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This course is appropriate for mathematics students who are interested in applications and numerical analysis, as well as mathematically-inclined engineering students. The main goals are (1) to provide a rigorous theoretical foundation for the application of the finite element method to approximate the solution of a (well-posed) partial differential equation and (2) to provide experience in coding the finite element method and verifying the correctness of the code. The course will draw upon results in linear algebra, real analysis, partial differential equations and some functional analysis on Hilbert spaces to analyze the properties of finite element approximations. The theoretical results will be illustrated by coding up examples in MatLab.Homework: Homework will be assigned periodically throughout the semester and will typically consist of a theoretical part and a computational part.