Полное описание

Agarwal, R. P. An Introduction to Complex Analysis : монография / by Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas. - Boston, MA : Springer, 2011. - on-line. - URL: http://dx.doi.org/10.1007/978-1-4614-0195-7. - Загл. с экрана. - ISBN 978-1-4614-0195-7. - Текст : электронный.
Содержание:
Preface.-Complex Numbers.-Complex Numbers II -- Complex Numbers III.-Set Theory in the Complex Plane.-Complex Functions.-Analytic Functions I.-Analytic Functions II.-Elementary Functions I -- Elementary Functions II -- Mappings by Functions -- Mappings by Functions II -- Curves, Contours, and Simply Connected Domains -- Complex Integration -- Independence of Path -- Cauchy–Goursat Theorem -- Deformation Theorem -- Cauchy’s Integral Formula -- Cauchy’s Integral Formula for Derivatives -- Fundamental Theorem of Algebra -- Maximum Modulus Principle -- Sequences and Series of Numbers -- Sequences and Series of Functions -- Power Series -- Taylor’s Series -- Laurent’s Series -- Zeros of Analytic Functions -- Analytic Continuation -- Symmetry and Reflection -- Singularities and Poles I -- Singularities and Poles II -- Cauchy’s Residue Theorem -- Evaluation of Real Integrals by Contour Integration I -- Evaluation of Real Integrals by Contour Integration II -- Indented Contour Integrals -- Contour Integrals Involving Multi–valued Functions -- Summation of Series. Argument Principle and Rouch´e and Hurwitz Theorems -- Behavior of Analytic Mappings -- Conformal Mappings -- Harmonic Functions -- The Schwarz–Christoffel Transformation -- Infinite Products -- Weierstrass’s Factorization Theorem -- Mittag–Leffler’s Theorem -- Periodic Functions -- The Riemann Zeta Function -- Bieberbach’s Conjecture -- The Riemann Surface -- Julia and Mandelbrot Sets -- History of Complex Numbers -- References for Further Reading -- Index.

ГРНТИ	УДК
27.27	517.53/.55

Рубрики:
mathematics
mathematical analysis
analysis (Mathematics)
functions of complex variables
mathematics
functions of a Complex Variable
analysis

Аннотация: This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner.   Key features of this textbook: -Effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures - Uses detailed examples to drive the presentation -Includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section -covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics -Provides a concise history of complex numbers     An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.
Доп. точки доступа:
Perera, K.
Pinelas, S.

http://dx.doi.org/10.1007/978-1-4614-0195-7

Держатели документа:
Государственная публичная научно-техническая библиотека России : 123298, г. Москва, ул. 3-я Хорошевская, д. 17 (Шифр в БД-источнике (KATBW): -188112151)

Шифр в сводном ЭК: 7e19a7e57b226279b27cf1398686ab61

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