00000cmm a22000004a 4500 UP-99796217611212068 Buklod 20230215085534.0 m go j cr |n |||auu|a 110629s2011 xxu u | eng d 9781461401957 (eBook) 146140195X (eBook) (iLib)UPD-00214608225 DML eng DMLUC QA 255 A33 2011eb Agarwal, Ravi P. An introduction to complex analysis [electronic resource] Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas. New York Springer c2011. 1 online resource (xiv, 331 p.) 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 -- Cauchys Integral Formula -- Cauchys Integral Formula for Derivatives -- Fundamental Theorem of Algebra -- Maximum Modulus Principle -- Sequences and Series of Numbers -- Sequences and Series of Functions -- Power Series -- Taylors Series -- Laurent?s Series -- Zeros of Analytic Functions -- Analytic Continuation -- Symmetry and Reflection -- Singularities and Poles I -- Singularities and Poles II -- Cauchys 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-Lefflers Theorem -- Periodic Functions -- The Riemann Zeta Function -- Bieberbachs Conjecture -- The Riemann Surface -- Julia and Mandelbrot Sets -- History of Complex Numbers -- References for Further Reading -- Index. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. 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 Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink Numbers, Complex. Mathematical analysis. Electronic books. Perera, Kanishka 1969. Pinelas, Sandra. SpringerLink (Online service. Electronic Resourc Available for University of the Philippines Diliman via SpringerLink. Click here to access http://link.springer.com/book/10.1007/978-1-4614-0195- Monograp UPD DMLR Electronic Resource