1550078481-Ordinary_Differential_Equations__Roberts_

nonhomogeneous linear system,

342, 366

Index

associated homogeneous system,

370

representation theorem, 371

nonhomogeneous n-th order linear

equation, 182

initial value problem 219 - 220

with constant coefficients, 211-

218

nonhomogeneous system of equa-

tions, 316

nonlinear differential equation, 8

first-order, 51

system, 316

nonlinear first-order initial value

problem, 51

nonlinear spring, 489

nonlinear system of first-order

equations, 316

nontrivial solution, 310

numerical instability, 105

numerical solution, 73 - 116

Nystrom, E. J., 100

Nystrom formulas, 100

Nystrom methods, 100 - 101

0
Ohm, Georg Simon, 278
one-parameter family of solutions,
17
one-step method, 77
operation loss rate, 445
operator
linear, 226
orbit, 417
order of the reaction, 158
ordinary differential equation, 6
linear, 8
nonlinear, 8
overdamped, 284
overflow, 75

p

parameters

essential, 18

partial differential equation, 7

partial fraction expansion, 236

particular solution, 182

form of, 215

581

nonhomogeneous linear system,

370

path of an electron, 300 - 301, 392 -

397

Peano, Giuseppe, 43

Pearl, Raymond, 133

pendulum, 480 - 489

coupled, 363 - 364, 390 - 391

double, 299 - 300, 391 - 392

Foucault, 485 - 486

linearized, 202

simple, 200 - 203, 275 - 276, 480-

484

spring, 486 - 487

variable length, 484- 485

percentage relative error , 76

period of oscillation, 283

periodic trajectory, 455

Petri, Nicolas, 199

phase angle , 282

phase-plane, 417

phase-plane portrait, 417

Picard, Charles Emile, 5, 45, 416

piecewise continuous function, 229

Poincare, Henri, 5, 416

pollution in the Great Lakes, 152 -

153, 402 - 405, 493 - 494

polynomial, 189

root of, 189

POLYRTS, 197 - 199, 499- 504

population models, 131- 137

PORTRAIT, 438 - 439, 525 - 536

predictor formula, 102

predictor-corrector methods, 102 -

104