1550078481-Ordinary_Differential_Equations__Roberts_

578 Ordinary Differential Equations

function continued

discontinuous, 229

exponential order, 231

forcing, 257

Heaviside, 257

piecewise continuous, 229

unit impulse, 268

unit step, 257

uptake, 465

fundamental existence and unique-

ness theorems

first-order initial value problem,

46

linear system initial value

problem, 322

system initial value problem, 319

fundamental existence theorem

first-order initial value problem,

43

fundamental theorem of algebra, 6,

192

fundamental theorem of calculus, 2

fundamental theorem of integral

calculus, 118

G
Galileo, 2
Gauss, Carl Friedrich, 191 - 192
general n-th order differential equa-
tion, 8
general n-th order nonhomogeneous
linear differential equation, 182
general solution
homogeneous linear system, 368
homogeneous linear system with
constant coefficients, 373
n-th order differential equation,
19
n-th order homogeneous linear
differential equation, 181
n-th order nonhomogeneous,
linear differential equation, 184

general solution continued

nonhomogeneous linear system,

371

global discretization error, 79 , 83

Gompertz population model, 136

GRAPH, 499, 510 - 513

Gregory, James, 79

H

half-life, 30

Hamer, William, 139

Harriot, Thomas, 189

harvesting

coefficient, 456

indiscriminate, constant-effort,

456

Heaviside function, 257

Heaviside, Oliver, 223, 257

Henry, Joseph, 278

Heun, Karl, 73, 86

Heun method, 73, 87

homogeneous differential equation

first-order, 64

n-th order, 163

system, 316

homogeneous linear equation

initial value problem 219

with constant coefficients, 200-

211

homogeneous linear system, 366

linear independence of solutions,

368

representation theorem, 367

superposition theorem, 367

homogeneous system of linear first-

order equ ations, 316, 342

Hooke, Robert, 277

Hooke's law, 277

Horner, W. G., 193

Homer's method, 193, 196 - 197

hypocycloid, 128