Teaching Spring 2019 Math6540

Basic Information

Course: Math6540 Topics in Numerical Analysis -- Numerical Linear Algebra;

Section: 10;

Semester: Spring 2019;

Time: 01/14/19 - 04/29/19, T&R 04:45pm - 06:00pm;

Location: 1776 G C-118

Instructor: Yanxiang Zhao, Phillips Hall 709

Phone: 202-994-0606

Email: yxzhao at email dot gwu dot edu

Office Hour: T&R 01:00pm--02:20pm or by appointment

Course Description

This course introduces numerical methods for linear algebra. Some selected topics are: Direct methods for solving the linear systems; Iterative methods for solving the linear systems; Eigenvalue problems; Least Squares problems; Optimizations;

Prerequisites

Linear algebra;
Numerical analysis;

Textbook

Matrix computations by G. H. Golub and C. F. Van Loan;
Numerical linear algebra by L. N. Trefethen and D. Bau, III;
Applied numerical linear algebra by J. W. Demmel;

Learning Outcomes

As a result of completing this course, the students will be able to:

apply power iteration, inverse iteration, simultaneous iteration and QR iteration for solving eigenvalue problems ;
Understand the Arnold iteration and Lancoz iteration for eigenvalue problems;
Apply steepest descent method and conjugate gradient method for solving linear system Ax = b;
Interpret the iteration methods for eigenvalue problem and linear system as Krylov subspace method.

Average minimum amount of independent, out-of-class, learning expected per week

More than 2/3 of the time you devote to this class should take place outside the classroom (lecture and recitation). Even the best students in the class should plan on spending an average of at least 6 hours a week on homework and other studying. Students who struggle with the material may need to spend more time in order to earn a grade they will find acceptable.

Calendar

	Mon	Tue	Wed	Thu	Fri
Week 1	Jan14	Jan15	Jan16	Jan17	Jan18
Week 2	Jan21	Jan22	Jan23	Jan24	Jan25
Week 3	Jan28	Jan29	Jan30	Jan31	Feb01
Week 4	Feb04	Feb05	Feb06	Feb07	Feb08
Week 5	Feb11	Feb12	Feb13	Feb14	Feb15
Week 6	Feb18	Feb19	Feb20	Feb21	Feb22
Week 7	Feb25	Feb26	Feb27	Feb28: Oral midterm	Mar01
Week 8	Mar04	Mar05	Mar06	Mar07	Mar08
Week 9	Mar11	Mar12	Mar13	Mar14	Mar15
Week 10	Mar18	Mar19	Mar20	Mar21	Mar22
Week 11	Mar25	Mar26	Mar27	Mar28	Mar29
Week 12	Apr01	Apr02	Apr03	Apr04	Apr05
Week 13	Apr08	Apr09	Apr10	Apr11	Apr12
Week 14	Apr15	Apr16	Apr17	Apr18	Apr19
Week 15	Apr22	Apr23	Apr24	Apr25	Apr26
Week 16	Apr29	Apr30	May01	May02	May03
Week 17	Final Exam Week

NOTE: In accordance with university policy, the final exam will be given during the final exam period and not the last week of the semester.

Homework

Homework 01 (due on 02/21/19)
- Golub: P5.1.2; P5.1.8; P5.2.5; P5.2.12; P5.2.13; P5.3.3;
- Trefethen: 2.3; 2.4; 6.1; 6.3; 6.5; 11.1;
Homework 02 (PDF); Solution (PDF);
Homework 03 (PDF); Solution (PDF);
Homework 04 (PDF); Solution (PDF);
Homework 05 (PDF); Solution (PDF);
Homework 06 (PDF); Solution (PDF);
Homework 07 (PDF); Solution (PDF);

Exams

Oral midterm exam;
Oral final exam;

Grading

Your course grade will be determined by your cumulative average at the end of the term and will be based on the following scale:

	A	A-	B+	B	B-	C+	C	C-	D+	D	D-
scale	95%	90%	87%	83%	80%	77%	73%	70%	67%	63%	60%

Your cumulative average will be the following weighted average:

	HW	Class performance	Midterm	Final
Scheme I	20%	10%	30%	40%

Class Policies

University policy on Religious Holidays:

Students should notify faculty during the first week of the semester of their intention to be absent from class on their day(s) of religious observance;
Faculty should extend to these students the courtesy of absence without penalty on such occasions, including permision to make up examinations;
Faculty who intend to observe a religious holiday should arrange at the beginning of the semester to reschedule missed classes or to make other provisions for their course-related activities.

Academic Integrity

Academic dishonesty is defined as cheating of any kind, including misrepresenting one's own work, taking credit for the work of other without crediting them and without appropriate authorization, and the fabrication of information. For the remainder of the code, see: http://www.gwu.edu/~ntegrity/code.html.

Support for Students Outside the Classroom

Disability Support Services (DSS): Any student who may need an accommodation based on the potential impact of a disability should contact the DSS office at 202-994-8250 in the Rome Hall, Suite 102, to establish eligibility and to coordinate reasonable accommodations. For additional information please refer to: http://gwired.gwu.edu/dss/.
University Counseling Center (UCC): The UCC (202-994-5300) offers 24/7 assistance and referral to address students' personal, social, career, and study skills problems. Services for students include: crisis and emergency mental health consultations; confidential assessment, counseling services (individual and small group), and referrals. For additional information please refer to: http://counselingcenter.gwu.edu/.

Security

In the case of an emergence, if at all possible, the class should shelter in place. If the buliding that the class is in is affected, follow the evacuation procedures for the building. After evacuation, see shelter at a predetermined rendezvous location.

Student Responsibilities and Classroom Courtesy:

You are responsible for knowing about all announcements made in class related to homeworks, exams etc., and for all material covered in class.
Be aware of the University's Code of Academic Integrity, see http://www.gwu.edu/~ntegrity for details. If cases of academic dishonesty arise, whether on homeworks, quizzes or exams, they will be pursued to their conclusion.
Each student must conduct him or herself in a manner that promotes a positive atmosphere, conveys mutual respect, and creates no distractions, thereby allowing all students to focus on our goal: learning NUMERICAL ANALYSIS. In particular:
cell phones, texting devices, laptops, and all other potentially distracting must be turned off during class;
- cell phones, texting devices, laptops, and all other potentially distracting must be turned off during class;
- everyone should make a serious effort to arrive promptly for the start of class;
- except for serious reasons, once in class everyone should remain in class until the class is over;
- apart from the lecture, students asking the instructor questions, and students responding to the instructor's questions, the class should be silent.

Questions

Everyone is strongly encouraged to ask questions during class, and during office hours! Should you need further assistance, you may consider hiring a tutor (the department keeps a list of tutors; copies are available outside Phillips Hall 739).

Library

Calculus (library call number: QA303.2 .S73 2016) is available on reserve as part of the Top Textbooks program at GW Libraries. Top Textbooks can be checked out for three hours at a time, can be taken outside the library, and have no cost to use.