630 INDEX
Magnet ism , 446
Magnification, 57, 400
Mand elbrot-Benoit, 136
Mand elbrot set, 132, 136
Maple™, 303, 318
Mapping, 49
z", 63, 67
z l/2, 80
zlf"', 63
~) 85
expz, 158, 160, 410
Log(z), 167, 411
(z2 -1)1/2, 414
sinz, 420
tan z, 418
bilinear, 402, 404 , 407
conformal, 395, 433 , 450, 469
linear, 58, 402
Mobius, 402 , 404, 407
one-to-one, 53, 402
trigonometric function, 418
Mathema.tica™, 303, 318
Mathematical models, 444 , 459,
466, 500
difference equation, 348
electrostatiC8, 459, 500
ideal fluid flow, 117 , 466, 496
steady state temperatures, 446
Maximum modulus principle for
analytic functions, 242, 244
Maximum principle for harmonic
functions, 248
Mean value principle for analyt ic
functions, 242
Mechanical system, 529
Meromorphic function, 328
ML ineq uality, 210
Mobius t ransformation, 402, 404,
407
Modulus, 17
principle for integrals, 24 2
product, 19
quotient, 19
Morera.'s Theorem, 241
Moving average filter, 384 , 385
M-test, 251
Multiplication of complex
numbers, 8
Multiplicative inverse, 11
Multiply connected domain, 214
Multivalued function, 80
Multivalued Logarithm , 163
""value Dirichlet problem, 430 ,
432
""cycle, 139
Negative orientation, 215Neighborhood, 40
Newton's law of cooling, 348
Newton's method, 132
Normal derivative, 451
n t h root, 33, 68
Nyquist stability criterion, 329
!, 11 , 85
6 ne--to-one function 1 53, 402
Onto, 52
Open
disk, 40
neighborhood, 40
set, 42
Opposite curve, 20 0, 208
Orbit, 135
O rder
pole, 277
zer o, 278
Orientation, 40, 198, 200, 208, 215
negative, 215
positive, 215
Orthogonal families, 119 , 445, 446,
459, 468
Output response, 380
Parameterizatio n of curve, 38,
198 , 209
Parametric equations, 38, 198 ,
206, 496
Partial fractions, 297
Partial sums, 127
Pa.th, 198, 200
integration, 200, 206
Period
expz, 157
function, 159
strip for expz, 159 , 410
trigonometric function, 179
Picture o f Wallis's complex
numbers, 4
Piecewise continuous, 514
Point
exterior, 41
infinity, 86
interior, 41
stagnat ion , 482
Poisson integral formula
unit disk, 524
upper half plane, 439
P oisson kernel, 439, 526
Polar form
Cauchy-Riemann equations,
1 05, 108
complex number, 22
coordinates, 22
Laplace's equation, 120
Pole, 86, 277