A Collection of Problems on Complex Analysis
Lev Izrailevich Volkovyski?, Grigori? L?vovich Lunt?s?, Isaak Genrikhovich Aramanovich, J. Berry, T. Kovari
Courier Corporation, 1991 - Mathematics - 426 pages
Over 1500 problems on theory of functions of the complex variable; coverage of nearly every branch of classical function theory. Topics include conformal mappings, integrals and power series, Laurent series, parametric integrals, integrals of the Cauchy type, analytic continuation, Riemann surfaces, much more. Answers and solutions at end of text. Bibliographical references. 1965 edition.
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_f(z absolute convergence algebraic branch points analytic function angle argz centre Chapter circles of Apollonius complex number complex potential conformal mapping Construct the Riemann continuous coordinate origin corresponding curves deﬁned deﬁnition domain bounded domain G doublet doubly connected domain edition ellipse equal equation equipotential lines essential singularity expansion exterior ﬁnd ﬁrst order ﬂow formula function f(z half-strip harmonic function harmonic measure HINT imaginary axis inﬁnite linear transformations logarithmic branch points maps the upper natural number neighbourhood parameters plane with cuts point 20 point at inﬁnity principal value Prove the following radius of convergence real axis real number rectangle respect Riemann surface ring satisﬁed segment semicircle sheets simple poles single-valued solution straight line stream lines strip symmetry principle theorem unit circle unit disk upper half-plane velocity vertices vortex source w-plane whole plane zero