One-dimensional applications: A = difference matrix 
One-dimensional applications: A = difference matrix
by MIT / Gilbert Strang
◀ ← Video Lecture 2 of 36 → ▶
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Date Added: March 23, 2009

Lecture Description

This video lecture, part of the series Computational Science and Engineering I by Prof. Gilbert Strang, does not currently have a detailed description and video lecture title. If you have watched this lecture and know what it is about, particularly what Mathematics topics are discussed, please help us by commenting on this video with your suggested description and title. Many thanks from,

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Course Index

  1. Positive definite matrices K = A'CA
  2. One-dimensional applications: A = difference matrix
  3. Network applications: A = incidence matrix
  4. Applications to linear estimation: least squares
  5. Applications to dynamics: eigenvalues of K, solution of Mu'' + Ku = F(t)
  6. Underlying theory: applied linear algebra
  7. Discrete vs. Continuous: Differences and Derivatives
  8. Applications to boundary value problems: Laplace equation
  9. Solutions of Laplace equation: complex variables
  10. Delta function and Green's function
  11. Initial value problems: wave equation and heat equation
  12. Solutions of initial value problems: eigenfunctions
  13. Numerical linear algebra: orthogonalization and A = QR
  14. Numerical linear algebra: SVD and applications
  15. Numerical methods in estimation: recursive least squares and covariance matrix
  16. Dynamic estimation: Kalman filter and square root filter
  17. Finite difference methods: equilibrium problems
  18. Finite difference methods: stability and convergence
  19. Optimization and minimum principles: Euler equation
  20. Finite element method: equilibrium equations
  21. Spectral method: dynamic equations
  22. Fourier expansions and convolution
  23. Fast fourier transform and circulant matrices
  24. Discrete filters: lowpass and highpass
  25. Filters in the time and frequency domain
  26. Filter banks and perfect reconstruction
  27. Multiresolution, wavelet transform and scaling function
  28. Splines and orthogonal wavelets: Daubechies construction
  29. Applications in signal and image processing: compression
  30. Network flows and combinatorics: max flow = min cut
  31. Simplex method in linear programming
  32. Nonlinear optimization: algorithms and theory
  33. Filters; Fourier integral transform (part 1)
  34. Fourier integral transform (part 2)
  35. Convolution equations: deconvolution; convolution in 2D
  36. Sampling Theorem

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."

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