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Course Introduction

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

Lecture 8: Springs and Masses

Recitation 3

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 14: Exam Review

Lecture 13: Kirchhoff's Current Law

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

Recitation 9

Lecture 22: Gradient and Divergence

Lecture 23: Laplace's Equation

Lecture 25: Fast Poisson Solver (part 1)

Lecture 24: Laplace's Equation (part 2)

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

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

Recitation 10

Lecture 28: Fourier Series (part 1)

Lecture 29: Fourier Series (part 2)

Recitation 11

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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