This course introduces some fundamental scientific computing tools including algorithms and computing techniques, with illustrations on how they are used to solve real world problems. We focus on how to choose the most appropriate algorithms for the targeted applications, to implement the algorithms, to conduct numerical experiments, to evaluate the results, and to learn what to do when things go wrong. We take the viewpoint of "learning by doing." In addition to lectures, we emphasize hands-on experiences and discussions by conducting projects.

Tentative contents are listed as follows (not in order). The notation "*" stands for homework.

(I) Scientific Computing Software (3 weeks)
1 week for
- Chap 3 * Case Study: Computer Memory and Arithmetic: A Look under the Hood
- Chap 4 * Design of Computer Programs: Writing Your Legacy
- MATLAB, Linux, Coding Style, Naming Convention
2 weeks for
- Parallel Computing
- PETSc, SLEPC, MKL

(II) Dense Matrix Computation (3 weeks)
- Chap 5 Matrix Factorizations
- Chap 6 * Case Study: Image Deblurring: I can See Clearly Now

(III) Sparse Matrix Computation with Applications to Partial Differential Equations (8 weeks)
3 weeks for
- Chap 23 Case Study: Finite Differences and Finite Elements Getting to Know You
- Chap 28 Iterative Methods for Linear Systems
- Chap 30 * Case Study: Fast Solvers and Sylvester Equations Both Sides Now
5 weeks for
- Chap 31 Case Study: Eigenvalues: Valuable principles
- Large-scale Eigenvalue Solvers for Photonic Crystals Simulation
(* Hands-On numerical experiment worksheets)

(IV) Project Presentation (1 week)