Linear partial differential equations: analysis and numerics

Lectures: 3 sessions / week, 1 hour / session

18.06 Linear Algebra, 18.700 Linear Algebra or equivalent.

This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson equations.

Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems including operator adjoints and eigenproblems, series solutions, Green's functions, and separation of variables.

Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems, including stability and convergence analysis and implicit/explicit time-stepping.

Julia programming language (a MATLAB®-like environment) is introduced and used in homework for simple examples. Julia is a high-level, high-performance dynamic language for technical computing, with syntax that is familiar to users of other technical computing environments. It provides a sophisticated compiler, distributed parallel execution, numerical accuracy, and an extensive mathematical function library.

There is no required text for this course, though the following books are recommended:

Strang, Gilbert. Computational Science and Engineering. Wellesley-Cambridge Press, 2007. ISBN: 9780961408817.
(emphasizing more the numerical part of the course). More information, including online chapters, can be found on Prof. Strang's CSE website.

Olver, Peter. Introduction to Partial Differential Equations. Springer, 2013. ISBN: 9783319020983. [Preview with Google Books] (free online book)

There will be five problem sets and a mid-term exam. There is a final project instead of a final exam. Late problem sets are not accepted, however the lowest problem set score will be dropped at the end of the term.

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