Course 18.086: Mathematical Methods for Engineers II (Spring 2009)

Past:

Wednesday, February 4, 2009
Introduction. dwarves, porridge, circulant matrix
Friday, February 6, 2009
ODEs, finite differences. multistep methods, Runge-Kutta, Euler, Adams
Monday, February 9, 2009
More finite differences, one-way wave. Lax-Friedrichs, Lax-Wendroff
Wednesday, February 11, 2009
Stability for one-way wave. CFL, von Neumann
Friday, February 13, 2009
Lax equivalence. Lax
Tuesday, February 17, 2009
Two-way wave, leapfrog method. wave equation, CEM
Wednesday, February 18, 2009
Heat equation. heat equation, Crank-Nicolson
Friday, February 20, 2009
Convection-diffusion. convection-diffusion
Monday, February 23, 2009
Black-Scholes. options, arbitrage, binomial options pricing, Black-Scholes
Wednesday, February 25, 2009
Conservation laws, shocks, fans. shock/fan example
Friday, February 27, 2009
Finite volume methods, flux limiters. Finite volume, Flux limiters
Monday, March 2, 2009
Level set method. Sethian's webpage, level set method, Fedkiw's animations
Wednesday, March 4, 2009
Linear algebra review, big and sparse matrices. condition number, sparse matrix
Friday, March 6, 2009
Elimination with reordering. Cholesky decomposition, minimum degree
Monday, March 9, 2009
Iterative methods. preconditioner, Jacobi, Gauss-Seidel, SOR
Wednesday, March 11, 2009
Multigrid. multigrid
Friday, March 13, 2009
Krylov methods. Arnoldi, Lanczos
Monday, March 16, 2009
Conjugate gradients. (pdf)
Wednesday, March 18, 2009
Fast Poisson. Poisson
Friday, March 20, 2009
Optimization (introduction). optimization
Monday, March 30, 2009
Weighted Least Squares. least squares
Wednesday, April 1, 2009
Calculus of Variations. action, calculus, FEM
Friday, April 3, 2009
Error estimates
Monday, April 6, 2009
Inf-sup condition
Wednesday, April 8, 2009
Two Squares, limit weights. lagrange multipliers
Friday, April 10, 2009
Regularization. Tikhonov regularization
Monday, April 13, 2009
Discrepancy principle
Wednesday, April 15, 2009
Linear programming and duality. linear programming
Friday, April 17, 2009
Simplex and interior point methods. simplex algorithm, Karmarkar algorithm patent
Wednesday, April 22, 2009
Brachistochrone with reflections. brachistochrone
Friday, April 24, 2009
Guest lecture: Benjamin Seibold, particle methods
Monday, April 27, 2009
Guest lecture: Gil Strang, SVD and circle-to-polygon
Wednesday, April 29, 2009
Analytic functions and complex calculus. holomorphic function, line integral, residue theorem
Friday, May 1, 2009
Analytic approximation, spectral method. spectral method

Future:

Project presentations