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Volume 36 of "Modern Analytic and Computational Methods in Science and Mathematics: A Group of Monographs and Advanced Textbooks", edited by Richard Bellman, University of Southern California.
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Text: English, Polish (translation)
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Book Description Elsevier, 1972. Condition: Good. Former Library book. Shows some signs of wear, and may have some markings on the inside. Seller Inventory # 9985832-6
Book Description Elsevier & PWN, 1971. Condition: Good. A+ Customer service! Satisfaction Guaranteed! Book is in Used-Good condition. Pages and cover are clean and intact. Used items may not include supplementary materials such as CDs or access codes. May show signs of minor shelf wear and contain limited notes and highlighting. Seller Inventory # 0444000984-2-4
Book Description Elsevier & PWN, New York, 1971. Hardcover. Condition: Near Fine. Name stamp on endpapers, light wear, spine faded ; Modern Analytic And Computational Methods In Science And Mathematics; 283 pages. Seller Inventory # 50678
Book Description Elsevier & PWN, 1971. Hardcover. Condition: Good. Hardcover, xvii + 283 pages, NOT ex-library. Very good interior, clean and bright throughout, free of inscriptions/stamps, with unmarked text; no foxing, no age-spotting. Firm, secure binding. Faint dusty marks on page edges externally. Shelfworn, dulled boards with scuffing, dusty handling marks, sunning to spine. -- "This collection of exercises in analytic functions is an enlarged and revised English edition of a Polish version first published in 1962. The book is mainly intended for mathematics students who are completing a first course in complex analysis, and its subject matter roughly corresponds to the material covered by Ahlfors's book. Some chapters (ie. evaluation of residues, determination of conformal mappings, and applications in the two-dimensional field theory) may be of interest to engineering students. Most exercises are just examples illustrating basic concepts and theorems, some are standard theorems contained in most textbooks. However, the author does believe that the reconstruction of certain proofs could be instructive and is possible for an average mathematics student. When the subject matter of a particular chapter is not covered by standard textbooks, the numbers in parantheses given in the contents indicate a corresponding bibliography position which may be consulted for further information. The second part of the book contains solutions of problems. In most cases a complete solution is given; in some cases, where no difficulties could be expected, or when an analogous problem has been already solved in a detailed manner, only a final solution is given." -- Contents: PROBLEMS 1 Complex Numbers. Linear Transformations [Sets & Sequences of Complex Numbers; Spherical Representation; Similarity & Linear Transformations; Symmetry; Conformal Mappings Realized by & Invariant Points of Linear Transformations; Hyperbolic Geometry] 2 Regularity Conditions. Elementary Functions [Continuity. Differentiability; Harmonic Functions; Geometrical Interpretation of the Derivative; Conformal Mappings Connected with w=z2; Mapping w=1/2(z+z-1); Exponential Function & Logarithm; Trigonometric & Hyperbolic Functions; Inverse Trigonometric & Hyperbolic Functions; Conformal Mapping of Circular Wedges] 3 Complex Integration [Line Integrals. Index; Cauchy's Theorem & Integral Formula; Isolated Singularities; Residue Evaluation & Theorem; Evaluation of Definite Integrals Involving Trigonometric Functions; Integrals over an Infinite Interval; Integration of Many-Valued Functions; Argument Principle. Rouché's Theorem] 4 Sequences & Series of Analytic Functions [Almost Uniform Convergence; Power & Taylor & Laurent Series; Boundary Behavior of Power Series; Summation of Series by Means of Contour Integration; Integrals Containing a Complex Parameter. Gamma Function; Normal Families] 5 Meromorphic & Entire Functions [Mittag-Leffler's Theorem; Partial Fractions Expansions of Meromorphic Functions; Jensen's Formula. Nevanlinna's Characteristic; Infinite Products; Factorization of Entire & Elementary Functions; Order of Entire Function] 6 Maximum Principle [Maximum Principle for Analytic & Harmonic Functions; Schwarz's Lemma; Subordination] 7 Analytic Continuation. Elliptic Functions [Analytic Continuation; Reflection Principle; Monodromy Theorem; Schwarz-Christoffel Formula; Jacobian Elliptic Functions sn, en, dn; Functions  of Weierstrass; Conformal Mappings Associated with Elliptic Functions] 8 Dirichlet Problem [Riemann's Mapping Theorem; Poisson's Formula; Dirichlet Problem; Harmonic Measure; Green's Function; Bergman Kernel Function] 9 Two-Dimensional Vector Fields [Stationary 2D Flow of Incompressible Fluid; 2D Electrostatic Field] 10 Univalent Functions [Functions of Positive Real Part; Starshaped & Convex Functions; Univalent Functions; Inner Radius. Circular & Steiner Symmetrization; Method of Inner Radius Majorization]; SOLUTIONS. Seller Inventory # 005965