Homework, workload, and testing
There will be weekly written homework assignments and frequent programming computing assignments. Late homework may be accepted at the discression of the instructor, but there will be a lateness penalty. Each homework assignment is designed to take 10 hours or less. Please let the instructor know if your are spending significantly more time than this. The final exam is the only testing.
Source materials
See the Resources page.
Grading
The final grade will be determined by the grades on the homework assignments and the final exam, each counting for about half the total. Homework grades will be posted on the nyuHome web site. Homework should be submitted in class in hard copy. Homework by email will not be accepted except in very rare circumstances with prior approval of the instructor. Students will be able to access their homework grades on the NYU Blackboard system.
Communication
Most class communication will be on the NYU Blackboard site through the class message board there. Check the message board before starting any homework assignment, as there may be corrections or hints. Please post questions about the homework or the class there. You may also communicate with fellow students, setting up group meetings or exchanging ideas about homework. Please email the instructor or TA only for personal matters (schedule an appointment, request to submit an assignment late, etc.).
Collaboration and cheating policy
Students are encouraged to discuss homework exercises with each other. Each student must write the solutions himself or herself. Copying of solutions or allowing others to copy your solutions is considered cheating and will be handled according to NYU cheating policies and the more stringent policies of the Mathematics and Computer Science Departments. Code sharing is not allowed. You must type (or create from things you've typed using an editor, script, etc.) every character of code you use.
Schedule (tentative)
| Class | Topics |
|---|---|
| 1 | Adams methods, implicit and explicit, stability, accuracy, convergence. Predictor/corrector methods. |
| 2 | Other linear multistep methods -- Nystrom, BDF, etc. The stability polynomial and root conditions for stability. |
| 3 | Boundary value problems. Finite difference approximations for some elliptic partial differentiatl equations and boundary condtions. Energy arguments for stability and convergence. |
| 4 | The discrete Fourier transform and application to stability analysis. |
| 5 | The FFT (fast Fourier transform) and fast poisson solvers in simple geometries. |
| 6 | Simple iterative methods -- Jacobi, Gauss Seidel, extrapolation. The importance of conditioning and pre-conditioning. |
| 7 | Orthogonalization methods (conjugate gradients, gmres). Newton's method for nonlinear problems. |
| 8 | Parabolic partial differential equations. Semi-discrete methods and stiff systems of ordinary differential equations. Fully discrete methods and time step constraints. |
| 9 | A-stability for multistep methods. Dahlquist saturation theorems. |
| 10 | Brief introduction to finite difference methods for wave propagation problems. |
| 11 | Runge Kutta methods. |
| 12 | Finite elements methods, variational principles for elliptic boundary value problems. |
| 13 | Finite element methods, convergence rates in various norms. |
| 14 | Specific finite element constructions, linear and high order elements. |
| ** | Final exam, same time, same room |