00000cmm a22000004a 4500 UP-99796217611212348 Buklod 20250204111608.0 m go j cr |nu|||auu|a 250204s2011 mau o j eng d 9780817682804 (eBook) 0817682805 (eBook) (iLib)UPD-00215704110 DMLR rda. eng DMLUC QA 371 M45 2011eb Melnikov, Yu. A. author. Green's functions and infinite products bridging the divide [electronic resource] Yuri A. Melnikov. Boston, Massachusetts Birkhäuser Boston 2011. 1 online resource (x, 165 pages) text rdacontent computer rdamedia online resource rdacarrier INTRODUCTION -- CHAPTER 1: Infinite Products & Elementary Functions -- 1.1 Classical Euler representations -- 1.2 Alternative derivations -- 1.3 Other elementary functions -- 1.4 Chapter exercises -- CHAPTER 2: Green's Functions for the Laplace Equation -- 2.1 Construction by the method of images -- 2.2 Conformal mapping method -- 2.3 Chapter exercises -- CHAPTER 3: Green's Functions for ODE -- 3.1 Construction by defining properties -- 3.2 Method of variation of parameters -- 3.3 Chapter exercises -- CHAPTER 4: Method of Eigenfunction Expansion -- 4.1 Hilbert's theorem -- 4.2 Cartesian coordinates -- 4.3 Polar coordinates -- 4.4 Chapter exercises -- CHAPTER 5: New Infinite Product Representations -- 5.1 Method of images extends frontiers -- 5.2 Trigonometric functions -- 5.3 Hyperbolic functions -- 5.4 Chapter exercises -- HINTS AND ANSWERS TO CHAPTER EXERCISES -- REFERENCES -- INDEX. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. This textbook accounts for two seemingly unrelated mathematical topics drawn from two separate areas of mathematics that have no evident points of contiguity. Green's function is a topic in partial differential equations and covered in most standard texts, while infinite products are used in mathematical analysis. For the two-dimensional Laplace equation, Green's functions are conventionally constructed by either the method of images, conformal mapping, or the eigenfunction expansion. The present text focuses on the construction of Green's functions for a wide range of boundary-value problems. Green's Functions and Infinite Products provides a thorough introduction to the classical subjects of the construction of Green's functions for the two-dimensional Laplace equation and the infinite product representation of elementary functions.  Every chapter begins with a review guide, outlining the basic concepts covered. A set of carefully designed challenging exercises is available at the end of each chapter to provide the reader with the opportunity to explore the concepts in more detail. Hints, comments, and answers to most of those exercises can be found at the end of the text. In addition, several illustrative examples are offered at the end of most sections. This text is intended for an elective graduate course or seminar within the scope of either pure or applied mathematics Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink Green's functions. Products, Infinite. Differential equations. SpringerLink (Online service). Electronic Resource Available for UP System via SpringerLink. https://doi.org/10.1007/978-0-8176-8280-4 FO UPD DMLR QA 371 M45 2011eb Electronic Resource