Black Scholes PDE and its many solutions I know the general Black-Scholes formula for Option pricing theory (for calls and puts), however I want to know the other solutions to the Black-Scholes PDE and its various boundary conditions. Can someone start from the B-S PDE and derive its various solutions based on different boundary conditions? Even if you could provide some links/sources where it is done, I'll appreciate that. The point is that I want to know various other solutions and their boundary conditions which are derived from Black-Scholes PDE. Thank you.

Wikipedia has a fairly good explanation of this. In particular, look at
http://en.wikipedia.org/wiki/Black%E2%80%93Scholes#Derivation
The relevant problems (1 and 2) in Stein and Shakarchi's Fourier Analysis text (they derive the fundamental solution to the heat equation via the Fourier transform within the chapter):
http://books.google.com/books?id=FAOc24bTfGkC&pg=PA169
Finally, John Hull's Options, Futures, and Other Derivatives text has a derivation of the Black-Scholes formulas in the appendix to Chapter 13. 
