Complex Analysis - Maths KU

IND-4 Word Index
7.2 Word Index
Word Index
Absolute convergence of a
series, 306
Absolute value, 10
Addition of complex numbers, 3-4
Additive identity, 4
Additive inverse, 6
Adjoint matrix, 405
Amplitude spectrum, 385
Analytic function(s):
definition of, 145
derivative of, 155
on a domain, 145
at a point, 145
product of two, 146
quotient of two, 146
singular point of, 146
sum of two, 146
zeros of, 279, 337-338, 363, 365
Analytic mapping, 223, 429
Analytic part of a Laurent series, 325
Angle between curves, 391-392
Angle magnification, 393
Angle of rotation, 70
Angles equal:
in magnitude, 390
in sense, 390
Annular region, 32
Annulus, circular, 31
Antiderivative:
definition of, 266
existence of, 269
Arc length, 252
integration with respect to, 239
Arcsine, 215
Argument:
of a complex number, 17
of a conjugate, 22
as a multiple-valued function, 95
principal value of, 17
principle, 363
of a product, 18
of a quotient, 18
Arithmetic operations on complex
numbers, 3-5
Associative laws, 3
Auxiliary equation, 39
Bilinear transformations, 400
Binomial series, 331
Binomial theorem, 8
Boundary conditions, 223, 420,
429-430
mixed, 435
Boundary point of a set, 31
Boundary of a set, 31
Boundary value problem, 429
Bounded:
function, 124
polygonal region, 410
sequence, 312
set, 32
Bounds:
for analytic functions, 278, 280,
283-284
for a continuous function, 124
for a contour integral, 252
Branch:
of a complex power, 197
cut, 126
of an inverse hyperbolic function,
219
of an inverse trigonometric
function, 217
of the logarithmic function,
187-188, 190
of a multiple-valued function,
125
point, 127, 188
principal, 126, 187
of root functions, 126
Bromwich contour integral, 378
Capacitor, 40
Cauchy, Augustin Louis, 2
Cauchy-Goursat theorem:
for multiply connected domains,
259-261
proof of, 257, APP-4
for simply connected domains, 258
Cauchy principal value of an
integral, 355
Cauchy product of two infinite series,
322