Catalog

Computational Science and Engineering I

Mathematics MIT CC BY-NC-SA 4.0 50 lectures

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."

Syllabus

  1. 1 Course Introduction
  2. 2 Lecture 1: Four Special Matrices
  3. 3 Recitation 1: Key Ideas of Linear Algebra
  4. 4 Lecture 2: Differential Eqns and Difference Eqns
  5. 5 Lecture 3: Solving a Linear System
  6. 6 Lecture 4: Delta Function Day
  7. 7 Recitation 2
  8. 8 Lecture 5: Eigenvalues (Part 1)
  9. 9 Lecture 6: Eigen Values (part 2) and Positive Definite (part 1)
  10. 10 Lecture 7: Positive Definite Day
  11. 11 Lecture 8: Springs and Masses
  12. 12 Recitation 3
  13. 13 Lecture 9: Oscillation
  14. 14 Recitation 4
  15. 15 Lecture 10: Finite Differences in Time
  16. 16 Lecture 11: Least Squares (part 2)
  17. 17 Lecture 12: Graphs and Networks
  18. 18 Recitation 5
  19. 19 Lecture 14: Exam Review
  20. 20 Lecture 13: Kirchhoff's Current Law
  21. 21 Recitation 6
  22. 22 Lecture 15: Trusses and A^(T)CA
  23. 23 Lecture 16: Trusses (part 2)
  24. 24 Lecture 17: Finite Elements in 1D (part 1)
  25. 25 Recitation 7
  26. 26 Lecture 18: Finite Elements in 1D (part 2)
  27. 27 Lecture 19: Quadratic/Cubic Elements
  28. 28 Lecture 20: Element Matrices; 4th Order Bending Equations
  29. 29 Recitation 8
  30. 30 Lecture 21: Boundary Conditions, Splines, Gradient, Divergence
  31. 31 Recitation 9
  32. 32 Lecture 22: Gradient and Divergence
  33. 33 Lecture 23: Laplace's Equation
  34. 34 Lecture 25: Fast Poisson Solver (part 1)
  35. 35 Lecture 24: Laplace's Equation (part 2)
  36. 36 Lecture 27: Finite Elements in 2D (part 2)
  37. 37 Lecture 26: Fast Poisson Solver (part 2); Finite Elements in 2D
  38. 38 Recitation 10
  39. 39 Lecture 28: Fourier Series (part 1)
  40. 40 Lecture 29: Fourier Series (part 2)
  41. 41 Recitation 11
  42. 42 Lecture 30: Discrete Fourier Series
  43. 43 Lecture 31: Fast Fourier Transform, Convolution
  44. 44 Recitation 12
  45. 45 Lecture 32: Convolution (part 2), Filtering
  46. 46 Lecture 33: Filters, Fourier Integral Transform
  47. 47 Lecture 34: Fourier Integral Transform (part 2)
  48. 48 Recitation 13
  49. 49 Lecture 35: Convolution Equations: Deconvolution
  50. 50 Lecture 36: Sampling Theorem

Course materials