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Course18.08629 lectures25 h 25 min

Mathematical Methods for Engineers II

Prof. Gilbert Strang · Massachusetts Institute of Technology

Start with lecture 1 At MIT OpenCourseWare

About

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.

Lectures

Video Lectures

  1. Lecture 1: Difference Methods for Ordinary Differential Equations 45 min · Video
  2. Lecture 2: Finite Differences, Accuracy, Stability, Convergence 56 min · Video
  3. Lecture 3: The One-way Wave Equation and CFL / von Neumann Stability 56 min · Video
  4. Lecture 4: Comparison of Methods for the Wave Equation 1 h 4 min · Video
  5. Lecture 5: Second-order Wave Equation (including leapfrog) 55 min · Video
  6. Lecture 6: Wave Profiles, Heat Equation / point source 53 min · Video
  7. Lecture 7: Finite Differences for the Heat Equation 1 h 1 min · Video
  8. Lecture 8: Convection-Diffusion / Conservation Laws 54 min · Video
  9. Lecture 9: Conservation Laws / Analysis / Shocks 45 min · Video
  10. Lecture 10: Shocks and Fans from Point Source 57 min · Video
  11. Lecture 11: Level Set Method 54 min · Video
  12. Lecture 12: Matrices in Difference Equations (1D, 2D, 3D) 58 min · Video
  13. Lecture 13: Elimination with Reordering: Sparse Matrices 57 min · Video
  14. Lecture 14: Financial Mathematics / Black-Scholes Equation 50 min · Video
  15. Lecture 15: Iterative Methods and Preconditioners 52 min · Video
  16. Lecture 16: General Methods for Sparse Systems 48 min · Video
  17. Lecture 17: Multigrid Methods 52 min · Video
  18. Lecture 18: Krylov Methods / Multigrid Continued 50 min · Video
  19. Lecture 19: Conjugate Gradient Method 53 min · Video
  20. Lecture 20: Fast Poisson Solver 49 min · Video
  21. Lecture 21: Optimization with constraints 51 min · Video
  22. Lecture 22: Weighted Least Squares 53 min · Video
  23. Lecture 23: Calculus of Variations / Weak Form 52 min · Video
  24. Lecture 24: Error Estimates / Projections 51 min · Video
  25. Lecture 25: Saddle Points / Inf-sup condition 52 min · Video
  26. Lecture 26: Two Squares / Equality Constraint Bu = d 53 min · Video
  27. Lecture 27: Regularization by Penalty Term 50 min · Video
  28. Lecture 28: Linear Programming and Duality 57 min · Video
  29. Lecture 29: Duality Puzzle / Inverse Problem / Integral Equations 52 min · Video

Syllabus and materials

At MIT OpenCourseWare, as the course publishes them.

Credits and licence

Institution
Massachusetts Institute of Technology
Department
Mathematics
Teacher
Prof. Gilbert Strang
Term
Spring 2006
Level
Graduate
Language
English
Subjects
Mathematics, Engineering
Source
MIT OpenCourseWare
Licence
CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only. MIT OpenCourseWare's terms
Attribution
Prof. Gilbert Strang. Mathematical Methods for Engineers II. Spring 2006. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
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