Page 898 - Advanced_Engineering_Mathematics o'neil
P. 898
878 Index
Heat conduction, 636–639 Homogeneous differential equations,
heat equations for, 636–639 26–27, 45–48, 213–219, 296–312
infinite cylinders, 636–638 coefficient of system, 213
rectangular plates, 638–639 complex eigenvalue occurrence,
Heat equation, 405–407, 611–639 306–308
boundary conditions for, 611–612, defined, 26, 213
622–624 first-order, 26–27
constants, effects of on, 611–612, free variables, 214–215
622–624 fundamental matrix for system,
convection, 612 300–301
general solution of, 300, 302–304
diffusion problems, 631–635
linear dependence and independence
Fourier transforms for solution of,
of, 46–47, 296–300
627–628, 630
linear systems, 213–219, 296–312
free radiation, 612
matrix of coefficients, 213–215
Gauss’s divergence theorem and,
mixing problem application of,
405–407
304–306
half-line problems, 629–630
nontrivial solution, 218–219
heat conduction problems, 636–639
reduced (matrix) systems, 213–219
infinite medium, solutions in,
second-order, 45–47
626–630
solution space of system, 216–217
initial conditions for, 611–612
solutions of, 45–47, 296–312
initial-boundary value problem,
system solutions, 296–312
611–612
trivial solution, 219
insulation conditions for, 612
without linearly independent
interval [0, L], 612–624
eigenvectors, 308–312
Laplace transform techniques for,
Wronskian (W) of, 46–47
631–635
Hyperbolic parabloid, surface integrals
Laplace’s equation and, 407 of, 388
real line problems, 626–628
temperature distribution, 612–624
I
vector integral calculus analysis
Identity matrix, 192–193
using, 405–407
Imaginary axis, 670
Heaviside function (H), 86–95, 481
Improper node, 334–336
Dirac delta function δ(t) and, 481 Impulses (δ),102–106
inverse transform formula, 93–95 Inclined planes, sliding motion on,
jump discontinuities, 86–87 31–33
pulses and, 87–89 Inconsistent system, 220–221
shifted, 86–89 Indicial equations, 127–129
shifting theorems and, 86–95 Inequality, complex numbers and, 672
Hermitian matrix, 288–290 Infinite medium, 626–630
Higher derivatives, Laplace transform Fourier transforms for solution of,
theorem of, 82 627–628, 630
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