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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 07 - Finite Differences for the Heat Equation


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