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888 Index
Series representations, 121–135, Fourier transform, 490–491, 586–587,
715–728 630
Frobenius, 126–135 heat equation solution using, 630
isolated zeros, 722–724 integral evaluation using, 742–745
Laurent expansion, 725–727 rational functions of, 743–754
power series, 121–126, 715–724 rational functions times, 742–743
solutions, 121–135 residue theorem and, 742–745
Taylor expansion, 718–722 wave equation solution using,
Shannon sampling theorem, 485–486 586–587
Shifting theorems, 84–95, 103, 484 Singular matrix, 227, 229–230
Singular point, 126, 416
Dirac delta fuction,103
first (s variable), 84–86 Singular solutions, 4
Singularities, 729–750
Heaviside formula, 86–89
classification of, 729–733
Heaviside function H and, 86–95
essential, 730
second (t variable), 88–93
isolated, 729
window function, 484
pole of order m, 730–732
Signals, 461–463, 471–472, 483–489
poles of quotients, 732–733
band-limited, 485
removable, 729
bandpass filtering, 488–489
residue theorem and, 729–750
bandwidth, 485
Skew-hermitian matrix, 288–290
Cesàro filter function Z(t), 462–463
Skin effect, 548
energy of, 483
Sliding motion on inclined planes,
filter function Z, 461
31–33
filtering, 461–463
Smooth surface, 392
Fourier series used for, 461–462
Solenoidal fluid, 780
Fourier transform used for, 471–472, Solutions of differential equations, 3–13,
483–489 19–20, 44–45, 47–49, 81–84,
frequency ω, 471–472 106–110, 121–135, 137–144,
Gauss filter, 463 218–226
Hamming filter, 463 approximation, 134–144
low-pass filtering, 487–488 closed-form, 121
Shannon sampling theorem for, defined, 3–4
485–486 first-order equations, 4–6, 19–20
shifted windowed Fourier transform fundamental set of, 47
for, 484 general, 4, 47
windowed Fourier transform for, homogeneous, 218–219
483–485 integral curves, 4–6, 44–45
Sine functions, 443–445, 468–470, Laplace transform used for, 81–84,
490–491, 586–587, 630, 742–745 106–110
convergence of, 444–445, 469–470 matrix operations for, 218–226
Fourier integral, 468–470 nonhomogeneous, 48–49, 220–226
Fourier series, 443–445 nontrivial, 218–219
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