576 Ordinary Differential Equationscharacteristic polynomial, 350
characteristic value, 349
characteristic vector, 349
chemical reactions, 157 - 161
circle, 124
involute of, 128
coefficient functions, 8, 163
column, 308 - 311
ideal, 308
column vector, 336
combat loss rate, 445
compartment, 301
compartmental analysis, 301 - 303
compartmental system
closed, 301
open, 301
competitive hunters model, 467
complementary solution, 183 - 184,
371
conjugate root theorem, 209, 376
constant matrix, 336
continuation theorem
first-order initial value problem,
47
system initial value problem, 321
continuing method, 77
convergent numerical method, 105
convolution, 251
convolution theorem, 252
corrector formula, 102
Coulomb, Charles Augustine De,
278
coupled pendulums, 363 - 364,
390 - 391
coupled spring-mass system,
297 - 299, 383- 389
critical load, 309
critical point, 418
asymptotically stable, 418
neutrally stable, 418, 424 - 425
stable, 418
unstable, 418
critically damped, 284
CSODE user's guide, 499 - 523
cycloid, 128D
damped motion
forced, 293 - 295
free, 283 - 291
damped oscillatory motion, 283 - 284
damping constant, 387
damping factor, 284
deflation, 196
deflection of a beam, 307
dependent variable, 6
derivative, 11
left-hand, 11
right-hand, 11
Descartes, Rene, 1-2, 127 , 189- 190
determinant, 341
differential equation, 6
homogeneous, 64, 163
linear, 8
linearized, 202
n-th order, 8, 163
nonhon1ogeneous, 66 , 163
nonlinear, 8
order of, 7
ordinary, 6, 8
partial, 7
separable, 58
solution of, 9
Diophantus, 189 - 190
Dirac delta. function, 268
Dirac, Paul Adrien Maurice, 268
direction field, 34- 42
DIRFIELD, 37, 499, 513 - 515
discontinuity
jump, 229
removable, 229
discretization error, 79
global, 79 , 83
local, 79
double pendulum, 299 - 300, 391 - 392
Duffing's equation, 489 - 490