Complex Analysis - Maths KU

Word Index IND-9
principal square root, 86
range of, 50
rational, 100, 146
real, 51
real part of, 51-52
reciprocal, 100
regular, 145
single-valued, 94
singular point of, 146
squaring, 81
stream, 167
trigonometric, 200-201
value of, 50
vector, 284
zeros of, 337-338
Fundamental region for exponential
function, 179-180
Fundamental theorem:
of algebra, 279, 283
of calculus, 236
of contour integrals, 266
Gauss, Carl Friedrich, 2
Gauss’ mean value theorem, 283
Generalized circle, 109
Geometric series, 303-304
Goursat, Edouard, 258
Gradient:
field, 166
of a scalar function, 165-166
Green’s theorem, 257
Group, 79
Half plane, 29-30
Harmonic conjugate function, 160
Harmonic function, 159
under an analytic mapping, 223
Harmonic series, 308
Heat flow, 132, 167, 435
Hermitian matrix, 44
Holomorphic, 145
Hyperbolic functions:
defined, 209
derivatives of, 209-210
inverses of, 219
properties of, 210
relationship to trigonometric
functions, 210
zeros of, 211, 214
Ideal fluid, 167, 285
Identity mapping, 72
Image:
of a parametric curve, 63
of a point under a mapping, 58
of a set, 59
Imaginary axis, 10
Imaginary circle, 109
Imaginary part:
of a complex function, 52
of a complex number, 2
Imaginary unit, 2
Impedance, 40
complex, 41
Improper integrals:
convergent, 354
divergent, 354
principal value of, 355, 373
Incompressible fluid, 167, 285
Indefinite integral, 266
Indented contour, 359
Independence of path, 265
Indeterminate form(s), 33, 147
Inequalities:
Cauchy’s, 278
Jordan’s, 372
ML, 253
triangle, 12
Infinite limit, 127
Infinite series:
absolute convergence of, 306
Cauchy product of two, 322
convergent, 303
geometric, 303-304
partial sum of, 303
sum of, 303
tests of convergence, 306-307
Infinity point at, 32
Initial point:
of a curve, 237, 246
of a vector, 10
Input, 50
Insulated boundary, 434
Integrable, 237, 248
Integrals:
Cauchy principal value of, 355
complex, 247, 249-250
contour, 248
definite, 236-237