Partial Differential equations and applications- Reference request

Question

I will be taking up a PDEs course next semester and would like to find some good references. The topics covered in the syllabus is given below.

Partial differential equations: Conservation laws, classifications, elementary analytical methods, initial/ boundary value problems. Diffusion equation: Fundamental solution, similarity solution, qualitative behavior of diffusion initial value problems, Cauchy problem with infinite domain, Initial boundary value problems in the semi- infinite domain, Green’s function, homogeneous boundary value problem with inhomogeneous boundary condition. Hyperbolic equations: Characteristic methods, initial value problems with non- continuous initial data, introduction to weak solutions. Basic option theory: Call option, put option, Asian option, Black – Sholes model and its derivatives. Numerical methods: Discretization of derivatives, boundary conditions, grids, finite difference methods for initial/ boundary value problems, consistency, stability, convergence, applications of finite difference methods in financial derivatives.

I hope someone could suggest a some reference books or maybe even a single book that may cover the above topics. Thanks and looking forward for some assistance. Cheers

Answer 1

For something that has a little bit of everything, check out Partial Differential Equations by Walter A Strauss

It is a great intro to all of these topics.

For more in depth references, I reccommend these to anyone studying this field:

Partial Differential Equations- Lawrence C Evans

Numerical Solution of Partial Differential Equations: An Introduction- Morton, K. W.

Numerical Methods to Conservation Laws- Randall J. Leveque

Green's Functions and Boundary Value Problems - Ivar Stakgold

Answer 2

A nice book focused on examples and treating much of the classical families of PDE step by step is the Partial Differential Equations of L. C. Evans. It seems to cover near all your syllabus, maybe without the discretization part.

Whatever, it is typically a good first course companion.

Hoping it will be of some help.