000 03828nam a22004695i 4500
001 978-0-8176-8280-4
003 DE-He213
005 20140220083711.0
007 cr nn 008mamaa
008 110829s2011 xxu| s |||| 0|eng d
020 _a9780817682804
_9978-0-8176-8280-4
024 7 _a10.1007/978-0-8176-8280-4
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515
_223
100 1 _aMelnikov, Yuri A.
_eauthor.
245 1 0 _aGreen's Functions and Infinite Products
_h[electronic resource] :
_bBridging the Divide /
_cby Yuri A. Melnikov.
264 1 _aBoston :
_bBirkhäuser Boston,
_c2011.
300 _aX, 165p. 32 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aINTRODUCTION -- 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.
520 _aThis 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.
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aDifferential Equations.
650 0 _aDifferential equations, partial.
650 1 4 _aMathematics.
650 2 4 _aAnalysis.
650 2 4 _aOrdinary Differential Equations.
650 2 4 _aPartial Differential Equations.
650 2 4 _aApplications of Mathematics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817682798
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-8280-4
912 _aZDB-2-SMA
999 _c105104
_d105104