Course Information Day One Handout The course meets in slot 19, from 2:00-3:15 PM on Tuesdays and Thursdays, in HH 3015. My office hours are on Mondays and Thursdays from 10:00 - noon, in HH-2019, or by appointment. Textbook No textbooks are required for this course. Relevant e-books from the library's collection (or elsewhere) include: Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems by Leveque A First Course in the Numerical Analysis of Differential Equations by Iserles Finite elements and fast iterative solvers with applications in incompressible fluid dynamics by Elman, Silvester, and Wathen Finite Elements: Theory, Fast Solvers, and Applications in Elasticity Theory by Braess Finite Volume Methods by Eymard, Gallouët, and Herbin Iterative methods for sparse linear systems by Saad (full text pdf available here) D2L This course will not be using D2L; all material online will be posted here.
 Approximate Schedule 9/8: Introduction; Taylor's theorem and differencing 9/13: Differencing in 1D, Taylor's Theorem in nD, HW1 Distributed, Solutions 9/15: 2D meshes and differencing, approximating DEs 9/20: Convergence Theory, HW1 Due, HW2 Distributed, Solutions 9/22: Convergence Theory, continued 9/27: Boundary conditions, HW2 Due, HW3 Distributed, Solutions, Matlab routines for HW3: FD Code, Uniform-mesh driver, Random-mesh driver 9/29: Boundary conditions continued, complications 10/4: Meshless Finite Differences, HW3 Due, HW4 Distributed, Solutions, Matlab routines for HW4: Driver, O(h) routine, O(h^2) routine 10/6: Weak forms and Ritz-Galerkin 10/11: Fall Break, no lecture 10/13: Approximation Theory, HW4 Due 10/18: Piecewise linears 10/20: Midterm Exam, Solutions 10/25: Piecewise polynomial approximation, HW5 Distributed, Solutions, Matlab routines for HW5: Driver, solution routine 10/27: Hilbert Spaces, Lax-Milgram Lemma, Céa's Lemma 11/1: Poincaré-Friedrichs, Reaction-convection-diffusion equations, HW6 Distributed, Solutions 11/3: Finite elements in 2D and 3D, approximation properties, HW5 Due 11/8: Finite volumes in 1D, HW7 Distributed, Solutions 11/10: Finite volumes in 2D and 3D, HW6 Due 11/15: Spectral Methods, HW8 Distributed, Solutions, Fast Poisson Solver code and driver, Spectral Method code and driver 11/17: Fast Fourier Transform and Fast Poisson Solver, HW9 Distributed, Solutions, Jacobi, Gauss-Seidel, matrix, and driver routines, HW7 Due 11/22: Direct Methods 11/24: Iterative Methods and Matrix Splitting, HW8 Due 11/29: Krylov Methods and GMRES 12/1: MINRES and CG, HW9 Due 12/8: Final Exam, 9-11am, HH3017