Page 892 - Advanced_Engineering_Mathematics o'neil
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872 Index
Differential equations (Continued) residue theorem integral evaluation of,
eigenfunction expansion and, 506, 748–750
518–519 temperature distribution in a
Euler’s, 72–74 semi-infinite bar, 633–635
exact, 21–25 temperatures in a homogeneous slab,
first-order, 3–42 631–633
forcing function ( f ), 43, 77–79 Diffusivity constant k, 623–624
homogeneous, 26–27, 45–48 Dimension, vector space, 172
initial value problems, 6–8, 40–41, Dirac delta function δ(t),102–106,
45–47 481–482
integral curves for, 4–6, 44–45 circuit transient modeling using,
105–106
Laplace transform, 77–120
defined, 102–103
Legendre, 518–519
filtering property of, 103–104,
linear, 16–20, 43–75
481–482
MAPLE operations, 791–793
Fourier transforms and, 481–482
nonhomogeneous, 48–49, 55–60
Heaviside function H(t) and, 481
ordinary, 3
impulses (δ),102–106
partial, 563–666
shifted, 103, 481
partial fractions decomposition and,
Direction fields, 137–139
84, 118–120
Directional derivative, 357–358
polynomial coefficients and, 112–114
Dirichlet problems, 641–655, 776–779
Riccati, 28–29
boundary data for D, 641–642
second-order, 43–75
conformal mapping solutions of,
separable, 3–13
776–779
series solutions, 121–135
cube, for a, 654–655
solutions of, 3–6, 45–49, 121–135,
disk, for a, 645–647
137–144
Laplace’s equation and, 641–642
Sturm-Liouville, 506
Poisson’s integral formula for,
systems of linear, 187–246, 295–342 648–649
Differentiation, 445–446, 448, 718 potential equations for, 641–655
Fourier series, 445–446, 448 rectangle, for a, 642–644
power series, 718 unbounded regions, for, 649–653
Diffusion, 631–635, 748–750 Discrete Fourier transform (DFT),
complementary error function (erfc), 492–504
631 approximation of Fourier coefficients,
cylinder, in a, 748–750 495–497
discontinuous temperature in a approximation of Fourier transform,
semi-infinite bar, 634–635 501–504
error function (erf), 631 inverse of, 494–495
heat equations for, 631–635 linearity of, 494
Laplace transform techniques for, N-point, 492–494
631–635 partial sums from, 498–501
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