IamMitul

Instructors: Prof. Gilbert Strang
MIT Course Number: 18.085
Level: Graduate
Course Description
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."


Instructors: Prof. Gilbert Strang
MIT Course Number: 18.085
Level: Graduate
Course Description
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."
1. Lecture 1: Four Special Matrices
2. Recitation 1: Key Ideas of Linear Algebra
3. Lecture 2: Differential Eqns and Difference Eqns
4. Lecture 3: Solving a Linear System
5. Lecture 4: Delta Function Day
6. Recitation 2
7. Lecture 5: Eigenvalues (Part 1)
8. Lecture 6: Eigen Values (part 2) and Positive Definite (part 1)
9. Lecture 7: Positive Definite Day
10. Recitation 3
11. Lecture 8: Springs and Masses
12. Lecture 9: Oscillation
13. Recitation 4
14. Lecture 10: Finite Differences in Time
15. Lecture 11: Least Squares (part 2)
16. Lecture 12: Graphs and Networks
17. Recitation 5
18. Lecture 13: Kirchhoff's Current Law
19. Lecture 14: Exam Review
20. Recitation 6
21. Lecture 15: Trusses and A^(T)CA
22. Lecture 16: Trusses (part 2)
23. Lecture 17: Finite Elements in 1D (part 1)
24. Recitation 7
25. Lecture 18: Finite Elements in 1D (part 2)
26. Lecture 19: Quadratic/Cubic Elements
27. Lecture 20: Element Matrices; 4th Order Bending Equations
28. Recitation 8
29. Lecture 21: Boundary Conditions, Splines, Gradient, Divergence
30. Lecture 22: Gradient and Divergence
31. Lecture 23: Laplace's Equation
32. Recitation 9
33. Lecture 24: Laplace's Equation (part 2)
34. Lecture 25: Fast Poisson Solver (part 1)
35. Lecture 26: Fast Poisson Solver (part 2); Finite Elements in 2D
36. Recitation 10
37. Lecture 27: Finite Elements in 2D (part 2)
38. Lecture 28: Fourier Series (part 1)
39. Recitation 11
40. Lecture 29: Fourier Series (part 2)
41. Lecture 30: Discrete Fourier Series
42. Lecture 31: Fast Fourier Transform, Convolution
43. Recitation 12
44. Lecture 32: Convolution (part 2), Filtering
45. Lecture 33: Filters, Fourier Integral Transform
46. Lecture 34: Fourier Integral Transform (part 2)
47. Recitation 13
48. Lecture 35: Convolution Equations: Deconvolution
49. Lecture 36: Sampling Theorem



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