632 INDEX
infinite, 128
Laurent, 267, 291
Maclaurin, 256
power, 148
product, 262
quotient , 286
ratio test, 143, 148
representation of f(z), 148, 257
root test, 145
Taylor, 256, 257
uniqueness, 26 1
Signal processing, 345
Similarity mapping, 59
Simple
closed curve, 40, 198, 199
pole, 278, 294
zero, 278
S imply connected domain, 214
s in z, 176, 178, 311 , 420
Sine
Fourier sine series, 517
Sine function, 176, 178, 311, 420
Sine inverse, 188
Singular point, 276 , 277
essential, 277, 288
isolated, 277 , 291
pole, 277
removable, 277
residue, 294
Singularity, 276
Si nk, 499
Smooth curve, 38 , 199
Solenoidal vector field, 111
Source, 499
i mage, 504
Sphere Riemann, 86
Square root, 63, 64 , 82
branch, 82
principal value, 64
Riemann sur face, 83
Stability difference equa t ion , 359
Stagnation point, 482
Steady s tate
difference equation, 370
differential equation, 533
Stereographic projection, 86
Streamline curve, ll8, ll9, 446,
468
Strip period for exp z, 159, 410
S ubtraction of complex numbers , 7
S um partial, 127
Table
integrals, 489
Laplace transforms, 547
Laplace transforms properties,
543, 548z-transform properties, 345
z-transfor ms, 342
tan z, 177 , 182, 418
Tangent vector, 199 , 396, 486
Tartaglia, 2
Taylo r series, 256, 257
Taylor's T heorem, 257
Temperature steady state, 446
Terminal point, 198
Theorem Laurent's, 269
Transfer function, 380, 382
Transfor m Laplace, 541
Transformation, 49
zn, 63, 67
z^112 80
zt/n' 63
! SS
ex' ' pz, 158, 160, 410
Log(z), 167 , 411
(z^2 - 1)^112 , 414
sinz, 420
tanz, 418
bilinear, 402, 404, 407
composition, 410
conformal, 395, 433, 450, 469
Fourier, 536, 538
linear, 5 8, 402
Mobius, 402, 404, 407
reciprocal, 85
rotation, 56
&hwarz-Christoffel, 487
t rigonometric functions, 418
Transient sol ution
difference equatio n , 369
differential equation, 533
Translation, 55
Triangle
inequali ty, 18
inequality for integrals, 210
Trigonometric functions, 176
derivatives, 178
identities, 179
integrals, 301, 311
inverses, 188, 452
mapping, 418
zeros, 180
Two-dimensional
electrostatics, 459, 500
lluid llow, 117 , 466, 496, 500
mathemat ical models, 444, 459,
466 , 500
u(x,y), 50, 102, 193, 446
Unbounded set , 44
Undamped, 530
Uniform convergence, 250
Uniqueness power series, 261