Thursday, November 25, 2010

MIT 18.085 Computational Science and Engineering I, Fall 2008



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."

Technical Requirements

Special software is required to use some of the files in this course:

Video Lectures
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Lecture 1: Four Special Matrices


Recitation 1: Key Ideas of Linear Algebra


Lecture 2: Differential Eqns and Difference Eqns


Lecture 3: Solving a Linear System


Lecture 4: Delta Function Day


Recitation 2


Lecture 5: Eigenvalues (Part 1)


Lecture 6: Eigen Values (part 2) and Positive Definite (part 1)


Lecture 7: Positive Definite Day


Recitation 3


Lecture 8: Springs and Masses


Lecture 9: Oscillation


Recitation 4


Lecture 10: Finite Differences in Time


Lecture 11: Least Squares (part 2)


Lecture 12: Graphs and Networks


Recitation 5


Lecture 13: Kirchhoff's Current Law


Lecture 14: Exam Review


Recitation 6


Lecture 15: Trusses and A^(T)CA


Lecture 16: Trusses (part 2)


Lecture 17: Finite Elements in 1D (part 1)


Recitation 7


Lecture 18: Finite Elements in 1D (part 2)


Lecture 19: Quadratic/Cubic Elements


Lecture 20: Element Matrices; 4th Order Bending Equations


Recitation 8


Lecture 21: Boundary Conditions, Splines, Gradient, Divergence


Lecture 22: Gradient and Divergence


Lecture 23: Laplace's Equation


Recitation 9


Lecture 24: Laplace's Equation (part 2)


Lecture 25: Fast Poisson Solver (part 1)


Lecture 26: Fast Poisson Solver (part 2); Finite Elements in 2D


Recitation 10


Lecture 27: Finite Elements in 2D (part 2)


Lecture 28: Fourier Series (part 1)


Recitation 11


Lecture 29: Fourier Series (part 2)


Lecture 30: Discrete Fourier Series


Lecture 31: Fast Fourier Transform, Convolution


Recitation 12


Lecture 32: Convolution (part 2), Filtering


Lecture 33: Filters, Fourier Integral Transform


Lecture 34: Fourier Integral Transform (part 2)


Recitation 13


Lecture 35: Convolution Equations: Deconvolution


Lecture 36: Sampling Theorem


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