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Mathematical Methods for Engineers II 18.086 MIT

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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.

Resources: OpenCourseware from MIT, UC Berkeley, Stanford along with many of the World's finest University's.

Language: English

Professors: Joshua Coleman, Michael Williams

Units: 29

Lesson content

Lec 1 Difference Methods for Ordinary Differential...
Lec 2 Finite Differences, Accuracy, Stability, Convergence
Lec 3 The One-way Wave Equation and CFL / von Neumann Stability
Lec 4 Comparison of Methods for the Wave Equation
Lec 5 Second-order Wave Equation (including leapfrog)
Lec 6 Wave Profiles, Heat Equation / point source
Lec 7 Finite Differences for the Heat Equation
Lec 8 Convection-Diffusion / Conservation Laws
Lec 9 Conservation Laws / Analysis / Shocks
Lec 10 Shocks and Fans from Point Source
Lec 11 Level Set Method
Lec 12 Matrices in Difference Equations (1D, 2D, 3D)
Lec 13 Elimination with Reordering: Sparse Matrices
Lec 14 Financial Mathematics / Black-Scholes Equation
Lec 15 Iterative Methods and Preconditioners
Lec 16 General Methods for Sparse Systems
Lec 17 Multigrid Methods
Lec 18 Krylov Methods / Multigrid Continued
Lec 19 Conjugate Gradient Method
Lec 20 Fast Poisson Solver
Lec 21 Optimization with constraints
Lec 22 Weighted Least Squares
Lec 23 Calculus of Variations / Weak Form
Lec 24 Error Estimates / Projections
Lec 25 Saddle Points / Inf-sup condition
Lec 26 Two Squares / Equality Constraint Bu = d
Lec 27 Regularization by Penalty Term
Lec 28 Linear Programming and Duality
Lec 29 Duality Puzzle / Inverse Problem / Integral Equations

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