Catalog

Mathematical Methods for Engineers II

Mathematics MIT CC BY-NC-SA 4.0 29 lectures

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.

Syllabus

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

Course materials