Numerical Methods II, Spring 2014

Course Details and Syllabus

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.


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.


Most class communication will be on the NYU Classes 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.

Outline (tentative)

Segment Topics
1 Laplace, heat, wave equations. Multiscale decompositions of functions: Fourier and wavelet analysis. The FFT algorithm and FFTW package. The Poisson problem on square domains.
2 Wave propagation. Hyperbolic PDE in one dimension, wave speeds and propagation modes. Hyperbolic PDE in more than one dimension, energy and domain of dependence. The equations compressible gas dynamics, shallow water, and linear accoustics. Basic finite difference methods: upwind, Lax Wendroff, their stability by Fourier (von Neumann) analysis and the CFL condition.
3 Semi-discretization and the method of lines. Time stepping methods for ODE. Runge-Kutta methods and their stability regions. Linear multi-step methods and their characteristic polynomials and stability regions. Application to higher order methods.
4 Introduction to finite element methods for elliptic problems. Variational formulations, finite element spaces, interpolation estimates. Multigrid solution strategies.
5 General solution, conjugate gradients and GMRES. The role of condition number and preconditioning.