Math 5620/6865 Introduction to Numerical Analysis II
Spring 2015, 4.0 units,
M,T,W,F 10:45-11:35 a.m., LCB 323.
Instructor: Dr. Qinghai Zhang
Contact: qinghai@math.utah.edu
Website: http://www.math.utah.edu/~tsinghai/teaching/math5620/index.html
Office hours: TBA
Prerequisite: (1) “C” or better in MATH 5610 and (2) basic matlab programming.
Text: “Finite Difference Methods for Ordinary and Partial Differential Equations: Steady
State and Time Dependent Problems” by Randall J. LeVeque,
SIAM 2007. ISBN: 978-0-898716-29-0. http://bookstore.siam.org/ot98/
Description: This is the second of a two-semester series of classes on numerical analysis.
Topics include:
• §1. Finite difference and finite volume approximations;
• §2. Boundary value problems;
• §3. Elliptic equations;
• §5. Initial value problems;
• §6. Zero-stability and convergence;
• §7. Absolute stability;
• §8. Stiff ODEs;
• §9. Method of lines;
• §10. Hyperbolic systems;
• Multigrid methods (if time permits).
Other reference textbooks:
• Numerical Methods for Ordinary Differential Systems: The Initial Value Problem by J. D.
Lambert, Willey 1991, ISBN-13: 978-0471929901.
• An Introduction to Numerical Analysis by K. E. Atkinson, 2nd edition, ISBN: 0-471-62489-6.
• Finite Difference Schemes and Partial Differential Equations by J. C. Strikwerda, 2nd edition,
SIAM 2007, ISBN-13: 978-0898716399
• Introduction to Partial Differential Equations: a Computational Approach by A. Tveito and R.
Winther, Springer 2009, ISBN: 978-3-540-88704-1
You are not required to buy the above books; I will sometimes use examples from them, or
occasionally follow their sections in the lecture.
Homework: There will be a homework assignment every one or two weeks, due on Mondays
by the end of class. If you turn in your homework after class on Monday and before 5 p.m.
on Wednesday, your homework score will be multiplied by a factor of 0.8. No homework will
be accepted after Wednesday 5p.m. The lowest homework grade will be dropped.
Programming: Programming is an important part of the homework. You are strongly
encouraged to familiar yourself with matlab before taking this class.
Grading: I will use Canvas (accessible through cis.utah.edu) to post your grades. Please
check to make sure what is posted is consistent with what you received on paper and if not,
let me know within a week from the day the assignment was returned. The breakdown for
the course grade is as follows:
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• Homework: 40%,
• Projects: 30% (details to be announced),
• Final exam: 30%
Math 6865 Option: For graduate students, you can take this class as Math 6865. In
addition to the requirements for Math 5620, you are supposed to
• turn in solutions for all extra-credit homework problems,
• work on a harder final project,
• do all extra-credit problems in the exams.
ADA statement: “The University of Utah seeks to provide equal access to its programs,
services and activities for people with disabilities. If you will need accommodations in the
class, reasonable prior notice needs to be given to the Center for Disability Services, 162
Union Building, 581-5020 (V/TDD). CDS will work with you and the instructor to make
arrangements for accommodations.”
Note: This syllabus is not a binding legal contract. It may be modified by the instructor to cater
to the progress and averaged background of the students. Then the student will be given reasonable
notice of the modification.
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