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18.085 Computational Science and Engineering I

18.085 Computational Science and Engineering I (Fall 2008, MIT OCW). This consists of 36 video lectures and 13 review sessions given by Professor Gilbert Strang, focusing on applied linear algebra, applied differential equations, Fourier methods, and Algorithms. 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. (from ocw.mit.edu)

Introduction


Lecture 01 - Four Special Matrices
Recitation 01 - Key Ideas of Linear Algebra
Lecture 02 - Differential Equations & Difference Equations
Lecture 03 - Solving a Linear System
Lecture 04 - Delta Function Day
Recitation 02 - Review
Lecture 05 - Eigenvalues
Lecture 06 - Eigenvalues (cont.), Positive Definite Matrices
Lecture 07 - Positive Definite Matrices (cont.)
Recitation 03 - Review
Lecture 08 - Springs and Masses
Lecture 09 - Oscillation
Recitation 04 - Review
Lecture 10 - Finite Differences in Time; Least Squares
Lecture 11 - Least Squares (cont.)
Lecture 12 - Graphs and Networks
Recitation 05 - Review
Lecture 13 - Kirchhoff's Current Law
Lecture 14 - Exam Review
Recitation 06 - Review
Lecture 15 - Trusses and ATCA
Lecture 16 - Trusses (Part 2)
Lecture 17 - Finite Elements in 1D (Part 1)
Recitation 07 - Review
Lecture 18 - Finite Elements in 1D (Part 2)
Lecture 19 - Quadratic/Cubic Elements
Lecture 20 - Element Matrices; 4th Order Bending Equations
Recitation 08 - Review
Lecture 21 - Boundary Conditions, Gradient, Divergence
Lecture 22 - Gradient and Divergence
Lecture 23 - Laplace's Equation (Part 1)
Recitation 09 - Review
Lecture 24 - Laplace's Equation (Part 2)
Lecture 25 - Fast Poisson Solver
Lecture 26 - Fast Poisson Solver (cont.); Finite Elements in 2D
Recitation 10 - Review
Lecture 27 - Finite Elements in 2D (cont.)
Lecture 28 - Fourier Series (Part 1)
Recitation 11 - Review and Preview
Lecture 29 - Fourier Series (Part 2)
Lecture 30 - Discrete Fourier Series
Lecture 31 - Fast Fourier Transform, Convolution
Recitation 12 - Review
Lecture 32 - Convolution (cont.), Filtering
Lecture 33 - Filters, Fourier Integral Transform
Lecture 34 - Fourier Integral Transform (cont.)
Recitation 13 - Review
Lecture 35 - Convolution Equations: Deconvolution
Lecture 36 - Sampling Theorem

References
18.085 Computational Science and Engineering I
Instructors: Prof. Gilbert Strang. Exams and Solutions. Subtitles/Transcript. Assignments and Solutions. Applied linear algebra, Applied differential equations, Fourier methods, and Algorithms.