18.085 Computational Science and Engineering I

MIT OCW - 18.085 Computational Science and Engineering I (Fall 2008). 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

01 - Four Special Matrices 19 - Quadratic/Cubic Elements
01b - Key Ideas of Linear Algebra 20 - Element Matrices; 4th Order Bending Equations
02 - Differential Equations & Difference Equations 20b - Recitation 8: Review
03 - Solving a Linear System 21 - Boundary Conditions, Gradient, Divergence
04 - Delta Function Day 22 - Gradient and Divergence
04b - Recitation 2: Review 23 - Laplace's Equation (part 1)
05 - Eigenvalues (Part 1) 23b - Recitation 9: Review
06 - Eigenvalues (part 2) and Positive Definite 24 - Laplace's Equation (part 2)
07 - Positive Definite Day 25 - Fast Poisson Solver (part 1)
07b - Recitation 3: Review 26 - Fast Poisson Solver (part 2); Finite Elements in 2D
08 - Springs and Masses 26b - Recitation 10: Review
09 - Oscillation 27 - Finite Elements in 2D (part 2)
09b - Recitation 4: Review 28 - Fourier Series (part 1)
10 - Finite Differences in Time; Least Squares 28b - Recitation 11: Review and Preview
11 - Least Squares (part 2) 29 - Fourier Series (part 2)
12 - Graphs and Networks 30 - Discrete Fourier Series
12b - Recitation 5: Review 31 - Fast Fourier Transform, Convolution
13 - Kirchhoff's Current Law 31b - Recitation 12: Review
14 - Exam Review 32 - Convolution (part 2), Filtering
14b - Recitation 6: Review 33 - Filters, Fourier Integral Transform (part 1)
15 - Trusses and ATCA 34 - Fourier Integral Transform (part 2)
16 - Trusses (part 2) 34b - Recitation 13: Review
17 - Finite Elements in 1D (part 1) 35 - Convolution Equations: Deconvolution
17b - Recitation 7: Review 36 - Sampling Theorem
18 - Finite Elements in 1D (part 2)

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.