580 Ordinary Differential Equations
linear operator, 226
inverse La place transform, 236
Laplace transform, 227
linear spring, 489
linear system of first-order equa-
tions, 315
initial value problem, 322
linearly dependent set of constant
vectors, 343
linearly dependent set of func-
tions, 171
linearly independent set of con-
stant vectors, 343
linearly independent set of func-
tions, 171
lo cal discretization error, 79
logarithmic spiral, 127
logistic curve, 134
logistic law model, 133
Lotka, Alfred James, 452M
Malthus, Thomas Robert, 131
Malthusian population model, 131
m ass on a spring, 276 - 278
matrix, 335
addition, 337
constant, 336
determinant of, 341
elements of, 336
entries of, 336
equality, 337
identity, 340
multiplication, 339
scalar multiplication, 338
size of, 336
square, 336
subtraction, 337
zero, 338
Ma uchly, John W., 74
May's prey-predator model, 466 -
467
McKendrick, A. G., 472Menton, M., 162
method of undetermined coefficients,
212- 218
Mich aelis, L., 162
midpoint rule, 101
Milne predictor-corrector iteration,
103
Milne, William E., 103
mixture problems, 146 - 15 3, 39 7- 405,
49 1- 494
modified E uler's method, 89
modified Richardson's arms race,
433 - 445
mole, 157
motion
forced, 292
forced damped, 293 - 295
forced undamped, 292 - 293
free damped , 283 - 285
free undamped, 282 - 283
Moulton, Forest Ray, 101
multistep method, 77 , 97- 102
closed, 97
open, 97
mutual disarmament, 412N
n-th order differential equ ation, 8,
163
homogeneous, 163
nonhomogeneous , 163
neutrally stable critical point, 418 ,
424 - 425
Newton, Isaac, 1, 3, 142, 19 3, 494
Newton-Raphson method, 193 - 197
Newton's law of cooling, 69- 71
Newton's laws of motion, 142
nonhomogeneous differential equation
equation
first-order, 66
n-th order, 163
system, 316