9/7: Introduction; Taylor's theorem and differencing
9/12: Differencing in 1D, Taylor's Theorem in nD, HW1 Distributed, Solutions
9/14: 2D meshes and differencing, approximating DEs
9/19: Convergence Theory, HW2 Distributed, Solutions
9/21: Convergence Theory, continued, HW1 Due
9/26: Boundary conditions, HW3 Distributed, Solutions, Discretization code, Part (a) wrapper, Part (b) wrapper
9/28: Boundary conditions continued, complications, HW2 Due
10/3: Meshless Finite Differences, HW4 Distributed, Solutions, Discretization code for first-order approx, Discretization code for ghost point approach, Wrapper
10/5: Finite volumes in 1D, HW3 Due
10/10: Fall Break, no lecture
10/12: Finite volumes in 2D and 3D, HW4 Due, HW5 Distributed, Solutions
10/17: Spectral Methods
10/19: Fast Fourier Transform and Fast Poisson Solver, HW6 Distributed, Solutions, Fast Poisson Solver, Driver, Spectral Solver, Driver
10/24: Midterm Exam, Solutions
10/26: Weak forms and Ritz-Galerkin
10/31: Approximation Theory
11/2: Piecewise linears, HW5 Due
11/7: Piecewise polynomial approximation, HW7 Distributed, Solutions, 1D linear FEM, Driver
11/9: Hilbert Spaces, Lax-Milgram Lemma, Céa's Lemma, HW6 Due
11/14: Poincaré-Friedrichs, Reaction-convection-diffusion equations, HW8 Distributed, Solutions
11/16: Finite elements in 2D and 3D, approximation properties, HW9 Distributed, Solutions, matrix code, Jacobi, GS, driver, HW7 Due
11/21: Direct Methods
11/23: Iterative Methods and Matrix Splitting, HW8 Due
11/28: Krylov Methods and GMRES
11/30: MINRES and CG, HW9 Due
12/6: Final Exam, 9:00 - 11:00 AM, HH3013
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