Lectures
- 1. Four special matrices
- 2. Differential and Difference equations
- 3. Solving a linear system
- 4. Delta function
- 5. Eigenvalues (part 1)
- 6. Eigenvalues (part 2)
- 7. Positive definite
- 8. Springs and masses
- 9. Oscillation
- 10. Finite differences in time, Least squares
- 11. Least squares (part 2)
- 12. Graphs and networks
- 13. Kirchhoff's Current Law
- 14. Review
- 15. Trusses
- 16. Trusses (part 2)
- 17. Finite elements in 1D
- 18. Finite elements in 1D (part 2)
- 19. Quadratic and cubic elements
- 20. Element matrices
- 21. Boundary conditions, splines, gradient and divergence
- 22. Gradient and divergence (part 2)
- 23. Laplace's equation
- 24. Laplace's equation (part 2)
- 25. Fast Poisson solver
- 26. Fast Poisson solver (part 2), Finite elements in 2D
- 27. Finite elements in 2D (part 2)
- 28. Fourier series
- 29. Fourier series (part 2)
- 30. Discrete Fourier series
- 31. Fast Fourier transform, Convolution
- 32. Convolution (part 2), Filtering
- 33. Filters, Fourier integral transform
- 34. Fourier integral transform (part 2)
- 35. Convolution equations: deconvolution; convolution in 2D
- 36. Sampling Theorem
Computational Science and Engineering I
Course Summary
This course is based on 18.085 Computational Science and Engineering I, Fall 2008 made available by Massachusetts Institute of Technology: MIT OpenCourseWare under the Creative Commons BY-NC-SA license.
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.
The course is conducted by Prof. Gilbert Strang who has taught at MIT for more than 50 years. He is one of the most recognized mathematicians in the world and is the author of ten books, and has served as editor for more than 20 journals.
Reading Material
1. Textbook: Computational Science and EngineeringStrang, Gilbert. Computational Science and Engineering. Wellesley, MA: Wellesley-Cambridge Press, 2007. ISBN: 9780961408817.
2. Four Special Matrices
Chapter 1: Applied Linear Algebra; Section 1.1 Four Special Matrices
(389 KB pdf file)
3. Fourier Series for Periodic Functions
Chapter 4: Fourier Series and Integrals; Section 4.1 Fourier Series for Periodic Functions
(560 KB pdf file)
4. Linear algebra in a nutshell
Appendix: Linear algebra in a nutshell
(231 KB pdf)
Course Material
1. Sample exam questions and solutionsExam 1 (676 KB pdf file)
Exam 2 (52 KB pdf file)
Exam 3 (93 KB pdf file)
Other Resources
Not available.Software
1. Signals, Systems, and Control DemonstrationsSignals, Systems, and Control Demonstrations (Johns Hopkins University)
These demonstrations were developed in a project directed by Wilson J. Rugh from 1994 to 2003 exploring the use of the World Wide Web in engineering education.
2. Java Digital Signal Processing Tool
J-DSP stands for Java Digital Signal Processing. J-DSP has been developed at Arizona State University (ASU) and is written as a platform-independent Java applet. J -DSP has a rich suite of signal processing functions that facilitate interactive on-line simulations of modern statistical signal and spectral analysis algorithms filter design tools, QMF banks, and state-of-the-art vocoders.
3. Linear Algebra Java Demos
Linear Algebra Java Demos developed by Pavel Grinfeld.
Discussion Forum
For discussion on this topic, please go to the relevant forum for Computational Science and Engineering I. Click the button below to open the forum page in a new window.
