Green's Functions and Infinite Products Bridging the Divide /

• Κύριος συγγραφέας: Melnikov, Yuri A. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston : Birkhäuser Boston, 2011.
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Differential equations.; Partial differential equations.; Applied mathematics.; Engineering mathematics.; Analysis.; Ordinary Differential Equations.; Partial Differential Equations.; Applications of Mathematics.

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...

Πίνακας περιεχομένων:

• 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.