Complex Analysis - Maths KU

Word Index IND-7
Convergence of an improper integral,
356
Convergence of an infinite series:
absolute, 306
conditional, 306
definition of, 303
necessary condition for, 305
tests for, 306-307
Convergence of a power series, 307
circle of, 307
radius of, 307-308, 318
tests for, 306-307
Convergence of a sequence, 302-303
in terms of real and imaginary
parts, 303
Convex set, 35
Cosine:
hyperbolic, 209
inverse of, 216
Maclaurin series for, 318
as a mapping, 208
trigonometric, 200, 204
zeros of, 205
Critical point, 393
Crosscut, 259, 261
Cross ratio, 406
invariance of, 406-407
Commutative laws, 3
Cubic formula, 44
Curl of a vector field, 167, 285
Curve:
closed, 237, 246
initial point of, 237
opposite, 246
oriented, 246
piecewise smooth, 237, 246
simple closed, 237, 246
smooth, 237, 246
terminal point of, 237
Definite integral, 236-237
Deformation of contours, 259
Deleted neighborhood, 29
de Moivre’s formula, 20
Depressed cubic equation, 44
Derivative:
of complex exponential function,
177
of complex hyperbolic functions,
209-210
of complex inverse hyperbolic
functions, 220
of complex inverse trigonometric
functions, 218
of the complex logarithm, 188
of complex trigonometric
functions, 206
definition of, 142, 146
evaluation of, 142
formula for, 155
of power series, 314
rules for, 143
symbols for, 142
Differentiability implies continuity,
146
Differentiable at a point, 142
Differential equation, 38
Differentiation of a power series, 314
Differentiation, rules of, 143
Dirichlet problem, 168, 420, 429
in a half-plane, 228, 420-421
steps for solving, 225, 429
for unit disk, 425-426
Discontinuous at a point, 120
Disk, 29
closed, 31
open, 31
punctured, 32
Distance between two points, 11
Distributive law, 3
Divergence:
of improper integrals, 354
of sequences, 302
of an infinite series, 304, 305, 306,
307
of a vector field, 167, 285
Division of complex numbers, 3, 5
in polar coordinates, 18
Domain:
connected, 31
definitions of, 31, 50
doubly connected, 257
of a function, 50
multiply connected, 257
simply connected, 256
triply connected, 257
Electrostatic potential, 166, 432