Infinity, 86, 288 , 402, 407
lnitial conditions difference
equation, 361
Initial conditions z..tra.nsform, 344
Initial point, 198
Insulated boundary, 450, 455
Integral
around branch point, 322, 323
Cauchy principal value, 307,
311, 317, 323
Cauchy's formula, 235, 258
Cauchy's formula for
derivatives, 237
complex, 193, 202
contour, 202, 206
definite, 231
Fresnel, 265, 327
improper, 306, 311
indefinite, 229
indented contour, 316
Leibniz's rule, 237
line, 202, 206
or rational function, 308
Poisson, 439, 524
representation for /(z}, 235
representation for /' ( z), 237
table or indefinite, 489
theorem of indefinite, 229
trigonometric functions, 301,
311
Interior curve, 45, 214
Interior point, 41
Invariance fluid flow, 469 , 496
Invariance Laplace's equation, 427
Inverse
bilinear transformation, 402,
407
conformal function, 400
function, 54., 188
hyperbolic function, 191
image, 52
Laplace transform, 563, 568
Mobius transformation, 402
s ine functioa, 188, 452
trigonometric function, 188, 452
z..transform, 338
Irrotationa.l vector field, 111, 467
Isolated singularity, 276
IsothermaIB,446,447, 448
Iterates, 132
Jacobian determinant, 400
Jordan curve theorem, 44
Jordan's Lemma, 313
Joukowski airfoil, 477
Julia, Gaston, 134, 135
Julia set, 132, 136
Lagrange's Identity, 37
Laplace transform, 541
convolution, 572
derivatives, 549
existence, 543INDEX 629heaviside expansion, 569
integrals, 550
inverse, 563, 568
linearity, 544
properties, 543, 548
shifting theorem, 554
table, 547
uniqueness, 544
unit step function, 554
Laplace's equation, 113, 427, 452,
523
invariance, 427
polar form, 120, 524
Laurent series, 267 , 291
Laurent's Theorem, 269
Legendre polynomial, 240
Leibniz's Formula for series, 263
Leibniz's Rule, 237
Leibniz's Rule for integrals, 237
Length of contour, 205
Level curves, 119, 445, 459 , 468
L'Hopital's Rule, 98, 286
Limit, 70
Limit comple.x function, 72 , 75
Limit infinity, 86, 91
Limit sequence, 124
Limit supremum, 148, 154, 144
Line
charged, 459, 500
equation, 39, 200
flux, 408, 446 , 459
beat flow, 446, 447, 448
integral, 202, 206
Lill ear
approximation, 395
fractional transformation, 58,
402, 404, 407
transformation, 58, 402, 404,
407
Liouville's Theorem, 245
logz, 163
Log(z), 163, 411
Logarithm function
branch, 167
derivative, 167
mapping, 167 , 411
multivalued, 163
principal value, 163
Riemann surface, 168
LRC circuit, 185
Maclaurin series, 256