Page 402 - Schaum's Outline of Differential Equations
P. 402
INDEX 385
Scalar multiplication, 132 Standard form, 14
Second-order linear equations, 83, 262, 275 Starting values, 178
(See also Linear differential equations) Steady-state current, 65, 117
Separable equations, 15, 21 Steady-state motion, 117
Separation of variables, method of Step size, 158
for partial differential equations, 306 Sturm-Liouville problems, 310, 318
Series solutions: Superposition, 80
existence theorems for, 263 Systems of differential equations, 249
indicial equation, 276 homogeneous, 254
method of Frobenius, 275 in matrix notation, 148
near an ordinary point, 263 solutions of, 195, 249, 254
recurrence formula, 263
near a regular singular point, 276
Taylor series method, 273
Simple harmonic motion, 118 Taylor series, 163, 273
Singular point, 262 Temperature problems, 50
Solutions of difference equations: 77-89 ®, 337
general, 326 Transient current, 65, 117
particular, 326 Transient motion, 117
Solutions of ordinary differential equations, 2, 73 Trivial solution, 307, 310
boundary-value problems, 2, 309
from the characteristic equation, 83, 89
complementary, 74 Underdamped motion, 117
for exact, 31 Undetermined coefficients, method of
existence of (see Existence of solutions) for difference equations, 326
general, 74, 276 for differential equations, 94
by graphical methods, 157 Uniqueness of solutions:
homogeneous, 21, 74, 83, 89 of boundary-value problems, 310
by infinite series (see Series solutions) of first-order equations, 19
for initial-value problem, 2, 73, 110 of linear equations, 73
by integrating factors, 32 Unit step function, 233
by Laplace transforms, 242
for linear first order, 42
linearly independent, 74
by matrix methods, 254 Variable coefficients, 73, 262, 275
by the method of Frobenius, 275 Variables separated
by numerical methods (see Numerical methods) for ordinary differential equations, 15
near an ordinary point, 262 for partial differential equations, 305, 306
particular, 74 Variation of parameters, method of, 103
by power series, 263 Vectors, 131
near a regular singular point, 275 Vibrating springs, 114
for separable equations, 21
by superposition, 80
of systems, 195, 249, 254 Wave equation, 304
by undetermined coefficients, 94 Weight function, 291
uniqueness of (see Uniqueness of solutions)
by variation of parameters, 103 Wronskian, 74
Spring constant, 115
Spring problems, 114
Square matrix, 131 Zero factorial, 298
