L. I. Volkovyskii, G. L. Lunts, I. G. Aramanovich,'s A Collection of Problems on Complex Analysis PDF

By L. I. Volkovyskii, G. L. Lunts, I. G. Aramanovich, Mathematics

ISBN-10: 0486669130

ISBN-13: 9780486669137

This finished assortment includes over 1,500 difficulties at the concept of capabilities of the complicated variable and covers approximately each department of classical functionality idea. it is going to be of precise curiosity to working towards engineers and researchers within the actual sciences, for huge recognition is given to these difficulties which illustrate the applying of the idea of capabilities of a posh variable to difficulties facing the mechanics of continuing media and electric engineering.

The difficulties themselves diversity in trouble from effortless to these encountered in simple terms in additional complicated treatments.

The first 4 chapters contain complicated numbers and features of a fancy variable; conformal mappings hooked up with straightforward capabilities; supplementary geometrical questions and generalized analytic capabilities; and integrals and tool series.

Chapters V via VIII disguise the Laurent sequence, singularities of single-valued services, and vital capabilities; numerous sequence of features, parametric integrals, and endless items; residues and their functions; integrals of the Cauchy type;and necessary formulae of Poisson and Schwarz.

The ultimate 3 chapters talk about analytic continuation, singularities of many-valued personality, and Riemann Surfaces; conformal mappings; and functions to mechanics and physics. solutions and suggestions are grouped on the finish of the text.

Unabridged Dover (1991) republication of the variation released via Pergamon Press, Oxford, England, 1965

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Additional info for A Collection of Problems on Complex Analysis

Sample text

242. Find the function w(z), which maps the semicircle lzlO onto the disk lwlI, Imz>O onto the upper half-plane. 244. Map onto the upper half-plane: (1) The sector lzl R, O

Then the function J1 (z) which at points symmetrical with respect to 0 assumes values symmetrical to the values of f 1 (z) with respect to O*t, will be analytic in the domain D 1 symmetrical to the domain D 1 with respect to 0 and will map it onto the domain n:, symmetrical to D~ with respect to O*. The function f1(z) in D 1 , w = f1(z) = f 1(z) on 0, J1 (z) in D 1 effects the conformal mapping of the domain D 1 +0+D1 onto the domain l n~+o•+n:tt. The principle of corresponding boundaries Let D and D* be simply connected domains with boundaries 0 and o• the domain D* being situated entirely in the finite part of the plane.

Long the rays (-ex>, -1 ], [l, + ex>), (- i=, - i] and [i, + i=). 283. rg z = :n/n (0 < a < 1) pass into the corresponding radii. rg z = 2lc:7t/n (le= 0, 1, 2, ... , n -1) onto the lz! segments 1 exterior of the unit circle. jwj

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A Collection of Problems on Complex Analysis by L. I. Volkovyskii, G. L. Lunts, I. G. Aramanovich, Mathematics


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