628 INDEX
FIR filter, 345, 346
Fixed point
attracti ng, 138
bilinear t ransformation, 410
F low circulation, 481
Fluid flow, 117, 446, 466, 469, 478,
496
a.bout a. cylinder, 471, 474
a.bout a. Joukowski airfoil, 478
a.bout a plate, 472, 476
at a wall, 508
complex potential, 468, 500
in a channel, 510
over a •tep, 497
through a. slit, 477
velocity, IJ 7 , 446
Font ana., Niccolo, 2
Forced vibrations, 532
Fourier
cosine series, 517
expansion, 515
series, 275 , 513
series properties, 539
s ine series, 517
transform, 536, 538
Fro.eta.I, 134 , 135
Fresnel integral, 265, 327
Function
ana.lytic, 95, 229
Bessel, 152 , 275
bilinear, 402, 404, 407
bounded, 245
branch, 64, 79, 163
complex, 49
continuous, 75
cosz, 176, 179
differentiable, 93, 102 , 105
doma.in of definition, 49
entire, 95, 245
exponential, 155
harmonic, 117 , 239, 42 5, 524
hyperbolic, 178, 183
image, 49
implicit, 404
integral of rational function, 308
inverse, 54, 188, 400
limit, 70 , 72 , 75
linear, 58, 402
logarithmic, 163
meromorphic, 328
multivalued, 80
one-to--one, 402
period, 159, 179
principa.l value, 64, 80
principal value log z, 163
range, 49rational, 308, 328
s in z, 176, 178
stream, 468
tangent , 177
transfer , 368, 3801 382, 388
trigonometric, 176
zeros, 32 , 246, 278
Fundamental period strip exp z,
159, 410
Fundamental theorem
algebra., 3 2, 246
integration, 229, 231
Gauss, K arl Ftiedrich, 5, 7, 14
Gauss's Mea.n Va.Jue t heorem, 242
Geometric series, 141
Goursat-Cauchy t heorem, 217
Goursat-Cauchy t heorem
Extended, 225
Green's Theorem, 216
Hadamard-Ca.uchy formula, 148
Harmonic
Harmonic conjugate, 113, 115,
117, 446
Harmonic function, 112 , 239, 42 5,
524
applications, 117, 425, 523
conjugate, 113, 115, 446
maximum principle, 248
Heat flow, 446
Heaviside expansion t heor em, 569
Hyperbolic functions, 178, 183
derivatives, 184
identities, 184
inverse, 191
Ideal fluid, 117, 446 , 466, 496
Identity t heorem for series, 261
Im(z}, 13, 51
Image
8uid flow, 469, 478, 496
function , 49
source, 504
Imaginary a.xis, 16
Imaginary unit, l
Implicit form bilinear
transformation, 404 , 407
Implicit function, 80, 404
Improper integral, 306
Indefinite integrals table, 489
Indefinite integrals theorem, 229
Indented contour integral, 3 16
Inequality
Cauchy's, 245
ML, 2 10
triangle, 18
triangle for integral, 210
Infinite series, 128