# Computational Science and Engineering I

### 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."

This image comes from "A Simple Mesh Generator in MATLAB" submitted to SIAM Review. The mesh was created using the truss model in Section 2.4 of the text; color shows distance to the boundary. (Image courtesy of Per-Olof Persson.)
1 rating

### Video Lectures & Study Materials

Visit the official course website for more study materials: https://ocw.mit.edu/courses/mathematics/18-085-computational-science-and-engineering-i-fall-2008/

# Lecture Play Lecture
1 Positive definite matrices K = A'CA (54:05) Play Video
2 One-dimensional applications: A = difference matrix (52:27) Play Video
3 Network applications: A = incidence matrix (54:40) Play Video
4 Applications to linear estimation: least squares (55:39) Play Video
5 Applications to dynamics: eigenvalues of K, solution of Mu'' + Ku = F(t) (56:12) Play Video
6 Underlying theory: applied linear algebra (50:19) Play Video
7 Discrete vs. Continuous: Differences and Derivatives (52:56) Play Video
8 Applications to boundary value problems: Laplace equation (55:14) Play Video
9 Solutions of Laplace equation: complex variables (53:27) Play Video
10 Delta function and Green's function (54:59) Play Video
11 Initial value problems: wave equation and heat equation (54:00) Play Video
12 Solutions of initial value problems: eigenfunctions (50:28) Play Video
13 Numerical linear algebra: orthogonalization and A = QR (54:37) Play Video
14 Numerical linear algebra: SVD and applications (52:30) Play Video
15 Numerical methods in estimation: recursive least squares and covariance matrix (46:42) Play Video
16 Dynamic estimation: Kalman filter and square root filter (48:41) Play Video
17 Finite difference methods: equilibrium problems (54:22) Play Video
18 Finite difference methods: stability and convergence (51:36) Play Video
19 Optimization and minimum principles: Euler equation (52:35) Play Video
20 Finite element method: equilibrium equations (50:13) Play Video
21 Spectral method: dynamic equations (53:21) Play Video
22 Fourier expansions and convolution (51:19) Play Video
23 Fast fourier transform and circulant matrices (49:53) Play Video
24 Discrete filters: lowpass and highpass (54:21) Play Video
25 Filters in the time and frequency domain (52:22) Play Video
26 Filter banks and perfect reconstruction (51:28) Play Video
27 Multiresolution, wavelet transform and scaling function (52:33) Play Video
28 Splines and orthogonal wavelets: Daubechies construction (49:23) Play Video
29 Applications in signal and image processing: compression (49:41) Play Video
30 Network flows and combinatorics: max flow = min cut (50:12) Play Video
31 Simplex method in linear programming (51:42) Play Video
32 Nonlinear optimization: algorithms and theory (52:04) Play Video
33 Filters; Fourier integral transform (part 1) (51:23) Play Video
34 Fourier integral transform (part 2) (51:27) Play Video
35 Convolution equations: deconvolution; convolution in 2D (51:21) Play Video
36 Sampling Theorem (40:57) Play Video

marissa wrote 9 years ago.
He seems to be a really great professional, but it is
clearly that he is talking to himself while he teaches, he
makes the question he answers them. I have not listen any of
the students say anything, he just keep writing, talking. He
is just speaking to himself aloud, that is why mathematics
feels as it is so difficult, but in reality it is that very
few are able to transmit their knowledge.

Patrick Gaffney wrote 10 years ago.
Truly excellent video course by the master. Lecture 14 does
not cover the SVD even though the title says it does.

Patrick Gaffney wrote 10 years ago.
Truly excellent video lectures from the master. Lecture 14
though only mentions SVD in the title not in the content.

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