By L. I. Volkovyskii, G. L. Lunts, I. G. Aramanovich, Mathematics
This complete assortment includes over 1,500 difficulties at the concept of features of the complicated variable and covers approximately each department of classical functionality idea. it is going to be of exact curiosity to practising engineers and researchers within the actual sciences, for massive cognizance is given to these difficulties which illustrate the appliance of the speculation of capabilities of a posh variable to difficulties facing the mechanics of constant media and electric engineering.
The difficulties themselves diversity in trouble from basic to these encountered simply in additional complex treatments.
The first 4 chapters contain advanced numbers and features of a posh variable; conformal mappings attached with simple services; supplementary geometrical questions and generalized analytic features; and integrals and gear series.
Chapters V via VIII conceal the Laurent sequence, singularities of single-valued features, and essential features; quite a few sequence of services, parametric integrals, and countless items; residues and their functions; integrals of the Cauchy type;and fundamental formulae of Poisson and Schwarz.
The ultimate 3 chapters speak about analytic continuation, singularities of many-valued personality, and Riemann Surfaces; conformal mappings; and purposes to mechanics and physics. solutions and recommendations are grouped on the finish of the text.
Unabridged Dover (1991) republication of the version released through Pergamon Press, Oxford, England, 1965
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Additional resources for A Collection of Problems on Complex Analysis
KELDYsH, (1939) Conformal representations of multiply connected domains (Konformnyye otobrazheniya mnogosvyaznykh oblastei), Uape'/chi, matem. naulc, vol. VI, 90-119. 30 PROBLEMS ON COMPLEX ANALYSIS to points, can be conformally mapped onto a concentric ring with well-defined ratio µ of the radii of the outer and inner circles (µ is the modulus of the doubly connected domain). 216. Map the semicircle Rez > 0 with the disk lz-hl < R (h > R) deleted onto the ring (! < lwl < 1 so that the imaginary axis passes into the circle jwj = 1.
Plane and use the principle of symmetry in virtue of which the exterior of the cross is mapped onto the whole plane with a cut along a segment of the real axis. 285. Map the plane with outs along the ray [-a, + oo) (a ;;;;i: 0) and along the segment [- ci, ci] (c > 0) onto the upper half-plane. HINT. See the hint to problem 184. 286. Map onto the exterior of the unit circle the plane with outs along the negative part of the imaginary axis and along the lower half of the unit circle. HINT. It is reduced to problem 182, (1) by a linear transformation.
2) Explain the same questions for the mapping of the exterior of the disk lzJ <1 by means of the function w = R(z+ (m/zn)) and of the interior of the same disk by the function w = R((l/z)+mzn). °' 240. (1) Map the angle 0 < argz < nx, (0 < ~ 2) onto the upper half-plane. (2) Map the angle -n/4