626 INDEX
Cauchy's residue theorem, 293
Cauchy's root test, 148
Causal sequence, 373
Cayley, Arthur, 132
Chain rule, 96, 396
Characteristic equation difference
equation, 358
Characteristic polynomial
difference equation, 358
Charged line, 459, 500
Circle, 402
equation, 40
image, 89
Circle of convergence, 150
Circulation flow, 481
Closed
curve, 39, 198
disk, 41
region , 44
set, 42
Commutative law of addit ion, 10
Commutative law o f
multiplication , 11
Comparison test for series, 130
Complex
conjugate, 13
der ivative, 93
differential, 205
exponents, 171
Fourier series, 536
function, 49
function Cartesian form, 50
function polar form, 51
infinity, 86
integral, 193, 202, 206
plane, 16
potential, 445, 468, 500
Complex n umber, l
absolute value, 17
argument, 23
conjugate, 13
exponential form, 26
imaginary part , 13
m odulus, 17
po lar form, 22
powers, 31, 171
real part, 13
roots, 33
Wallis's picture, 4
Confor mal mapping, 395, 433,
450, 469
angle of inclination, 396, 486
applications, 446, 459, 466
bilinear, 402, 404 , 407
inverse, 400, 402
properties, 396, 400scale factor, 400
Schwa.rz..Christoffel formula, 487
Conjugate comp lex number, 13
Conjugate harmonic function, 113,
115, 446
Connected set, 42, 136, 214
Continuity, 70, 75
Continuity equation, 467
Contin uous fu nction, 75, 514
Contou r, 198, 200
closed, 39, 198
deformation, 222
indented, 316
integral along, 202, 206
length, 205
simple closed, 40, 198
Convergence
a bsolute, 128 , 130, 145
circle, 150
complex series, 129
Laurent series, 269
power series, 148
radius of convergence, 148, 150
seq uences, 124
series, 128, 141, 145, 148, 150,
250
uniform, 250
Weierstrass M-test, 251
Convolution
difference equation, 349, 361,
368
Laplace transforms, 572
solution of d ifference equation,
349
z-transform, 344
cosz, 176, 179, 311
Cosine Fourier series, 517
C ritical point, 398
Cubic equation, 2
Curve, 38, 198
closed, 39, 40, 198
equipotential, 118 , 459, 468
exterior, 214
interior, 214
length, 205
level, 12 0, 446
opposite, 200, 208
orthogonal families, 119, 445
simple, 40, 198
simple closed, 199
s mooth, 38, 199
stream1ine 1 118
Cycle, 139
D. (zo), 40- (zo), 41
o; (zo), 4 1