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

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.
*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.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 Engineering**

Strang, 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 solutions**

Exam 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 Demonstrations**

Signals, 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.