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