# Computational Science and Engineering I

- Institution: Massachusetts Institute of Technology
- Department: Mathematics
- Teacher: Prof. Gilbert Strang
- Term: Fall 2008
- Level: Graduate
- Language: English
- Subjects: Mathematics, Engineering
- Source: [MIT OpenCourseWare](https://ocw.mit.edu/courses/18-085-computational-science-and-engineering-i-fall-2008/)
- 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/18-085-computational-science-and-engineering-i-fall-2008/pages/syllabus/)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace’s equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.

Note: This course was previously called “Mathematical Methods for Engineers I.”

## Lectures

1. [Course Introduction](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/46d9fe68cc66), 5 min (Video)
2. [Lecture 1: Four Special Matrices](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/c100627ffcd1), 55 min (Video)
3. [Recitation 1: Key Ideas of Linear Algebra](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/53f7364d481f), 50 min (Video)
4. [Lecture 2: Differential Eqns and Difference Eqns](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/6932aab1590f), 53 min (Video)
5. [Lecture 3: Solving a Linear System](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/1bcb18ef213e), 55 min (Video)
6. [Lecture 4: Delta Function Day](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/2ddc1a2c080b), 56 min (Video)
7. [Recitation 2](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/a8fa503538c9), 52 min (Video)
8. [Lecture 5: Eigenvalues (Part 1)](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/ccc2e1578514), 57 min (Video)
9. [Lecture 6: Eigen Values (part 2) and Positive Definite (part 1)](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/1655963bdc3d), 51 min (Video)
10. [Lecture 7: Positive Definite Day](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/18a59b447671), 53 min (Video)
11. [Lecture 8: Springs and Masses](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/0811650cd4f4), 56 min (Video)
12. [Recitation 3](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/e4a08ab9a1f6), 57 min (Video)
13. [Lecture 9: Oscillation](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/659307d665ef), 54 min (Video)
14. [Recitation 4](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/24450aeb662b), 57 min (Video)
15. [Lecture 10: Finite Differences in Time](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/a2ffb930b4af), 55 min (Video)
16. [Lecture 11: Least Squares (part 2)](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/897eab847cbf), 54 min (Video)
17. [Lecture 12: Graphs and Networks](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/84f77606e481), 51 min (Video)
18. [Recitation 5](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/9bd6f911b780), 55 min (Video)
19. [Lecture 14: Exam Review](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/4ec9fb16507a), 53 min (Video)
20. [Lecture 13: Kirchhoff's Current Law](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/fabea5cc8cc4), 55 min (Video)
21. [Recitation 6](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/d232995dede0), 55 min (Video)
22. [Lecture 15: Trusses and A^(T)CA](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/fbc4b87cb2af), 47 min (Video)
23. [Lecture 16: Trusses (part 2)](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/a47f99dcac9c), 49 min (Video)
24. [Lecture 17: Finite Elements in 1D (part 1)](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/8b482e61ce95), 55 min (Video)
25. [Recitation 7](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/439b784ac504), 54 min (Video)
26. [Lecture 18: Finite Elements in 1D (part 2)](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/8e0a91d43a02), 52 min (Video)
27. [Lecture 19: Quadratic/Cubic Elements](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/37c3b433179c), 53 min (Video)
28. [Lecture 20: Element Matrices; 4th Order Bending Equations](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/47dd7ea47fd2), 51 min (Video)
29. [Recitation 8](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/35b7e7e3c68f), 49 min (Video)
30. [Lecture 21: Boundary Conditions, Splines, Gradient, Divergence](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/842584a52b30), 54 min (Video)
31. [Recitation 9](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/cd028f91da65), 52 min (Video)
32. [Lecture 22: Gradient and Divergence](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/c7d038bafa78), 52 min (Video)
33. [Lecture 23: Laplace's Equation](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/e3ca925c0c28), 50 min (Video)
34. [Lecture 25: Fast Poisson Solver (part 1)](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/39252dffb6be), 53 min (Video)
35. [Lecture 24: Laplace's Equation (part 2)](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/71f94cb1d582), 55 min (Video)
36. [Lecture 27: Finite Elements in 2D (part 2)](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/13235f257e4f), 53 min (Video)
37. [Lecture 26: Fast Poisson Solver (part 2); Finite Elements in 2D](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/55dfa9ae7b20), 52 min (Video)
38. [Recitation 10](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/164e399a43cb), 46 min (Video)
39. [Lecture 28: Fourier Series (part 1)](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/0207f7c155f5), 50 min (Video)
40. [Lecture 29: Fourier Series (part 2)](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/61a71876aea3), 49 min (Video)
41. [Recitation 11](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/03850ad035ca), 55 min (Video)
42. [Lecture 30: Discrete Fourier Series](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/a918674186da), 51 min (Video)
43. [Lecture 31: Fast Fourier Transform, Convolution](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/50f46e006e2f), 52 min (Video)
44. [Recitation 12](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/208540a88256), 52 min (Video)
45. [Lecture 32: Convolution (part 2), Filtering](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/2e505a8deea3), 53 min (Video)
46. [Lecture 33: Filters, Fourier Integral Transform](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/4831b168beac), 52 min (Video)
47. [Lecture 34: Fourier Integral Transform (part 2)](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/2a9170f37433), 52 min (Video)
48. [Recitation 13](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/d58fef4d8a64), 51 min (Video)
49. [Lecture 35: Convolution Equations: Deconvolution](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/abde2e626ee2), 52 min (Video)
50. [Lecture 36: Sampling Theorem](https://invisiblenetwork.ai/learn/mit/18-085-computational-science-and-engineering-i-fall-2008/e50b78356e54), 41 min (Video)