solution continued
particular, 17, 215 , 370
singular, 19
steady-state, 294
system of first-order equ ations,
317
transient, 294
trivial, 310
two-parameter family, 18
solution curves, 17IndexSOLVEIVP, 94, 108 , 114, 115 , 119,
123 , 125, 129, 135, 140 , 144, 147,
151 , 158, 499, 515 - 519
SOLVESYS, 436 , 499, 520- 523
spiral of Archimedes, 127
spring-mass system
co upled, 297 - 299, 383- 389
linear spring, 489
nonlinear spring, 489
spring pendulum, 486 - 487
square matrix, 336
stability theorem, 443 - 444
stable, 418
stable arms race, 412
stable equilibrium point, 418
starting method, 77
steady-state solution, 294
Stefan's law of radiation, 161
stepsize, 78
selection of, 93 - 94
stepwise method, 77
superposition theorem
linear homogeneous n-th order
equations, 169
linear homogeneous system, 367
susceptibles , 139, 4 70
system of first-order equations, 313
homogeneous, 316
initial value problem, 318
linear, 315
nonhomogeneous, 316
nonlinear, 316
solution, 317
583T
table of inverse Laplace transforms,
235
t a ble of Laplace transforms, 235
tangent line method, 73, 83
Tartaglia (Niccolo Fontana), 191,
199
Taylor, Brook, 79
Taylor series expansion method of
order m, 78
Taylor series m ethod, 78 - 85
Taylor's formula with remainder, 78
terminal velocity, 144
Thomson, J. J., 300, 407
three species models, 460 - 462
threshold phenomenon, 4 72
threshold theorem, 472
Torricelli, Evangelista, 2
tractrix, 153
trajectory, 417
periodic, 455
transient solution, 294
translation property of Laplace
transform, 228 , 261
trapezoidal scheme, 101
trivial solution, 310
truncation error, 79
two-parameter family of solutions,
18u
undamped
forced motion 292 - 293
free motion, 282 - 283
underflow, 75
undetermined coefficients, 212
unit impulse function, 268
unit step function, 257
uptake function, 465
unstable, 418, 423 , 425
unstable arms race, 412
unstable critical point, 423
unstable node, 422