1550251515-Classical_Complex_Analysis__Gonzalez_

Index

Continuity of the first derivative,

385-387

Convergence:

absolute, 186, 201

almost uniform, 522

conditional, 189

of integrals, 687

pointwise, 197, 200

of sequences, 111-112, 174-

175

of series, 185

Correspondence (see Mapping)

Critical algebraic points, 287

Curve(s), 157-158, 511

Cycle, 160

D'Alembert test, 194
Darboux's inequality, 423
Degree of a polynomial, 260
De Moivre theorem, 43
De Morgan's laws, 80
Derivative:
angular, 310
directional, 311, 338-339,
341-349
for the inverse function,
362
transformations induced
by, 379-380
of an integral, 499-501
logarithmic, 7 40
mean, 341, 355
ordinary, 308
partial, 326, 328-331
phase (or areolar), 341
second directional, 354
rectilinear, 354
Deviation from analyticity, 342
Diameter of a set, 98
Differentiability of u(x, y),
313-316
Differentiable function, 309

761

Differential:

invariant, 246

oper<!ctors~326', 328-331, 338

total,"'!313-'--::S14, 326, 343

Differentiatioh:

rules, 312-313

of sequences and series,

·523-525

Dirichlet's

discontinuous function, 704

test, 564

Discrete Green theorem, 448-449

Distance, 63, 65, 91-92, 98,

243-246

Distortion angle, 343, 346,

371-377

Domain (see Region)

Domain of existence of a

function, 3

Duplication formula for I'(z),

616, 620-621

Entire (or integral) function, 309

Equation of continuity, 512

Equivalence relation, 77

Equivalent infinitely large

functions, 142

infinitesimals, 139-140

Essential singularity, 653-654,

661

Euclidean geometry, 241

Euler (or Gauss) formula,

622-623

Eulerian integrals, 613

Euler numbers, 548-549, 738-739

Evaluation of real improper

integrals, 687-732

Exponential function, 272-274

Exterior:

of a curve, 158

point of domain of f, 653

of a set, 96