Welcome to AMATH 586 (Spring 2020)

On this page you will find homeworks, sample code, usually in the form of Jupyter notebooks, and additional materials and resources.

For assignment discussion and submission we will use:

GitHub Classroom

Each assignment will need to be copied from this repository over to the relevant assignent over there. The reason for this is that GitHub Classroom currently doesn’t allow for the modification of assignments after they are posted.

The discussion board is found here: https://github.com/orgs/trogdoncourses/teams/586-students . If you do not have access and have created at least one git homework repository, let us know.

Exams

1. Midterm Exam (Due May 15 at 11pm) pdf
2. Final Project (Due June 9 at 11pm) pdf ipynb

Homework

1. Homework 0 (not for credit)
2. Homework 1 (Due April 10 at 11pm) pdf
3. Homework 2 (Due April 24 at 11pm) pdf
4. Homework 3 (Due May 8 at 11pm) pdf
5. Homework 4 (Due May 29 at 11pm) pdf

Lectures (login with UW netid)

1. Lecture 01, IVPs video pdf
2. Lecture 02, more on IVPs video pdf
3. Lecture 03, Euler methods video pdf ipynb
4. Lecture 04, Multistep methods and truncation errors video pdf
5. Lecture 05, Multistage Runge-Kutta methods video pdf
6. Lecture 06, Linear multistep methods video pdf
7. Lecture 07, Multistep and multistage demo video ipynb
8. Lecture 08, Convergence of one-step methods video pdf
9. Lecture 09, Zero-stability video pdf
10. Lecture 10, Absolute stability intro and demo video pdf ipynb
11. Lecture 11, Absolute stability video pdf ipynb
12. Lecture 12, More on stability and relative stability video pdf ipynb
13. Lecture 13, Stiff ODEs video pdf ipynb
14. Lecture 14, A-stability video pdf ipynb
15. Lecture 15, Methods for the heat equation video pdf
16. Lecture 16, Stability and convergence for PDEs video pdf
17. Lecture 17, Crank-Nicolson in Julia video ipynb
18. Lecture 18, von Neumann stability analysis video pdf
19. Lecture 19, Crank-Nicolson in 2D video ipynb
20. Lecture 20, Characterization of linear second-order PDEs video pdf
21. Lecture 21, The advection equation video pdf
22. Lecture 22, More methods for the advection equation video pdf
23. Lecture 23, Advection equation demo video ipynb
24. Lecture 24, Stability for advection methods video pdf
25. Lecture 25, Cautionary tale for advection methods video ipynb
26. Lecture 26, Beyond scalar advection and scalar diffusion video pdf
27. Lecture 27, Heat equation w/no flux BCs video ipynb
28. Lecture 28, Wave tank video ipynb
29. Lecture 29, Exponential integration video ipynb

Special Topics (login with UW netid)

These are optional additional lectures going into certain topics to a deeper level.

1. Functions of matrices video pdf
2. Runge-Kutta error analysis video pdf
3. Dahlquist's Theorem video pdf
4. Orthogonal polynomials video pdf