Math 526 -- Section 001 and 002 Spring 2005
Instructor
Dr. Lili Ju
Office: 418C LeConte College
Phone: (803) 576-5797
Email: ju@math.sc.edu
Office hours: TTh 1:30-3:00pm or by appointment.
URL:
http://www.math.sc.edu/~ju/Homepage_files/teaching/math526_S05.html
Teaching Assistant:
Shuang Li (sli@math.sc.edu)
Course Description and Meeting Times
Math 526, Numerical Linear Algebra, Cr. 4.
Prerequisite: Qualification through placement or a grade C or better
in Math 241
Lecture times: TTh 9:30am-10:45am, LeConte College 405
Lab times: Section 001 -- W 9:05am-9:55am, LeConte College 303A
Section 002 -- W 10:10am-11:00am, LeConte College 303A
Textbook and Course Outline
TEXTBOOK: No formal textbook, printed lecture notes will be
used.
Tentative Weekly Syllabus of Sections
Covered
Week |
Dates |
Tuesday |
Wednesday |
Thursday |
1 |
Jan. 10--Jan. 14 |
Lecture 1 |
Lab Intro. |
Lecture 2 |
2 |
Jan. 17--Jan. 21 |
Lecture 3 |
Lab 1 |
Lecture 4 |
3 |
Jan. 24--Jan. 28 |
Lecture 5 |
Lab 2 |
Lecture 6 |
4 |
Jan. 31--Feb. 4 |
Lecture 7 |
Lab 3 |
Lecture 8 |
5 |
Feb. 7--Feb. 11 |
Lecture 9 |
Lab 4 |
Lecture 10 |
6 |
Feb. 14--Feb. 18 |
Exam 1 |
Lab 5 |
Lecture 11 |
7 |
Feb. 21--Feb. 25 |
Lecture 12 |
Lab 6 |
Lecture 13 |
8 |
Feb. 28--Mar. 4 |
Lecture 14 |
Lab 7 |
Lecture 15 |
9 |
Mar. 7--Mar. 11 |
Spring Break |
10 |
Mar. 14--Mar. 18 |
Lecture 16 |
Lab 8 |
Lecture 17 |
11 |
Mar. 21--Mar. 25 |
Lecture 18 |
Lab 10 |
Lecture 19 |
12 |
Mar. 28--Apr. 1 |
Exam 2 |
Lab 10 |
Lecture 20 |
13 |
Apr. 4--Apr. 8 |
Lecture 21 |
Lab 11 |
Lecture 22 |
14 |
Apr. 11--Apr. 15 |
Lecture 23 |
Lab 12 |
Lecture 24 |
15 |
Apr. 18--Apr. 22 |
Lecture 25 |
No Lab |
Review |
17 |
Apr. 27--May 4 |
Final Exam: April 30 (Sat.),
9:00am-12:00am
|
** University policy of attendance will apply.
** All quizzes will be given on Thursday. The instructor reserves the
right to give a quiz at any time.
Lecture Contents
Lectures |
Content |
Lecture 1 |
Review of matrix and vector operations (Chapter
1 and 2) |
Lecture 2-4 |
Gaussian elimination I, II, III (Chapter 3,4,5) |
Lecture 5-6 |
Singular and nonsingular matrices (Chapter 6) |
Lecture 7 |
Tridiagonal matrices (Chapter 7) |
Lecture 8-9 |
Sherman-Morrison formula (Chapter 8) |
Lecture 10-11 |
Vector and matrix norms (Chapter 9) |
Lecture 12 |
Condition number (Chapter 10) |
Lecture 13-15 |
Iterative methods (Chapter 11) |
Lecture 16 |
Determinants (Chapter 12) |
Lecture 17-18 |
Eigenvalues and eigenvectors (Chapter 13) |
Lecture 19-21 |
Power methods (Chapter 14) |
Lecture 22-23 |
Linearly dependent/independent vectors (Chapter 15) |
Lecture 24-25 |
Symmetric matrices (Chapter 16) |
About the Lab
The purpose of the labs is to help you learn to solve linear algebra problems
numerically using the software package MATLAB.
You should know the concepts and algorithms concerning a particular lab before
you come to the lab.
Each lab is devided into two parts. In Part I you will learn some MATLAB
commands by following the instructions. In Part II you will be asked to
perform certain computational tasks using the commands you have learned from
Part I (and previous labs) and to hand in the results.
You are required to hand in the results at the end of the lab. If you
cannot finish in time, you should hand in as much as you can and the rest by
3:00pm the next day. The material handed in after the lab will be graded
with a 20% penalty.
If you do not hand in any results at the end of the lab, you will not receive
any point for that lab.
Each new lab is built upon what you have learned from the previous
labs. The labs will be
led by the Teaching Assistant of this course.
Lab 1:
Part I
Part II (Basic vector and matrix operations)
Lab 2:
Part I
Part II (Solve upper triangular systems)
Lab 3:
Part I
Part II (LU factorization)
Lab 4:
Part I
Part II (Solve Ax=b using L-U-P factorization)
Lab 5:
Part I
Part II (Solve tridiagonal system)
Lab 6:
Part I
Part II (Plot 2D graph)
Lab 7:
Part I
Part II (Sherman-Morrison algorithm)
Lab 8:
Part I
Part II (Condition number and realtive error)
Lab 9:
Part I
Part II (The Jacobi method)
Lab 10:
Part I
Part II (The Gauss-Seidel method)
Lab 11:
Part I
Part II (Condition number and iterative methods)
Lab 12:
Part I
Part II (Power method)
Grading Policy
Course grades will be determined from student performance on
exams,
quizzes and labs. There will be weekly 10 minute
quizzes and three
exams: two 75 minute in-class exams and a final exam. The two
lowest quiz scores will be dropped and no make-up quizzes will be
given. The two
in-class exams, which are indicated on the syllabus above, will be given
during the time normally used for lecture. Each of these exams will test
only the material covered since the previous exam. In contrast the final
exam, which will be given during the week of final exams, will be a
cummulative exam. Reason for missing an exam must be properly documented
and any missed exam must be made up within a week.
Homework will be assigned on a daily basis and should be done before
the
next class. Althought not collected, these homework assignments are an
essential part of the course for learning and understanding the course
material. They should be thought of as required for success in the course.
The grades for the course are determined as follows:
Exam 1 |
20% |
Exam 2 |
20% |
Final Exam |
25% |
Quizzes |
10% |
Labs |
25% |
----- |
Total |
100% |
85-100: A |
80-84: B+ |
73-79: B |
68-72: C+ |
60-67: C |
50-59: D |
<50: F |
Homework Assignments
Section
|
Page
|
Problems
|
Chapter 1 |
1-8 |
# 1.1-1.5 |
Chapter 2 |
2-10 |
# 2.1-2.7, 2.9 |
Chapter 3 |
3-10 |
# 3.1-3.7 |
Chapter 4 |
4-9 |
# 4.1-4.10 |
Chapter 5 |
5-11 |
# 5.1-5.7 |
Chapter 6 |
6-13 |
# 6.1-6.7, 6.10 |
Chapter 7 |
7-9 |
# 7.1-7.6 |
Chapter 8 |
8-10 |
# 8.1-8.8 |
Chapter 9 |
9-16 |
# 9.1-9.13 |
Chapter 10 |
10-7 |
# 10.1-10.13 |
Chapter 11 |
11-14 |
# 11.1-11.8 |
Chapter 12 |
12-16 |
# 12.2-12.9 |
Chapter 13 |
13-13 |
# 13.1-13.13, 13.15 |
Chapter 14 |
14-14 |
# 14.1-14.12 |
Homework Answers:
Chapters 1,2,
Chapters 3,
Chapters 4,5,6,
Chapters 7,
Chapters 8,9,10,
Chapter 11,
Chapter 12,
Chapter 13,
Chapter 14
The answer sheets for homeworks in Chapters 8,9,10 have been
distributed in class. Please come to my office if you didn't get them.
Quizzes and Exams
Quiz 1:
Problems and answers
Quiz 2:
Problems and answers
Quiz 3:
Problems and answers
Quiz 4:
Problems and answers
Test 1:
Problems and answers
Quiz 5:
Problems and answers
Quiz 6:
Problems and answers
Quiz 7:
Problems and answers
Quiz 8:
Problems and answers
Review Sheet for Test 2
Test 2:
Problems and answers
Quiz 9:
Problems and answers
Quiz 10:
Problems and answers
Quiz 11:
Problems and answers