I
ideal beam, 303
ideal column, 308
identity matrix, 340
implicit solution, 58
improved Euler's method, 86 - 88
impulse force, 267
impulse function, 267
independent variable, 6
indiscriminate, constant-effort
harvesting, 456
infection rate, 139 , 471
infectives, 139, 470
initial conditions, 21 - 22 , 33 , 165
system of first-order equations,
318
initial value problem, 21 - 22
first-order, 33 , 51
linear , 51
linear system, 322
n-th order linear homogeneous
165
n-th order linear nonhomogen-
eous 165 - 166
nonlinear, 51
system of first-order equations,
318
integral curves, 17
Indexinternal prey and internal predator
competition with h arvesting, 460
internal prey competition model,
459
interpolating polynomial, 97
inverse Laplace transform, 234
partial fraction expansion, 236
involute of a circle, 128
J
jump discontinuity, 229
K
Kermak, W. 0., 472
Kirchoff, Gustav, 279
Kirchoff's laws, 279
Kutta, Martin Wilhelm, 73, 86L
Lagrange, Joseph Louis, 494 , 497
Lanchester, F. W., 445
Lanchester's combat models,
445 - 451
conventional forces, 446 - 448
guerrilla force, 448579Laplace, Pierre Simon Marquis de,
223
Laplace transform, 223
existence theorem, 232
for y(n)(x), 243
inverse, 234 , 236
linearity property, 227
properties of, 538
second translation property, 261
table of, 537 - 538
translation property, 228
law of conservation of averages, 456
law of mass action, 157
learning theory models, 129 - 131
left-hand derivative, 11
Leibniz, Gottfried Wilhelm, 1, 3- 4
lemniscate, 124 - 125
Lesli e-Gower prey-predator model,
465
Lesli e's prey-predator model , 464
Libby, Willard F., 30
limac;on , 124
linear combination, 168
linear differential equ ation, 8
first-order, 51
n-th order, 163
system, 315
linear first-order initia l value prob-
lem, 51
linear independence of vector func-
tions, 346