Math 727 Spring 2025
Instructor
Dr. Lili Ju
Office: LeConte College 327
Phone: (803) 576-5797
Email: ju@math.sc.edu
Office hours: Mon,Wed 12:30pm-2:00pm or by appointment.
URL:
http://people.math.sc.edu/ju/Homepage_files/teaching/math727_S25.html
Course Description and Meeting Times
Math 727, Numerical Differential Equations II, Cr. 3.
Description: This course is designed for systematically studying the finite element method, which is a
general method for approximating the solutions of differential equations, especially partial
differential equations. Many theoretical and computational aspects of the method will be
investigated. In particular, we will consider weak formulations of differential equations (both
time independent and time dependent problems), finite element spaces, approximation properties of finite element spaces and error estimates as well as the numerical implementation of the method.
Prerequisite: Math 726 or permission of instructor
Times and Place: Mon,Wed 2:20pm-3:35pm, LeConte College 315
** The deadline to drop the course without a grade of "W" being
recorded is January 21, 2025 (Tuesday).
** The deadline to drop the course without a grade of "WF" being recorded is March 31, 2025
(Monday).
Reference textbooks
- The Mathematical Theory of Finite Element Methods, by Susanne C. Brenner and
L. Ridgway Scott, 2nd Edition, Springer-Verlag, 2008.
- Galerkin Finite Element Methods for Parabolic Problems, by Vidar Thomee, 2nd Edition, Springer-Verlag, 2006.
Learning Outcomes
Students are expected to master mathematical theory and algorithms for finite element
methods along with programming skills, and apply numerical methods that they learn from
this course to solve a great variety of differential equation-based application problems arising
from science and engineering.
Reading
Reading the reference textbooks in advance of the lecture is strongly encouraged. Benefits
of this preparation include obtaining a familiarity with the terminology and concepts that
will be encountered (so you can distinguish major points from side issues), being able to
formulate questions about the parts of the presentation that you do not understand, and
having a chance to review the skills and techniques that will be needed to apply the new
concepts.
Grading Policy
Graded work for this course will consist of homework (40%), computing assignments (30%),
and a final exam/project (take-home) (30%).
Attendance and Academic Honesty
Attendance at every class meeting is important and expected. Students missing
more than 10% of the class meetings (4 times) can have their grade lowered.
Cheating and plagiarism will not be tolerated. Violations of this policy will be
dealt with according to University guidelines.