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Partial Differential equations and applications- Reference request

Course Queries Syllabus Queries
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Dipti Singh


( 5 months ago )

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

Lucky Negi


( 5 months ago )

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

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