MIT 18.085 Computational Science and Engineering I - Fall 2007
32 Lectures ยท Jan 18, 2001
About
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
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Lecture 1: Positive definite matrices K = A'CA
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Lecture 2: One-dimensional applications: A = difference matrix
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Lecture 3: Network applications: A = incidence matrix
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Lecture 4: Applications to linear estimation: least squares
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Lecture 5: Applications to dynamics: eigenvalues of K, solution of Mu'' + Ku = F...
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Lecture 6: Underlying theory: applied linear algebra
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Lecture 7: Discrete vs. continuous: differences and derivatives
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Lecture 8: Applications to boundary value problems: Laplace equation
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Lecture 9: Solutions of Laplace equation: complex variables
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Lecture 10: Delta function and Green's function
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Lecture 11: Initial value problems: wave equation and heat equation
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Lecture 12: Solutions of initial value problems: eigenfunctions
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Lecture 13: Numerical linear algebra: orthogonalization and A = QR
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Lecture 14: Numerical linear algebra: SVD and applications
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Lecture 15: Numerical methods in estimation: recursive least squares and covaria...
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Lecture 16: Dynamic estimation: Kalman filter and square root filter
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Lecture 17: Finite difference methods: equilibrium problems
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Lecture 18: Finite difference methods: stability and convergence
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Lecture 19: Optimization and minimum principles: Euler equation
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Lecture 20: Finite element method: equilibrium equations
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Lecture 21: Spectral method: dynamic equations
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Lecture 22: Fourier expansions and convolution
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Lecture 23: Fast fourier transform and circulant matrices
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Lecture 24: Discrete filters: lowpass and highpass
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Lecture 25: Filters in the time and frequency domain
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Lecture 26: Filter banks and perfect reconstruction
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Lecture 27: Multiresolution, wavelet transform and scaling function
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Lecture 28: Splines and orthogonal wavelets: Daubechies construction
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Lecture 29: Applications in signal and image processing: compression
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Lecture 30: Network flows and combinatorics: max flow = min cut
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Lecture 31: Simplex method in linear programming
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Lecture 32: Nonlinear optimization: algorithms and theory
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