d' Alembert's ratio test, 143, 148
Damped system, 531
De Moi vre's Formula., 32
De Morgan, Augustus, 5
Definite integral, 231
Deformation of contour, 222
Derivative
definition, 93
expz, 156
hyperbolic function, 184
inverse tl'igonometric functions>
189
logarithm function, 165
normal, 4 51
rules, 96
rules for series> 150
series, 150
trigonometric functions, 177,
178
Descartes, Rene, 14
Difference equation, 347, 348 , 358
characteristic equation , 358
characteristic polynomial , 358
convolution, 349, 361, 368
filter, 378
first o rder, 347
genera l solution, 349, 368
higher order, 360
homogeneous solution, 358, 368
initia l conditions, 361
mathematical models, 348
particular solution, 368
r ecursion formula, 360 , 373, 379
residue, 349, 362
second order, 358
stability, 359
Differential, 205
Differentiation, 93
Cauchy-Riemann equations, 102
definition, 93
r ules, 96
rules for series, 150
series, 150
Diffusion, 446
Digital signal filter, 373
Dipole, 120, 408, 509
Dirichlet problem, 430, 523
n value, 430, 432
unit disk lzl < 1, 523
upper half-plane, 430
Disk, 40
Distance between points, 17
Distributive law, 1 J
Divergent sequence, 124
Divergent series, 128
Division of complex numbers, 9
INDEX 627DomaJn, 43
definition for a fwiction, 49
multiply connected, 214
simply connected, 214
e^19 , 25 , 26
e', 155, 410
Elasticity, 446
Electrostatic potential, 446, 459,
500
Entire function, 95, 245
Equation
Bernoulli's, 470
Cauchy-Riemann, 100 , 102,
105
circle, 40
continuity equation, 467
curve, 38
La.place's, 427, 452
line, 39, 200
parametric, 38, 198, 205, 496
Equipotential curves, ll8, 459,
468
Equivalence of x + iy with (x, y),
12
Essential singularity, 277, 288
Euler, Leona.rd, 5
Euler's formula, 25
Euler's formula for Fourier series,
518
expz, 155, 410
Exponential form of a. complex
number, 26
Exponential function, 155, 410
derivative, 156, 162
fundamental period strip, 159,
410
inverse, 159, 163
mapping, 158, 159, 410
per iod, 157
Extended Cauchy-Goursat
theorem, 225
Extended complex plane, 86
Exterior of curve, 45, 214
Exterior point, 41
Fatou, Pierre, 134, 135
Ferro, Scipione del, 2
Fibonacci numbers, 265, 372
Filter
attenuating, 383
boosting up, 374 , 377, 382
combination, 374, 383, 389
difference equation, 378
FIR, 345, 346
moving average, 385
signal processing, 373
2eroing out, 374, 382