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Green's Functions and Infinite Products Bridging the Divide /

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 ma...

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Bibliographic Details
Main Author: Melnikov, Yuri A. (Author, http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2011.
Edition:1st ed. 2011.
Subjects:
Mathematical analysis.
Analysis (Mathematics).
Differential equations.
Partial differential equations.
Applied mathematics.
Engineering mathematics.
Analysis.
Ordinary Differential Equations.
Partial Differential Equations.
Applications of Mathematics.
Online Access:https://doi.org/10.1007/978-0-8176-8280-4
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Table of Contents:
  • 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.

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