1550078481-Ordinary_Differential_Equations__Roberts_

582 Ordinary Differential Equations

prey-predator system in which

young protected, 461- 462

principal of competitive exclusion,

467

Pythagoreans, 190

Q

Quetelet , Lambert, 133

R
radioactive decay, 29 - 32
radiocarbon dating, 30
Raphson, Joseph, 193
Recorde, Robert, 189
Reed, Lowell, 133
reinforcement rate, 445
relative error, 76
relative removal rate, 472
removable discontinuity, 229
removal rate, 4 71
removeds, 4 70
representation theorem
homogeneous linear systems, 367
n-th order homogeneous linear
differential equation, 180
n-th order nonhomogeneous,
linear differential equation,
183
nonhomogeneous linear systems,
371
resonance, 293, 295
restricted three-body problem ,
494 - 498
Richardson, Lewis Fry, 407 - 408
Richardson's arms race
model, 407- 416
modified, 433 - 445
right-hand derivative, 11
RKF45, 94, 119
RLC circuit, 279 - 280
Roberval, Gilles, 2
root of a polynomial, 189
of multiplicity k , 205

rose curve, 124- 125

Roth, Peter, 192

round-off error, 75

row vector, 336

Ruffini, Paola, 192

runaway arms race, 412

Runge, Carl David Tolme, 73, 86

Runge-Kutta methods, 73

s

fourth order, 89 - 91

second order, 87

saddle point, 423, 426

second translation property, 261

separable equation, 58

sgn(x), 12

Shih-chieh, Chu, 193

signum function, 12

simple harmonic motion, 282

simple p endulum, 200 - 203, 275 - 276,

480 - 484

simultaneous linear equations

homogeneous, 342

nonhomogeneous, 342

single-step method, 77- 97

singular solution, 19

size of a matrix, 336

solution, 9

complementary, 183- 184, 371

explicit, 58

general, 19 , 368, 371

homogeneous linear first-order

equation, 65

homogeneous linear system, 368,

373

implicit, 58

linearly independent, 368

n-th order ordinary differential

equation, 8

nonhomogeneous linear first-

order equation, 68

nontrivial, 310

one-parameter family, 17