Jan 18, 2001 
32 videos 
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
Course features at MIT OpenCourseWare page: *Syllabus *Assignments *Exams *Study Materials *Related Resources *Download Course Materials
Lecture 23: Fast fourier transform and circulant matrices
Nov 24, 2008 13513 views
Lecture 18: Finite difference methods: stability and convergence
Nov 24, 2008 9115 views
Lecture 28: Splines and orthogonal wavelets: Daubechies construction
Nov 24, 2008 11939 views
Lecture 5: Applications to dynamics: eigenvalues of K, solution of Mu'' + Ku = F...
Nov 24, 2008 7993 views
Lecture 22: Fourier expansions and convolution
Nov 24, 2008 9486 views
Lecture 1: Positive definite matrices K = A'CA
Nov 24, 2008 26433 views
Lecture 2: One-dimensional applications: A = difference matrix
Nov 24, 2008 13799 views
Lecture 3: Network applications: A = incidence matrix
Nov 24, 2008 12120 views
Lecture 4: Applications to linear estimation: least squares
Nov 24, 2008 17899 views
Lecture 6: Underlying theory: applied linear algebra
Nov 24, 2008 8884 views
Lecture 7: Discrete vs. continuous: differences and derivatives
Nov 24, 2008 7420 views
Lecture 8: Applications to boundary value problems: Laplace equation
Nov 24, 2008 8834 views
Lecture 9: Solutions of Laplace equation: complex variables
Nov 24, 2008 10910 views
Lecture 10: Delta function and Green's function
Nov 24, 2008 13096 views
Lecture 11: Initial value problems: wave equation and heat equation
Nov 24, 2008 8101 views
Lecture 12: Solutions of initial value problems: eigenfunctions
Nov 24, 2008 7071 views
Lecture 13: Numerical linear algebra: orthogonalization and A = QR
Nov 24, 2008 10956 views
Lecture 14: Numerical linear algebra: SVD and applications
Nov 24, 2008 14290 views
Lecture 15: Numerical methods in estimation: recursive least squares and covaria...
Nov 24, 2008 16591 views
Lecture 16: Dynamic estimation: Kalman filter and square root filter
Nov 24, 2008 32441 views
Lecture 17: Finite difference methods: equilibrium problems
Nov 24, 2008 6804 views
Lecture 19: Optimization and minimum principles: Euler equation
Nov 24, 2008 8717 views
Lecture 20: Finite element method: equilibrium equations
Nov 24, 2008 11411 views
Lecture 21: Spectral method: dynamic equations
Nov 24, 2008 7909 views
Lecture 24: Discrete filters: lowpass and highpass
Nov 24, 2008 10925 views
Lecture 25: Filters in the time and frequency domain
Nov 24, 2008 9805 views
Lecture 26: Filter banks and perfect reconstruction
Nov 24, 2008 9977 views
Lecture 27: Multiresolution, wavelet transform and scaling function
Nov 24, 2008 30195 views
Lecture 29: Applications in signal and image processing: compression
Nov 24, 2008 12373 views
Lecture 30: Network flows and combinatorics: max flow = min cut
Nov 24, 2008 12662 views
Lecture 31: Simplex method in linear programming
Nov 24, 2008 21423 views
Lecture 32: Nonlinear optimization: algorithms and theory
Nov 24, 2008 12327 views