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Field name	Details
Dewey Class	515.9
Title	An Introduction to Complex Analysis ([Ebook]) / by Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas.
Author	Agarwal, Ravi P.
Added Personal Name	Perera, Kanishka
Added Personal Name	Pinelas, Sandra
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : Springer US , 2011.
Physical Details	XIV, 331 pages: 94 illus. : online resource.
ISBN	9781461401957
Summary Note	This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Â 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 âAnswers or Hintsâ 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 Â Â An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.:
Contents note	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 -- CauchyâGoursat Theorem -- Deformation Theorem -- Cauchyâs Integral Formula -- Cauchyâs Integral Formula for Derivatives -- Fundamental Theorem of Algebra -- Maximum Modulus Principle -- Sequences and Series of Numbers -- Sequences and Series of Functions -- Power Series -- Taylorâs Series -- Laurentâs Series -- Zeros of Analytic Functions -- Analytic Continuation -- Symmetry and Reflection -- Singularities and Poles I -- Singularities and Poles II -- Cauchyâs Residue Theorem -- Evaluation of Real Integrals by Contour Integration I -- Evaluation of Real Integrals by Contour Integration II -- Indented Contour Integrals -- Contour Integrals Involving Multiâvalued Functions -- Summation of Series. Argument Principle and RouchÂ´e and Hurwitz Theorems -- Behavior of Analytic Mappings -- Conformal Mappings -- Harmonic Functions -- The SchwarzâChristoffel Transformation -- Infinite Products -- Weierstrassâs Factorization Theorem -- MittagâLefflerâs Theorem -- Periodic Functions -- The Riemann Zeta Function -- Bieberbachâs Conjecture -- The Riemann Surface -- Julia and Mandelbrot Sets -- History of Complex Numbers -- References for Further Reading -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4614-0195-7
Links to Related Works	Subject References: Analysis . Functions of a Complex Variable . Functions of complex variables . Global analysis (Mathematics) . Mathematics . Authors: Agarwal, Ravi P. . author . Perera, Kanishka . Pinelas, Sandra . Corporate Authors: SpringerLink (Online service) . Classification: 515.9 . 515.9 (DDC 23) .

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An Introduction to Complex Analysis

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