Index
A(a, r, R), 268
Absolute convergence, 128, 130,
145
Absolute value, 17
Accumulation point 1 42
Addition of complex numbers, 7
Additive inverse, 11
Airfoil, 477
Amplitude response , 374, 381
Analytic function, 95 , 229
derivative formula, 102, 105
integral, 229
maximum modulus principle,
242, 244
mean value principle, 242
uniqueness theorem, 261
zeros, 278
Angle of inclination, 396, 486
Annulus, 268
Anti-Derivative, 229, 231
Arc
simple, 198
smooth, 38, 199
A re length, 205
arccos z, 188
aresinz, 188, 420, 452
arctan( ~ ), 24, 429
a.rctan z, 188
a.rgz, 23
Arg(z), 23 , 163, 430
Argument
complex number, 23
conjugate, 28
principle value, 23, 328
product of numbers, 27
quotient of numbers, 28
Associative law of addition, 10
Associative law of multiplication,
11
Attracting point, 138
Bernoulli's equation, 470
Bessel function, 152, 275
Bilinear transformation, 402
conformal, 410
625fixed point of, 410
implicit formula for, 404, 407
inverse of, 402
Binomial series, 264
Bombelli, Rafael, 3
Borda's mouthpiece, 511
Boundary
insulated, 450, 455
point, 41
value problem, 430, 432, 523
Bounded
function, 245
sequence, 126
set, 44
Branch
arcsine, 189
cut, 81
function, 79, 163
integral around, 322
logarithm, 163
point, 82
point integral, 322
square root, 64, 80
011, (zo), 42
Cardano, Girolamo, 2
Cauchy
Cauchy, Augustin Louis, 5, 100
principal value, 307, 317, 323
product of series, 130, 262
residue t heorem, 340
sequence, 127
Cauchy-Goursat t heorem, 217
Cauchy·Goursat t heorem
extended, 225
Cauchy-Hadamard formula, 148
Cauchy-Riemann equations,
100, 102
Cauchy-Riemann equations in
polar form, 105, 108
Cauchy's inequalities, 245
Cauchy's integral formulas, 235,
258
Cauchy's integral formulas for
derivatives, 237