Page 895 - Advanced_Engineering_Mathematics o'neil
P. 895
Index 875
integral curves for, 4–6 complex, 471–472
linear, 16–20 convergence of, 466–467, 469–470
orthogonal trajectories, applications cosine function, 468–470
for, 34–35 defined, 466
pursuit problem, application for, Fourier transform and, 471–472
35–37 functions and, 465–467
Riccati equation, 28–29 Laplace representations, 469–470
separable equations, 3–13 sine function, 468–470
sliding motion on inclined planes, Fourier-Legendre expansions, 525–528
applications for, 31–33 Fourier series, 427–464, 495–501
terminal velocity, applications for, amplitude spectrum of, 456, 460
30–31 Bessel’s inequalities, 448–450
velocity of unwinding chain, boundary conditions, 427–428
application for, 37–38 coefficients, 430, 442, 444
Flow lines, 355 complex, 457–460
Fluids, 397–399, 779–786 convergence of, 432–435, 442–445
circulation of, 780 cosine function, 441–442
conformal mapping of flow models, DFT approximation of coefficients,
779–786 495–497
flux across surfaces, 397–399 differentiation of, 445–446, 448
graphs of flow models, 783–784 discrete Fourier transform (DFT) and,
Joukowski transformation, 785–786 495–501
plane-parallel flow, 779–780 even functions, 436–438
solenoidal, 780 filtering signals using, 461–463
stationary flow, 780 functions, 429–440
vortex, 780 Gibbs phenomenon, 438–440
Flux, defined, 397, 780 harmonic form of, 454–455
Forced motion, 66–67, 599–601 integration of, 446–448
springs, 66–67 odd functions, 436–438
waves, 599–601 Parseval’s theorem, 450–451
Forcing function ( f ), 43, 77–79 phase angle form, 452–456
Forcing term, 567 piecewise continuous functions,
Forward wave, 596–598 431–432
Fourier analysis, 425–562 piecewise smooth functions, 432
discrete Fourier transform (DFT), sampled partial sum of, 498–501
492–504 sine function, 443–445
Fourier integral, 465–470 Fourier transforms, 470–504, 582–584,
Fourier series, 427–464 586–587, 627–628, 630
Fourier transforms, 470–504 amplitude spectrum of, 474–475
Fourier-Bessel expansions, 552–556 bandpass filters and, 488–489
Fourier integral, 465–471 complex Fourier integral and,
absolutely integrible, 465 471–472
coefficients, 466, 468–469, 471 convolution, 479–481
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