Math 572 - Numerical Mathematics II

3 Credit Hours

Section 001, CRN 20444

Meetings: TR 12:40p--1:55p Ayres Hall 112.

Spring 2018

Course Description: Numerical techniques for initial value problems of ordinary differential equations. Two-point boundary value problems. Finite difference and finite element methods for selected partial differential equations. Fast Poisson solvers.

Instructor Name: Abner J. Salgado.

Office Hours and Location: Wednesdays 2--3pm in Ayres 214. Office hours can also be arranged by appointment.


Course Communications: You may write to me at with questions, comments, etc. To avoid confusion, please write the course name (MATH572) in the Subject line. You must use your university e-mail account when sending me emails.

Course web page:

Goals: The successful student will be able to derive, apply and analyze elementary numerical algorithms. This course (together with Math 571) is intended to prepare mathematics students for the numerical preliminary examination. Topics in this class include numerical methods for ODEs (linear stability, stiff equations, A-stability, and convergence), and numerical methods for PDEs (stability, von Neumann analysis, convergence, and practical solution).



Course Requirements, Assessment and Evaluations:

Makeup Policy: Late programming assignments will NOT be accepted. Makeups for the quizzes, midterm and final will be given only if a student can present evidence that an absence was caused by serious illness, a death in the immediate family, religious observance, or participation in University activities at the request of University authorities. For an illness, you must present a signed statement from a doctor that your illness was sufficiently serious to make you miss class. A note saying only that you visited the doctor or the Health Center will not suffice.

Course Outline: This is a tentative list of topics to be covered in class.

  1. Review of the theory of initial value problems.
  2. Euler's method.
  3. Multistep methods.
  4. Runge-Kutta methods.
  5. Stiff equations.
  6. Finite difference schemes.
  7. The finite element method for the Poisson problem.
  8. Spectral methods (time permitting).
  9. Finite difference schemes for the heat equation.
  10. Finite difference schemes for the transport equation.

Campus Syllabus

If the instructor finds it necessary to make informational changes (e.g.  office hours, schedule adjustments) due to students' needs or unforeseen circumstances, students will be notified in writing/email of any such changes.

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