Page 400 - Schaum's Outline of Differential Equations
P. 400
INDEX 383
Electrical circuits, 52, 115 Homogeneous boundary conditions, 309
Equilibrium point: Homogeneous boundary-value problem, 309
for a buoyant body, 116 Sturm-Liouville problem, 310
for a spring, 114 Homogeneous difference equation, 325
Euler's constant, 300 Homogeneous linear differential equation, 73
Euler's equation, 287 characteristic equation for, 83, 89
Euler's method, 158 with constant coefficients, 83, 89, 254
modified, 177 solution of (see Solutions of ordinary differential
for systems, 196 equations)
Euler's relations, 87 with variable coefficients, 262, 275
Exact differential equation, 15, 31 Homogeneous first-order equations, 15, 22, 29
Existence of solutions: Homogeneous function of degree n, 29
of first-order equations, 19 Hooke's law, 115
of linear initial-value problems, 73 Hypergeometric equation, 288
near an ordinary point, 262 Hypergeometric series, 288
near a regular singular point, 275
Exponential of a matrix, 140
Ideal Gas law (see Perfect Gas law)
Identity matrix, 132
Factorial, 266, 298 Indicial equation, 276
Falling-body problem, 51 Initial conditions, 2, 148
Fibonacci numbers, 326, 327, 329 Initial-value problems, 2
First-order differential equations: solutions of, 2, 21, 110, 242, 254, 264
applications of, 50 Instability, numerical, 158
Bernoulli, 14, 42 Integral of a matrix, 132
differential form, 14 Integral equations of convolution type, 239
exact, 15, 31 Integrating factors, 32
existence and uniqueness theorem, 19 Inverse Laplace transform, 224
graphical methods, 157 Isocline, 157
homogeneous, 15, 22, 29
integrating factors, 32
linear, 14, 42, 73 Jp(x) (see Bessel functions)
numerical solutions of (see Numerical methods)
separable, 15, 21
standard form, 15
systems of (see Systems of differential equations) Kirchhoff's loop law, 116
Fourier cosine series, 319
Fourier sine series, 319
Free motion, 117 L(y), 73
Frequency, circular, 118 Laguerre's differential equation, 290
natural, 118 Laguerre's polynomials, 291
Frobenius, method of, 275 Associated polynomials, 294
Laplace differential equation, 305
Laplace transforms, 211
applications to differential equations, 242
Gamma function, 295 of convolution, 233
table of, 297
General solution, 74 (See also Solutions of ordinary of derivatives, 242
derivatives of, 211
differential equations)
212
Graphical methods for solutions, 157 of integrals, 224
inverse of,
Growth problems, 50
of periodic functions, 212
for systems, 249
table of, 330
Half-life, 57 of the unit step function, 234
Harmonic function, 308 Legendre's differential equation, 269, 290
Harmonic motion, simple, 118 Legendre's polynomials, 269, 291
Heat equation, 304 Limiting velocity, 52
Hermite's differential equation, 290 Line element, 157
Hermite's polynomials, 291 Linear dependence of functions, 74
