147, 149-150 performance analysis, 624, 646-647, 658

plotting, 253-254, 264, 268, 273-274, 287-288, 291, 293, 303

polynomials, 426-427, 430, 435, 468-469, 477, 488, 494, 499, 505, 507

relational operations, 561, 571, 574-575, 581, 586-587

successive, 73 sum, 366, 459 sumcol, 124 sumdiag, 125 sumdif, 459 sum_prod, 546-547 sumrow, 124 surf, 290-294, 301, 303, 502 surface, 294 svd, 120 switch-end, 537, 553 sym, 150-151, 461-462, 473 symadd, 435 symb, 496-497 symdiv, 435-436 symmatrix, 433 symmul, 435 syms, 431-432, 434, 436-439, 456, 458-459,

472-473, 509 symsub, 435 tab, 242 taylor, 458-459 text, 259-260, 303 tic-toc, 44, 623, 632, 653, 667-668 title

complex numbers, 374 performance analysis, 624, 629, 634,

637-638, 659 plotting, 257-260, 262, 269, 271, 273-276,

278-281, 285-288, 290, 293-294, 297-298, 301, 303

polynomials, 420, 426-427, 430, 468-469, 488, 490, 493-494, 499-500, 505, 507, 509

relational operations, 551, 561, 571-572, 574-577, 583, 586-587

tol, 467 trace, 100, 108-109, 452, 459-461 trapz, 100-102, 453 tri, 121 tril, 119-120 trimesh, 299-300 trisurf, 299-300 triu, 119-120 tustin, 479-480 unique, 138 valu, 171 vander, 129-130

Var, 95 vec, 171 ver, 44, 56 verify, 509 version, 44 view, 292-293, 295 vpa, 457-458 waitforbuttonpress, 617, 619 warning, 617, 619 waterfall, 292 what, 602, 635 whatsnew, 28, 30 which, 635 who

defi ned, 45 matrix creation, 71

whos defi ned 45 implications of, 498, 609, 635 matrix creation, 71, 148 polynomials, 432

xlabel complex numbers, 350, 374 performance analysis, 624, 629, 634, 638,

644, 647, 659, 665, 668 plotting, 258-259, 262, 266, 269, 271,

273, 275-276, 280-282, 284-288, 290, 293-294, 297-298, 301, 303

polynomials, 420, 426, 428, 430, 468, 473, 482, 488, 493-494, 499-500, 507

relational operations, 551, 561, 583, 586-587

X-OR, 530 ylabel

complex numbers, 350 performance analysis, 629, 634, 638, 644,

646-647, 659, 665, 668 plotting, 258-259, 262, 266, 269, 271,

273, 275-276, 280-281, 284-288, 290, 293-294, 297-298, 303

polynomials, 420, 426, 428, 430, 473, 482, 493-494, 509

relational operations, 561, 574-576, 581, 586-587

zeros, 133-134, 136, 483-484 zeta, 485 zoh, 479-480 zoom, 260-262, 302 zplane, 571

Comments, clarity in, 52, 597-598, 607, 614-615 Common business oriented language

(COBOL), 20 Comparisons, 524-525, 528, 599 Competition, globalization and, 6

Complementary angles, 197 Complex matrix, 98, 109, 367-368 Complex numbers

addition of, 360, 366 analytical exercises, 400-403 application examples, 377-400, 641-642 application problems, 403-409 characteristics of, 42, 82, 242, 273, 349, 355, 375 commands, 356, 365-376, 391, 393 conjugation, 357-358, 364-365, 369 division of, 360-361, 366 exponentials, 357-358, 366, 368, 373 expression of 355-356, 360 historical perspectives, 353-354 i, 356, 359 j, 356, 359 matrices, 367-368, 370 multiplication, 360, 366 natural logarithm, 363 operations, 352-353 principal value, 362-363 products of, 360 real numbers distinguished from, 349-350 reciprocal of, 361 relations, 364 roots, 350-352, 362-363, 398-399 storage of, 355 subtraction, 360, 366 theory of, 349, 353-354 transposition, 369

Comprehensive school mathematics program (CSMP), 21

Computer codes, 2, 600 defi ned, 17 evolution of, 1-2 hardware, 17-19, 22 software, 19, 22 solutions, 36-37

Computing, meaning of, 1 Concavity, 443 Condition number, 87, 169 Conditional statement, 537-538, 540, 542 Conjugates, polynomials, 415 Conjugation, complex numbers, 357-358,

364-365, 369 Constant

implications of, 42-43 matrix, 67 of the square, 124

Consulting applications, 5 Contingent work, 5 Continuous function, 449 Continuous time system, 425

Contract work, 5 Control

systems, 3, 12 theory, 474

Conversions, string commands, 116-117 Coordinate system, see Cartesian, coordinate

system characteristics of, 237 3-D, 292

Copernicus, 194 Copying fi les, 603 Cosecant functions, 196-210, 446 Cosine functions

complex numbers, 357, 361 plotting, 245-246, 248-249, 255, 258, 260, 269,

271-272, 280, 284 polynomials, 439, 445-447, 449, 454-455, 484 types of, 191-192, 194, 196-202, 204-212, 215,

218, 220-228 Cotangent functions, 196-201, 203,

205-210, 262, 448 Cote, Roger, 194 Cray super computers, 19 Creativity, 10 Cross product, in matrix creation, 78 Cumulative products, 96-97 Cumulative sums, 96 Currents, 449 Curve fi tting, 3 Cycloid, 269

Data analysis, statistical, 599 fi les, 46, 600, 611-612

DEC Alpha, 19 Decimal points, 42, 46, 242 Decision-making conditions

analytical exercises, 589-591 application examples, 555-588 application problems, 591-596 fl owchart, 538-539, 550 multiple conditions, 540 roots, 584-585 statements, 538-554

Default data, 46 fi lter, 294 folder, 50 value, 74

Degrees, conversion to/from radians, 196 Deleglise, M., 195

Deleting fi les, 603 variables, 43

Delta, 440 Demographic studies, cell phone

utilization, 11 Demo program, 27 DeMoivre, Abraham, 362n DeMoivre formula/theorem, 359, 362 Dependent variable, 211, 243, 247, 462-463 Derivatives, polynomials, 442-443, 446-447,

462-463, 471-475, 479 Descartes, Rene, 237, 353 Descarte’s rule of signs, 416 Determinant, in matrix, 83 Diagonal matrix, 81-82, 86, 120 Differential equations (DEs), 412, 425, 462-463 Differentiation, 432, 443, 447, 454, 501 Digital Equipment Corporation (DEC), 19 Digitization, 8 Dirac-delta, 484 Direct current (DC), 14 Directories

components of, 601-602 fi le search, 611

Discrete system, 428-431, 478 Division, 44, 77, 360-361, 366, 417, 432, 435 Domain

complex numbers commands, 375, 391, 393 plotting commands, 243, 245 polynomials, 473 standard trigonometric functions, 205

Dot (.), 76-77, 79, 97, 601 Drawings, 34

Economic Policy Institute, 5 Editing fi les, 603, 615 Editor/Debugger, 47 Edit window, 24-25, 47, 607 Educational organizations, 2 Effi cient computer programs, 37 Eigensolutions, matrix creations, 108-109 Eigenvalues, matrix creation, 106-111, 169 Eigenvectors, matrix creation, 106-111, 169 EISPACK, 3 Electrical circuit theory, 349 Electronics workbench, 21 Elevation, 292, 294 Ellipsis, 73 Elliptic parabolic surface, 282 Emerging Energy Research, 13

Employees benefi ts, trends in, 6-7 success factors, 10-11

Empty, implications of arrays, 135 matrix, 136-137

Energies, 449 Enhancements, 260-261 Entertainment industry, 2 Epicycloid, 270 ePOCRATeS®, 12 Equal matrices, 81 Erasable programmable read only memory

(E-PROM), 18 Error(s)

detection/correction, 598 functions, 484 messages, 43, 113

Essential knowledge, 9-11 Ethanol plants, 12 Euclid, 194 Euler, Leonard, 194, 353-354 euler function, 484 Euler’s identities, 380-381 European Organization for Nuclear Research

(CERN), 2 European Particle Laboratory, 2 Executable fi les, 600 Exit/exiting fi les, 24, 615 Exponential

factor, plotting, 242 form, complex numbers, 357-358, 368, 373 functions, example of, 54 mathematical relations, 211

Exponentiation, 44, 77 ez functions, 301, 482

Factorization, 432 Fan, Wan, 193 Fast Fourier transforms, 484 Fergunson, D. F., 193 Fermat, Pierre, 237 Ferrari, 353 Field theory applications, 79 Figure window

access to, 598 characteristics of, 24, 26 clearing, 43

File(s) analytic exercises, 670-672 application examples, 630-663

application problems, 672-675 contents of, 600 copying, 603 creation of, 603, 607 data analysis, 611-613 deleting, 603 editing, 603 extensions, 601 formats, 601, 607-608 loading, 601, 604-605 location of, 601-602 menu, 280, 605 mode, 604 moving, 603 names, 601. See also Filenames opening, 597, 601-602, 604 saving, 603, 605, 608 search for, 607, 611 storage, 601, 603 test, 603, 607, 609-610 types of, 600, 605-606

Filenames components of, 605-606 edit, 603 function fi les, 614-615 selection factors, 597-598, 607 type, 602

Filter design, 3 fi nal, matrix creation, 73-74 Finck, Thomas, 194 First-order

derivatives, 463, 468, 472, 473-475 differential equations, 413

Floating-point format, 46, 157 operations, 623 variable, 456

Floppy disks/diskettes, 18. See also Files, saving and storage

Flowcharts characteristics of, 34, 37-39, 56-57 performance analysis, 538-539, 540, 544,

554-555 Flow control, 523, 537-538 Flow diagram, 37 Folders, 601 Font, commands for, 257, 260 Format

binary, 47 case sensitivity, 46, 196 of commands, 43, 196 decision-making statements, 540 fl oating-point, 46, 147 in fi le creation, 601, 607-608

Format (contd.) function fi les, 47, 614 logarithmic functions, 213 matrix creation, 73, 91 modular, 597-598 precision, 46 selection of, 598 variable display, 242

Formula calculator (FOCAL), 20 Forth, 21 Fortran, 16, 20, 22, 523, 598 Fourier operators, 352, 424 Fourier transform, 14, 484. See also Fast Fourier

transform Fraction approximation, 84 French, John W., Jr., 193 Frequency, standard trigonometric

functions, 205 Fresnel function, 484 Function fi le

analytic exercises, 670-672 application examples, 630-637, 641-642,

647-652, 655-663 application problems, 672-675 characteristics of, 47, 50-51, 53, 599, 614 creation of, 47, 615 editing, 615 format, 614-615, 619 func_quad_sol, 50-51 parsing, 619, 622-623, 630 plotting example, 616, 618 saving, 597, 615 testing, 616-617

Gamma function, 485 Gates, Bill, 1 Gauss, Carl Frederick, 194, 353 Gauss, Karl Frederick, 415 Gauss-Jordan

elimination, 86 reduction procedure, 89

Gaussian distribution function, 131, 297 Gaussian fi lter, 294 General Electric, 6 General Motors (GM), 6-7 General purpose simulation system (GPSS), 21 Geothermal energy, 13 Gillette, 11 Globalization, impact of, 6 Global positioning satellite system (GPS), 14 Global warming, 13 Government agencies/organizations, 2, 8, 11

Graph importance of, 237 multiple plots, 247, 258, 262 plotting commands, 243, 247, 249 trigonometric functions, 202-205

Graph algorithm and software package (GASP), 21

Graying industry, 1 Greek characters, 257 Greek philosophers, 192 Green’s functions, 412

Hardware-based languages, 20 harmonic function, 485 Health care benefi ts trends, 6-7 Health organizations, 2 Heaviside, 484 Helix, 281-282 Help command, 26-30, 467, 484, 609, 616 Hermite function, 485 Hermitian matrix, 86, 109 Heuristic solutions

defi ned, 32 example of, 33 problem-solving techniques, 34-35

Hewlett-Packard (HP), 11-12 H function, 485 High-level language, 19-20 Higher-degree polynomials, 415 Higher-order polynomials, 412, 452 Hilbert matrix, 123, 128, 169, 457 Histograms, 276-277, 599 History window, 24 Home entertainment, digital, 12 Home offi ces, 5 Hong, Chang, 193 House matrix, 129 HP 9000 series, 19 humps, 294, 297-298 Hydrogen power, 12 Hyperbolic

cosine integral, 485 functions, 207-211, 282-283 parabolic surface, 282 sine integral, 485

Hypertext markup language (HTML), 21 Hypocycloid, 271

i, 44 Idempotent matrix, 131

Identity matrix, 169 if-end statement, 537-541, 551 Image processing, 3 Imaginary axis, 349, 356 Imaginary numbers, 349 Impedance, 349 Implied loop, 552, 558, 655 Improper integrals, 449 Independent variables

complex numbers, 366 plotting, 243, 247 polynomials, 424, 427, 440, 445, 447-448,

462, 464 trigonometric functions, 211

Index of matrix elements, 67, 72, 122 plotting commands, 250-251

India competition from, 6 research and development, 8

Information analysis, 10 Information fl ow, 46 Information processing, 10 Information resources

contact information, 23 online help facility, 22

Information revolution, 2 initial, matrix creation, 73-74, 477 Initial conditions (ICs), 425, 429, 463-468, 471,

473-474, 477 Innovation, 8 Inputs, 34. See Command(s); Commands list Institute of Electrical and Electronics

Engineers (IEEE) standards, 46, 135, 147

Instruction(s) accessing, 597 in fl owchart, 38-39 fl ow of, 523 input statement, 69-70 mathematical relations, 212 plotting, 248, 273 sequence of, 52, 602-603 statement, 46, 49-50

Integers, 46 Integrals

complex numbers, 364 hyperbolic, 485 polynomials, 447-449, 452, 454-455, 462

Integration, polynomials, 425, 432, 447-449, 451-452, 465

Intel, 12 International Business Machines (IBM),

11-12, 19-20

Internet, historical perspectives, 2 Inverse

hyperbolic functions, 209-211 in matrix creation, 83-84 standard trigonometric functions,

205-206, 212 Irrational numbers, 42n, 349 IRS series 4D, 19 Italics, 257, 260

j, 44 Jacobi function, 485 Japan, educational attainment, 8 Java, 21 Job market trends, 4, 9

Kaiser Foundation, 6 Keng-Chih, Tsu, 193 Kronecker tensor product, 141

Labor trends, 4-7 LabVIEW, 21 Laguerre function, 485 Lambert’s w function, 485 LAPACK, 623 Laplace, 14 Laplace operators, 352, 424 Laplace transform, 354, 425, 484 Law enforcement applications, 2 Law of cosines, 203 Law of sines, 203 Leading coeffi cient, 414 Leading term, 414 Left division, 76 Legendre, Andrien Marie, 194 Legendre function, 485 Lehmer matrix, 129 Leibniz, Gottfried, 193, 353 Lemniscate, 269 L function, 485 Libraries, 11 Limits, 440-441 Linear

derivatives, 463-464, 472 equations, 246, 599 matrix, 86 plots, 244, 246

LINPACK, 3 Lisp, 21 Little, Jack, 3 Loading fi les, 601, 604-605 Lobatto’s algorithm, 452 Logarithmic functions

application examples, 226-229 characteristics of, 211-213, 270 plotting commands, 247

Logical operations/operators application examples, 533-535 built-in functions, 534-535 characteristics of, 523, 530-533

long format, 46, 55 Loops

condition statements, 541, 547, 550-551 exit mechanisms, 552, 554 patterns of, 554 safety mechanisms, 552

Lower triangular matrix, 86, 118 LU

decomposition, 86 matrix creation, 118-119

Machine language, 19-20 Macintosh applications, 19, 606, 615 MacLaurin series representation, 192, 194, 198,

207 Magic matrix, 123-125 Magnitude, 426, 584 Managerial skills, 10 Manufacturing industry, 5 Maple functions, 412, 484-485 Market trends, 4-7 matdemo, 29 Mat fi les, 605-606 Mathcad, 21 Math coprocessor, 22 Mathematica, 21 Mathematical operations

algebraic symbols, 43 hierarchy of standards, 43-45 list of, 44

Mathematics, historical perspectives algebra, 415n calculus, 412 complex number theory, 353-354 coordinate system, 237 numbering system, 192-193 terminology, 353 theories, 192-194

MathSoft, Inc., 21 MATLAB (Matrix Laboratory)

applications, overview of, 4-7, 41, 191 basic elements of, 3 current applications, 3 defi ned, 22-23 development of, 3 evolution of, 3 popularity of, 3-4 utilization of, 3 windows, 23-24

Matrix algebra, demos, 28 Matrix/matrices

analytic exercises, 175-178 application problems, 178-189 application examples, 151-175 benefi ts of, 68 commands, 69-151 creation of, 68-69 defi ned, 67 empty, 70 elements of, 67, 69 extended, 73-74 fi ve-dimensional (5-D), 141 four-dimensional (4-D), 141 full, 142-143, 145-149, 599, 625, 667 ill condition, 87 multiple loop structure, 547 n-square matrix, 67, 81, 83-84, 86 polynomial, 419, 476 rank, 86-87 sequence of elements, 73-76, 80-81, 152-153 size, 22 sparse, 142-149, 599, 623, 625, 663-667 specifi c matrices

1 × 1, 67 2 × 2, 72, 82, 155 2 × 3, 80 2 × 4, 77 3 × 3, 80-81, 112, 169, 284, 457 4 × 4, 99, 102 5 × 5, 169 8 × 2, 103 n × m, 92-93, 95, 102, 131 n × n, 81, 106, 123, 131, 145, 297. See also

n-square matrix n × r, 80 u × v, 102

structure of, 67, 71-72, 153-154, 547 symbolic, 459-460 types of, overview, 82-83

means, 439-440 Medical records, 12 Medicare, 13

Memory, storage format, 47. See also Storage Menelaus, 194 MEX fi les, 22, 605-606 M-fi les, 16, 47, 51, 597-598, 602-603, 605-606,

614, 617 Microprocessors, 7, 12 Microsim Pspice, 21 Microsoft (MS) Windows, 19, 47, 600, 606, 615 Military organizations

applications for, 2 research and development, 13

Mobius, August Ferdinand, 195 Mobius functions, 194-195 Modeling, large-scale, 13 Modula-2, 21 Moler, Cleve, 3 Mononomial, 414 Moving fi les, 603 m × n matrix, 149, 250 Multiplication, 44, 77, 81, 86, 360, 366, 416, 432,

NaN, 135-136 Nanotechnology, 12 Napier, John, 194 Naperian, 213 Nasir ed-din, 194 National Science Foundation, 8, 12 Natural

defi ned, 213 logarithm, 363

Neumann, John von, 2 Neural network design, 3 New fi les, creation of, 47, 603, 607 Newton, Isaac, 353 Newton-Cotes formula, 452 Newton’s formula, 126-127 n-factorial, 207 Nilpotent matrix, 131 Nonlinear equations, 267-268, 483 Nonsingular matrix, 86 Nonsymmetric matrices, 108 Normal distribution, 276 Notation, 46, 72, 80, 196 Null

space, in matrix creation, 111 vector, 74

Number line, 349 Numbers

complex, see Complex numbers condition, 87, 169

with decimals, 42, 46 expression of, 42 imaginary, 349 irrational, 42n, 349 prime, 193, 195, 214 rational, 42n, 349, 416 real, 42n, 349-350, 356-358

Numerical evaluation, 483 Numerical integration, 451-452 Numerical matrices, 114 Numerical variable, 473

Oblique triangle, 203 One-dimensional (1-D) array, 67 Ones matrix, 123 Online jobs, 5 Opening fi les, 47, 601-602, 604 Operating system (OS), 19 Operational relations, 527 Operations, symbols, 76-77. See also Logical

operations; Mathematical operations; Relational operations

Optimization, 3 Ordered pairs, 246-247, 263, 272-273 Ordinary derivatives, 463-464, 467-468, 472 Ordinary differential equations, see ode Ordinates, 356 Orthogonal matrix, 84-85, 120, 131 Orthogonal vectors, 78, 96-97 Orthonormal system, 85 Outputs, 34 Outsourcing, 6 Overlay plots, 247-248

Parsing, 598, 619, 622-623 Partitioning, 598 Pascal, 21 Pascal triangle, 125-126, 169 Pattern recognition, 10 Pentagon applications, 14 Percentage (%), 45, 614 Performance analysis, 652-655 Period, standard trigonometric functions, 205 Periods (. . .), 73 Peripherals, 19 P function, 485 Pharmaceutical companies, applications for, 11 Phase angle, 357, 375

Phase plot, 426 Phasor representation, 375 Photovoltaic panels, 13 Physical model, construction of, 34 Physics applications, 78-79 Pi (π), 44, 193, 199, 458 Pie representations, 599 Planar triangles, 299 Plotting, see plot

analytic exercises, 339-342 application examples, 304-339 application problems, 343-347 boxes, 259 circle equation, 269-271 color coded, 250-251 commands, 237, 239-240, 243, 245 enhancements, 260 helix, 281-282 histograms, 276-277, 599 intervals, 263-265, 268 overlay, 247-248 three-dimensional (3-D), 140, 281, 285-287,

290, 298 two-dimensional (2-D), 243, 261, 279, 281,

287, 298 Poisson matrix, 129 Polar form, complex numbers, 358-359 Polynomial equation

defi ned, 414 roots of, 414

Polynomials, see specifi c types of polynomials

algebraic operations, 434-435, 465-466

analytic exercises, 510-513 application examples, 485-510 application problems, 513-522 arithmetic, 457 ascending order, 414 characteristics of, 126, 411, 414 coeffi cients, 418, 420, 424, 428, 443-444 commands, 245, 422, 457-462, 467-470, 478,

482-485 decomposition of, 416 defi ned, 414 degree of, 415, 421 derivatives, 463-468, 471-475, 479 descending order, 414, 417-418, 422, 424, 426,

439, 443, 451 differentiation, 443, 447, 454 discretization option, 479-480 Euler, 484 exponentials, 464-465, 467 factoring, 417-418

frequency/frequencies, 425-429, 473 frequently used, 411, 146 functions, 416, 421-426, 468 graphical, 412, 414 impulse response, 425 integration, 425, 447, 449, 451-452, 454, 465 integrals, 447-449, 452, 454-455, 462 mathematical operations, 416-417, 420 matrix creation, 107, 150 missing coeffi cients, 418, 424 partial fraction expansion, 423, 491 plot of, 419-420, 426-427 root(s) of, 415-416, 418-419 symbolic function, 471 symbolic variables, 412, 431-433,

436-439, 483 transfer function, 428, 474, 478-479 transform, 425 trigonometric functions, 446-447

Prime numbers, 193, 195, 214 Print

commands, 241-242, 561, 556, 565, 632, 638, 650, 653-654, 657, 664-665, 668-669

menu, 280-281 Problem-solving skills, 10 Procter & Gamble, 11 Profi ler, 619-620 Program fi les, 600 Programmation en logique (Prolog), 21 Programmers, functions of, 20 Programming Language One (PL/1), 16, 20 Programming languages, 19-21, 523, 598 Proofs, 35-36 Pseudocodes, 598 Ptolemy, 194 Punctuation

fi le construction, 614 in matrix, 67, 69, 70-73, 89, 99-100, 114-115,

122-123 plotting commands, 239-240, 251-252 types of, 45-47

Pythagorean theorem, 97, 194 Pythagorus, 192, 194

Quadrants Cartesian coordinate points, 243 trigonometric functions, 199-200

Quadratic equations, 47-50 Quadratic polynomials, 412 Quotes, 70, 115, 251-252 Quotient polynomial, 422

r, 357, 373 Radian

conversion to degrees, 196, 217-218 defi ned, 196 degrees converted to, 196, 217-218 examples, 215, 217-218

Radio frequency ID (RFID), 11 Radio tagging technologies, 11 Rand matrix, 123 Randn matrix, 123 Random access memory (RAM), 18-19, 43 Random matrix, creation of, 155-160, 169 Range, standard trigonometric functions, 205 Rational functions, 416, 423, 425 Rational numbers, 42n, 349, 416 Read only memory (ROM), 18 Reading fi les, 47, 604 Real axis, 349 Real matrix, 98 Real numbers

characteristics of, 42 compared with complex numbers, 349-350 standard operations, 356 z, 356-358

Reciprocal functions, 198-199 Recommendations, 599 Recordkeeping applications, 12 Rectangular form, complex numbers, 356-360,

364, 368 Reduced row echelon form (RREF), 86 Reed, Daniel, 8 Regiomontanus, 194 Relational operations

algebraic characters, 524, 527 analytical exercises, 589-591 application examples, 533-535,

555-588 application problems, 591-596 case sensitivity of commands, 529 characteristics of, 524, 532-533 characters, 527-528 comparison commands, 524-525, 528 conditional statements, 537-538, 540, 542 constants, 524 defi ned, 523 fl ow-control path, 537-538 logical operators/operations, 530-533, 537 truth tables, 530-531 vectors, 524, 526-528

Remainder polynomial, 422 Research and development (R&D)

investment, 8

Reserve variables, 43 Residue polynomial, 422 Revisions, 617 Rhaeticus, 194 Riemann, Friedrich Bernhard, 195 Riemann functions, 194-195, 485 Riemann hypothesis, 194 Right division, 76 Right triangle, 197 Rising Above the Storm, 9 Robotics, 12-13 Root-mean-square (rms), 98 Rounding functions, 213 Row(s)

elementary operations, 86 in matrix, 67, 69, 71-72, 74-76, 80-81, 83, 87,

91-113 vector, 71-72

RPG (report program generator), 21 RREF matrix, 86 Runge-Kutta method, 467 Running integral, 452

Sampling function, 456 Save/saving

ASCII fi les, 47 fi les, generally, 597, 601, 603, 605, 608-609 function fi les, 597, 615 M-fi les, 602 new fi les, 47, 51 script fi les, 48

Scalar, matrix creation, 67, 82, 106 Scientifi c industries, 2 Scientifi c notation, see Notation Script fi le

analytic exercises, 670-672 application examples, 626-633, 637-641,

645-647, 652-655, 667-669 characteristics of, 51, 53, 599, 605-606 complex numbers, 365, 368-372, 379,

383-385, 387-388, 390-391, 393, 395, 398 creation of, 606 as data fi les, 611, 614 decision-making conditions, 540-546, 548 defi ned, 47-49, 51, 53, 606 logarithmic functions, 226-229 matrix creation, 85, 110-111, 150 performance command, 620-622 plotting, 260, 266-269, 272-273, 275-276,

281-282, 284, 287-288, 292, 294, 301 polynomials, 430, 468, 476-477, 488, 507, 509

Script fi le (contd.) saving, 597, 609 testing fi les, 609-610 trigonometric functions, 215-226

Secant functions, 196-210, 262, 440, 446, 448 Second-order

derivatives, 463-464, 466, 473 differential equations, 412 equations, 599 polynomials, 412

Self-employment applications, 5 Semicolon, 45-46, 69, 71, 239-240 Sensitivity controls, 43 Sensors, electronic, 123 Shank, William, 193 short format, 46, 55 Signal analysis, 14 Signal processing, 3 Silicon Valley, 7, 12 Simplifi cation, 432 Simpson’s rule, 452 SIMSCRIPT, 21 Simula, 21 Simulation, 2, 10, 13, 35-36 Simultaneous equations, 67, 86 Sine functions

complex numbers, 357, 361 implications of, 194, 196-201, 204-299, 211,

215, 218-219, 221-225, 227-228 performance analysis, 615-616, 618 plotting, 248-249, 255, 258, 260, 264, 269,

271-272, 280, 284 polynomials, 445-449, 454, 466,

483-484 Sine integral, 485 Single value decomposition (svd), 120 Singularities, 449 Singular matrix, 83 Sinusoidal functions, 358, 375, 380 Skew matrix

defi ned, 82 symmetric, 131

Slope function, 423, 442 Smart phone systems, 11 Software, copyrighted, 26 Software programs, registration, 22 Solar power, 12-13 Solid-state memory, 18 Sony, 12 Source

fi les, 600 programs, 20

Spacing, 42, 69. See also Blank spaces Sparsity, 625 Special-purpose computers, 12 Spherical coordinate, 376 Square matrix, 67, 81-82, 85-86, 130 Square root, 349 Standard deviation, 95-96 Standard generalized markup language

(SGML), 21 Stander, 95 Statements, 45-46. See also specifi c types of

statements State model, 474 State-space

equation, 413, 473, 476, 478 matrices, 479-481

State variable, polynomials, 473-474 Statistical data, profi le

command, 619 Statistics, 3 Steady-state response, 471 Steinmetz format, 357 Stirline, James, 194 Storage, see Save

fi les, 601 media, types of, 600

String array, matrix creation, 115-116 commands, see string; stringvec matrix, 112-114 polynomials, 483 relational operators, 528 vectors, 112, 172, 257

Subdirectories, 602 Subtraction, 44, 77, 360, 366,

416, 420, 432, 435 Subwindows, 253-254 Sun Microsystems, 20-21 Surface area, 450 Symbolic evaluation, 483 Symbolic integration, 451 Symbolic matrices, 150-151, 459-460 Symbolic Toolbox, 412, 431-432, 484 Symbols

algebraic, 43 commands for, 257 Greek, 257 list of operations, 44 operations, 76-77 percentage (%), 45, 614

Symmetric matrix, 82, 130-131, 145 Syntax, 36, 257, 538, 614

System, generally maintenance, 598 optimization, 474 software, 18-19 transfer function, 425

Table construction, 34 Tangent functions, 196-202, 205-210, 262,

440, 446, 448 Taylor (MacLarin) polynomial series

approximation, 458-459 Technical knowledge, 7-9 Technological trends, 11-14 Telecommunications industry, 5 Temporary work, 5 Terafl op chip, 12 Termination of program, 24.