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.
Overview
Syllabus
- Lecture 1: Difference Methods for Ordinary Differential Equations
- Lecture 2: Finite Differences, Accuracy, Stability, Convergence
- Lecture 3: The One-way Wave Equation and CFL / von Neumann Stability
- Lecture 4: Comparison of Methods for the Wave Equation
- Lecture 5: Second-order Wave Equation (including leapfrog)
- Lecture 6: Wave Profiles, Heat Equation / point source
- Lecture 7: Finite Differences for the Heat Equation
- Lecture 8: Convection-Diffusion / Conservation Laws
- Lecture 9: 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
Taught by
Prof. Gilbert Strang
