Page 401 - Schaum's Outline of Differential Equations
P. 401
384 INDEX
Linear difference equation, 325 Nontrivial solutions, 307, 310
Linear differential equations: Numerical instability, 158
applications of, 50, 114 Numerical methods, 176
characteristic equation for, 83, 89 Adams-Bashforth-Moulton method, 177, 196, 207
with constant coefficients, 73, 83, 89, 94, 254 Euler's method, 158, 196
existence and uniqueness of solution of, 73 Milne's method, 177, 207
first-order, 14, 42 Modified Euler's method, 177
general solution of, 74 (See also Solutions of ordinary order of, 178
differential equations) Runge-Kutta method, 177, 196
homogeneous, 73, 262 stability of, 158
wth-order, 89 starting values, 178
nonhomogeneous, 73, 94, 103 for systems, 195
ordinary point of, 262
partial differential equation, 304
regular singular point of, 275
second-order, 83, 262, 275 Order:
series solution of (see Series solutions) of a difference equation, 325
singular point, 262 of an ordinary differential equation, 1
solutions of, 73 (See also Solutions of ordinary of a numerical method, 178
differential equations) of a partial differential equation, 304
superposition of solutions of, 80 Ordinary differential equation, 1
systems of (see Systems of differential equations) Ordinary point, 262
with variable coefficients, 73, 262, 275 Orthogonal trajectories, 53
Linear independence: Orthogonality of polynomials, 291
of functions, 74 Oscillatory damped motion, 117
of solutions of a linear differential equation, 74 Overdamped motion, 117
Logistics population model, 12, 57
Partial differential equation, 1, 304
Partial fractions, method of, 224
Mathematica ®, 337 Particular solution, 74
Mathematical models, 9 Perfect Gas law, 10
Matrices, 131
A(
e , 140, 254 Period, 118
function, 212
Periodic
Method of Frobenius, 275 Phase angle, 66, 118
general solutions of, 276
Milne's method, 177 Piecewise continuous function, 318
for systems, 207 Piecewise smooth function, 318
Power
263
series method,
Modeling (see Mathematical models) Powers of a matrix, 132
Modeling Cycle, 9, 10, 336 Predator-Prey model, 12
Modified Euler's method, 177
Multiplication of matrices, 132 Predictor-corrector methods, 176
122
Pure resonance,
Multiplicity of an eigenvalue, 133
Qualitative approach in modeling, 10
n\, 266, 298 Quasi-linear partial differential equations, 304
Natural frequency, 118
Natural length of a spring, 115
Newton's law of cooling, 50
Newton's second law of motion, 51, 115 RC circuits, 45
Nonhomogeneous boundary conditions, 309 RCL circuits, 115
Nonhomogeneous boundary-value problem, 309 Recurrence formula, 263
Nonhomogeneous difference equation, 325 Reduction to a system of differential equations, 148
Nonhomogeneous linear differential equations, 73 Regular singular point, 275
existence of solutions, 74 Resonance, 122
matrix solutions, 254 RL circuit, 45
power series solutions, 263 Runge-Kutta method, 177
undetermined coefficients, 94 for systems, 196
variation of parameters, 103 Rodrigues' formula, 290
