MIT 18.085 Computational Science and Engineering I - Fall 2007

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".

Course Homepage 18.085 Computational Science and Engineering I Fall 2007

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1776 views, 59:51 Lecture 1: Positive definite matrices K = A'CALecture 1: Positive definite matrices K = A'CA Gilbert Strang Gilbert Strang	322 views, 56:48 Lecture 2: One-dimensional applications: A = difference matrixLecture 2: One-dimensional applications: A = difference matrix Gilbert Strang Gilbert Strang	354 views, 57:15 Lecture 3: Network applications: A = incidence matrixLecture 3: Network applications: A = incidence matrix Gilbert Strang Gilbert Strang	465 views, 1:07:48 Lecture 4: Applications to linear estimation: least squaresLecture 4: Applications to linear estimation: least squares Gilbert Strang Gilbert Strang	190 views, 1:07:01 Lecture 5: Applications to dynamics: eigenvalues of K, solution of Mu'' + Ku = F(t)Lecture 5: Applications to dynamics: eigenvalues of K, solution of ... Gilbert Strang Gilbert Strang
189 views, 1:05:27 Lecture 6: Underlying theory: applied linear algebraLecture 6: Underlying theory: applied linear algebra Gilbert Strang Gilbert Strang	273 views, 1:07:34 Lecture 7: Discrete vs. continuous: differences and derivativesLecture 7: Discrete vs. continuous: differences and derivatives Gilbert Strang Gilbert Strang	351 views, 1:05:56 Lecture 8: Applications to boundary value problems: Laplace equationLecture 8: Applications to boundary value problems: Laplace equation Gilbert Strang Gilbert Strang	715 views, 1:09:57 Lecture 9: Solutions of Laplace equation: complex variablesLecture 9: Solutions of Laplace equation: complex variables Gilbert Strang Gilbert Strang 3 comments	834 views, 1:00:55 Lecture 10: Delta function and Green's functionLecture 10: Delta function and Green's function Gilbert Strang Gilbert Strang 2 comments
394 views, 1:06:07 Lecture 11: Initial value problems: wave equation and heat equationLecture 11: Initial value problems: wave equation and heat equation Gilbert Strang Gilbert Strang 1 comment	165 views, 1:06:12 Lecture 12: Solutions of initial value problems: eigenfunctionsLecture 12: Solutions of initial value problems: eigenfunctions Gilbert Strang Gilbert Strang	251 views, 1:11:02 Lecture 13: Numerical linear algebra: orthogonalization and A = QRLecture 13: Numerical linear algebra: orthogonalization and A = QR Gilbert Strang Gilbert Strang	725 views, 1:00:57 Lecture 14: Numerical linear algebra: SVD and applicationsLecture 14: Numerical linear algebra: SVD and applications Gilbert Strang Gilbert Strang	773 views, 1:06:32 Lecture 15: Numerical methods in estimation: recursive least squares and covariance matrixLecture 15: Numerical methods in estimation: recursive least squares and ... Gilbert Strang Gilbert Strang
1354 views, 1:02:22 Lecture 16: Dynamic estimation: Kalman filter and square root filterLecture 16: Dynamic estimation: Kalman filter and square root filter Gilbert Strang Gilbert Strang	198 views, 1:05:16 Lecture 17: Finite difference methods: equilibrium problemsLecture 17: Finite difference methods: equilibrium problems Gilbert Strang Gilbert Strang	444 views, 1:07:28 Lecture 18: Finite difference methods: stability and convergenceLecture 18: Finite difference methods: stability and convergence Gilbert Strang Gilbert Strang	271 views, 1:08:17 Lecture 19: Optimization and minimum principles: Euler equationLecture 19: Optimization and minimum principles: Euler equation Gilbert Strang Gilbert Strang	771 views, 1:01:47 Lecture 20: Finite element method: equilibrium equationsLecture 20: Finite element method: equilibrium equations Gilbert Strang Gilbert Strang
224 views, 1:09:48 Lecture 21: Spectral method: dynamic equationsLecture 21: Spectral method: dynamic equations Gilbert Strang Gilbert Strang	314 views, 1:02:33 Lecture 22: Fourier expansions and convolutionLecture 22: Fourier expansions and convolution Gilbert Strang Gilbert Strang	521 views, 1:15:38 Lecture 23: Fast fourier transform and circulant matricesLecture 23: Fast fourier transform and circulant matrices Gilbert Strang Gilbert Strang	357 views, 1:00:24 Lecture 24: Discrete filters: lowpass and highpassLecture 24: Discrete filters: lowpass and highpass Gilbert Strang Gilbert Strang	305 views, 1:21:59 Lecture 25: Filters in the time and frequency domainLecture 25: Filters in the time and frequency domain Gilbert Strang Gilbert Strang
274 views, 55:21 Lecture 26: Filter banks and perfect reconstructionLecture 26: Filter banks and perfect reconstruction Gilbert Strang Gilbert Strang	1359 views, 1:15:49 Lecture 27: Multiresolution, wavelet transform and scaling functionLecture 27: Multiresolution, wavelet transform and scaling function Gilbert Strang Gilbert Strang	462 views, 1:04:34 Lecture 28: Splines and orthogonal wavelets: Daubechies constructionLecture 28: Splines and orthogonal wavelets: Daubechies construction Gilbert Strang Gilbert Strang	422 views, 1:14:04 Lecture 29: Applications in signal and image processing: compressionLecture 29: Applications in signal and image processing: compression Gilbert Strang Gilbert Strang 2 comments	822 views, 1:02:47 Lecture 30: Network flows and combinatorics: max flow = min cutLecture 30: Network flows and combinatorics: max flow = min ... Gilbert Strang Gilbert Strang
1982 views, 1:05:07 Lecture 31: Simplex method in linear programmingLecture 31: Simplex method in linear programming Gilbert Strang Gilbert Strang	496 views, 50:13 Lecture 32: Nonlinear optimization: algorithms and theoryLecture 32: Nonlinear optimization: algorithms and theory Gilbert Strang Gilbert Strang

Reviews and comments:

1 mike smith, February 23, 2009 at 2:33 p.m.:

These lectures are good , but this guy Gilbert has some problem with the presentation. He needs write the notes on the board clearly and with some kind of order! Also most of the time you cannot read what the prof is writing because the camera is out of focus?? What is the point? Gilbert is very good though but as usual there are problems getting the info to the student. During the lecture it seems that the camera man is too focused on getting the prof in the shot and not what he is writing, I need to see what he is writing!!!!!

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MIT 18.085 Computational Science and Engineering I - Fall 2007