Complex Analysis - Maths KU

Word Index IND-13
of a real improper integral, 355,
373
Principle of deformation of contours,
259
p-series, 306
Product:
of two complex numbers, 3-4
of two series, 322-323
Properties of continuous functions,
123
Properties of limits, 117
Punctured disk, 31-32
Pure imaginary number, 2
Pure imaginary period, 54
Quadratic:
equation, 37
formula, 37
polynomial, 38
Quotient of complex numbers,
3, 5
Radius of convergence, 307
Range of a function, 50
Ratio test, 306
Rational function, 100
continuity of, 124
Rational power of a complex
number, 26-27
Reactance, 40
Real axis, 10
Real function, 50, 51
Real integrals:
definition of, 236-239
evaluation of, 236, 239, 240
Real limits, 111, 115
Real multivariable limits, 115
Real number system R, 3
Real part:
of a complex function, 52
of a complex number, 2
Real-valued function of a complex
variable, 55
Real-valued function of a real
variable, 50
Rearrangement of series, 309
Reciprocal of a complex number,
6
Reciprocal function, 100
on the extended complex plane,
104
Reflection about real axis, 67
Region, 31
Regular, 145
Removable singularity, 336
Residue:
definition of, 342
at an essential singularity, 349
at a pole of order n, 344
at a simple pole, 343, 345
theorem, 347
Riemann, Bernhard, 95
Riemann mapping theorem, 396
Riemann sphere, 33
Riemann surface:
for arg(z), 96-97
for e z , 191
for sin z, 212
for sin –1 z, 221
for z 2 , 95-96
Rigid motion, 69
Root:
of complex numbers, 23-24
test for infinite series, 307
of unity, 27
Roots of polynomial equations, 37,
383
Rotation, 69
angle of, 70
Rouché’s theorem, 365
Schwarz-Christoffel formula, 413
Sequences:
bounded, 312
convergent, 302
divergent, 302
real and imaginary parts of, 303
Series:
absolute convergence of, 306
conditional convergence of, 306
convergence of, 303
divergence of, 304, 305, 306
geometric, 303
harmonic, 308
Laurent, 324-327
Maclaurin, 316
necessary condition for
convergence, 305