1. Overview of EECS 639: Introduction to Scientific Computing Topics to be covered

2. Floating Point Representations: Accuracy and Stability

3. Linear Algebra: Computational Efficiency
Gaussian Elimination codes for solving Ax=b:
The order of operations matters.
>> test_ge
Enter n: 1200
Elapsed time is seconds.
Elapsed time is seconds.
Elapsed time is seconds.
Elapsed time is seconds.
Elapsed time is seconds.
Elapsed time is seconds.
The ordering of the algorithms is: kji < jki < ijk < kij < jik < ikj.

4. Linear Least Squares: Obtaining Good Data Fits

5. Eigenvalues: Image Compression

6. Nonlinear Equations

7. Optimization
Contour plot of function to minimize:

8. Various Algorithms Perform Differently

9. Interpolation: Global Interpolants

10. Local Interpolants

11. Quadrature and Differentiation: Mathematical Derivation

12. Derivation (continued)

13. Initial Value Problems: Planetary Orbits