Course Information

Course

Code:	18.085
Subject:	Mathematics
Topic:	Applied Mathematics
Views:	183,402

Educator

Name:	Massachusetts Institute of Technology (MIT)
Type:	University

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Instructor

Name

Gilbert Strang

Computational Science and Engineering I

Video Lectures

Displaying all 36 video lectures.

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