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Course Description: Scientific computing is a powerful approach to study and solve engineering, scientific, and interdisciplinary biomedical problems involving complex geometrical structure and function. The following topics are covered in this class to learn the theoretical foundation, to program and to use the finite element method to solve linear boundary value problems in 1-D and 2-D: 1) Review of tools and methods from ordinary differential equations, partial differential equations, and calculus of variation for solving boundary value problems; 2) Review of Hilbert and Banach spaces; 3) Overview of finite difference and finite element methods for solving boundary value problems; 4) Deriving strong and weak formulation, Galerkin approximation and matrix formulation; 5) Finite element formulation; 6) Conjugate gradient method and other numerical techniques for solving the finite element formulation; 7) Finite element formulation for solving 2-D boundary value problems; 8) Mesh generation; 9) Programming a finite element; 10) Convergence, exactness and error analysis of the finite element method; and 11) Student will complete a project work in their area of interest/research.


syllabus, syllabi, engineering, electrical engineering, scientific computing, differential equations, Hilbert and Banach spaces, boundary value problems, finite element formation, finite elements