Math 709 Spring 2013
Instructor
Dr. Lili Ju
Office: 424 LeConte College
Phone: (803) 576-5797
Email: ju@math.sc.edu
Office hours: MWF 10:00am-11:00am or by appointment.
URL:
http://www.math.sc.edu/~ju/Homepage_files/teaching/math709_S13.html
Course Description and Meeting Times
Math 709, Foundations of Computational Mathematics II, Cr. 3.
Description:
This course is an introduction to graduate-level
numerical algorithms related to linear algebra.
It emphasizes both theoretical development of concepts and practical algorithm implementation.
The content includes matrix factorizations like SVD and QR, least squares, conditioning and stability,
eigenvalue problems, iterative methods for solution of systems.
Prerequisite: Math 544 or Math 526, or equivalent upper level undergraduate courses in
linear algebra.
| Times and Place: |
MW 2:30pm-3:45pm, LeConte College 121 |
Textbook and Course Outline
TEXTBOOK:
Numerical Linear Algebra,
by Lloyd Trefethen and David Bau III, SIAM, 1997.
REFERENCES:
- Numerical Mathematics, by Alfio Quarteroni, Riccardo Sacco and Fausto Saleri,
Springer,
2000.
- Concise Numerical Mathematics, By Robert Plato, AMS, 2003.
- Iterative Methods for Linear and Nonlinear Equations, by C.T. Kelley,
SIAM, 1995.
- An Introduction to Numerical Analysis, By Endre Suli and David F. Mayers,
Cambridge University Press, 2003.
Matlab Tutorial
Learning Outcomes
A student who successfully completes this course
will master important concepts, formulas, algorithms and theorems in the area of
computational
mathematics, and
will also be able to apply methods and techniques learned from this course to
solve various types of numerical problems arisen
from practical applications.
Course Outline
Tentative Schedule and Lecture Contents
| Weeks |
Content |
| Weeks 1 |
Fundamental concepts |
| Weeks 2 |
Singular value decomposition |
| Weeks 3-5 |
QR factorization |
| Weeks 6 |
Least squares problems |
| Weeks 7-9 |
Conditioning and stability |
| Weeks 10 |
Gaussian elimination |
| Weeks 11-13 |
Eigenvalue problems |
| Weeks 14-16 |
Iterative methods for linear systems |
** The deadline to drop the course without a grade of "W" being
recorded is January 18, Friday.
** The deadline to drop the course without a grade of "WF" being recorded is March 4, Monday.
Grading Policy
Your course grade is determined by Homeworks (40%), Midterms (30%) and Final
Exam (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.
Homework Assignments
Homework 1, due 2/8/2013 (Fri.).
Homework 2, due 2/25/2013 (Mon.).
Homework 3, due 3/18/2013 (Mon.).
Midterm Exam, 3/20/2013 (Wed.).
Homework 4, due 4/10/2013 (Wed.).
Final Exam, due 5/3/2013 (Fri.)