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18.086 Mathematical Methods for Engineers II

18.086 Mathematical Methods for Engineers II (Spring 2006, MIT OCW). This consists of 29 video lectures given by Professor Gilbert Strang, focusing on initial value problems and solution of large linear systems. This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization. (from ocw.mit.edu)

Lecture 11 - Level Set Method

Go to the Course Home or watch other lectures:

Lecture 01 - Difference Methods for Ordinary Differential Equations

Lecture 02 - Finite Differences, Accuracy, Stability, Convergence

Lecture 03 - The One-way Wave Equation and CFL/ von Neumann Stability

Lecture 04 - Comparison of Methods for the Wave Equation

Lecture 05 - Second-order Wave Equation (including leapfrog)

Lecture 06 - Wave Profiles, Heat Equation/ Point Source

Lecture 07 - Finite Differences for the Heat Equation

Lecture 08 - Convection-Diffusion/ Conservation Laws

Lecture 09 - Conservation Laws/ Analysis/ Shocks

Lecture 10 - Shocks and Fans from Point Source

Lecture 11 - Level Set Method

Lecture 12 - Matrices in Difference Equations (1D, 2D, 3D)

Lecture 13 - Elimination with Reordering: Sparse Matrices

Lecture 14 - Financial Mathematics/ Black-Scholes Equation

Lecture 15 - Iterative Methods and Preconditioners

Lecture 16 - General Methods for Sparse Systems

Lecture 17 - Multigrid Methods

Lecture 18 - Krylov Methods/ Multigrid Continued

Lecture 19 - Conjugate Gradient Method

Lecture 20 - Fast Poisson Solver

Lecture 21 - Optimization with constraints

Lecture 22 - Weighted Least Squares

Lecture 23 - Calculus of Variations/ Weak Form

Lecture 24 - Error Estimates/ Projections

Lecture 25 - Saddle Points/ Inf-sup Condition

Lecture 26 - Two Squares/ Equality Constraint Bu = d

Lecture 27 - Regularization by Penalty Term

Lecture 28 - Linear Programming and Duality

Lecture 29 - Duality Puzzle/ Inverse Problem/ Integral Equations