# Mathematical Methods for Engineers II

- Institution: Massachusetts Institute of Technology
- Department: Mathematics
- Teacher: Prof. Gilbert Strang
- Term: Spring 2006
- Level: Graduate
- Language: English
- Subjects: Mathematics, Engineering
- Source: [MIT OpenCourseWare](https://ocw.mit.edu/courses/18-086-mathematical-methods-for-engineers-ii-spring-2006/)
- Licence: [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) (Non-commercial use only.)
- Syllabus: [at the source](https://ocw.mit.edu/courses/18-086-mathematical-methods-for-engineers-ii-spring-2006/pages/syllabus/)
- Readings: [at the source](https://ocw.mit.edu/courses/18-086-mathematical-methods-for-engineers-ii-spring-2006/pages/readings/)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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

1. [Lecture 1: Difference Methods for Ordinary Differential Equations](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/604f63e2bd5b), 45 min (Video)
2. [Lecture 2: Finite Differences, Accuracy, Stability, Convergence](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/22c5e6a0bdd3), 56 min (Video)
3. [Lecture 3: The One-way Wave Equation and CFL / von Neumann Stability](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/eb71fbb64fb0), 56 min (Video)
4. [Lecture 4: Comparison of Methods for the Wave Equation](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/3f62761a0681), 1 h 4 min (Video)
5. [Lecture 5: Second-order Wave Equation (including leapfrog)](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/69180fbf341a), 55 min (Video)
6. [Lecture 6: Wave Profiles, Heat Equation / point source](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/0ee3d26b6fb0), 53 min (Video)
7. [Lecture 7: Finite Differences for the Heat Equation](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/89e9821600db), 1 h 1 min (Video)
8. [Lecture 8: Convection-Diffusion / Conservation Laws](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/524e7809bac3), 54 min (Video)
9. [Lecture 9: Conservation Laws / Analysis / Shocks](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/b9120ef14768), 45 min (Video)
10. [Lecture 10: Shocks and Fans from Point Source](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/ace4ea160e90), 57 min (Video)
11. [Lecture 11: Level Set Method](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/4a2a2b4320fd), 54 min (Video)
12. [Lecture 12: Matrices in Difference Equations (1D, 2D, 3D)](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/dc587edb9f46), 58 min (Video)
13. [Lecture 13: Elimination with Reordering: Sparse Matrices](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/9d35417b90eb), 57 min (Video)
14. [Lecture 14: Financial Mathematics / Black-Scholes Equation](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/e04274adbf88), 50 min (Video)
15. [Lecture 15: Iterative Methods and Preconditioners](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/99c1a0a54484), 52 min (Video)
16. [Lecture 16: General Methods for Sparse Systems](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/9c4a3bed2d5c), 48 min (Video)
17. [Lecture 17: Multigrid Methods](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/0a17ba1b98bb), 52 min (Video)
18. [Lecture 18: Krylov Methods / Multigrid Continued](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/8f548a442569), 50 min (Video)
19. [Lecture 19: Conjugate Gradient Method](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/ca977df770c0), 53 min (Video)
20. [Lecture 20: Fast Poisson Solver](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/042994820433), 49 min (Video)
21. [Lecture 21: Optimization with constraints](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/9e848cb114fd), 51 min (Video)
22. [Lecture 22: Weighted Least Squares](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/885d131375b7), 53 min (Video)
23. [Lecture 23: Calculus of Variations / Weak Form](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/a0a612597770), 52 min (Video)
24. [Lecture 24: Error Estimates / Projections](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/b2263e5b376f), 51 min (Video)
25. [Lecture 25: Saddle Points / Inf-sup condition](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/7106494144c5), 52 min (Video)
26. [Lecture 26: Two Squares / Equality Constraint Bu = d](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/fa55890cafd1), 53 min (Video)
27. [Lecture 27: Regularization by Penalty Term](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/02589c4f1c1d), 50 min (Video)
28. [Lecture 28: Linear Programming and Duality](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/b900f4f182f3), 57 min (Video)
29. [Lecture 29: Duality Puzzle / Inverse Problem / Integral Equations](https://invisiblenetwork.ai/learn/mit/18-086-mathematical-methods-for-engineers-ii-spring-2006/773baa2e4b83), 52 min (Video)