Teaching Fall 2023 Math3553&6522

Basic Information

Course: Math 3553.80 Numerical Analysis

Semester: Fall 2023

Time: 08/24/2023-12/12/2023, Mon&Wed 12:45pm-02:00pm;

Location: Phillips Hall 109

Instructor: Yanxiang Zhao, Phillips Hall 709

Phone: 202-994-0606

Email: username at email dot gwu dot edu username equals yxzhao

Office Hour: Mon&Wed 05:00pm-06:00pm or by appointment

Course Description

This course covers: Linear systems and matrices; Direct and iterative methods for solving linear equations; Sparse matrices; Solution of nonlinear equations; interpolation and approximate representation of functions; splines.

Prerequisites

Calculus I & II;
Linear Algebra (Matrix theory);
Computing in Mathematics (Matlab);

Textbook

Numerical analysis, by Burden, 10th edition, published by Cengage Learning.

Learning Outcomes

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

solve linear systems by using different numerical methods (direct or indirect methods);
conduct some basic conditioning analysis on different numerical methods for linear methods;
understand the convergence and rate of convergence for fixed-point iteration methods for nonlinear problems;
use Matlab to numerically solve some simple linear or nonlinear problems.

AI and ChatGPT (University policies)

The use of AI and ChatGPT is completely forbidden for the homework assignments, quizzes and exams.

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 5 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

Monday Wednesday

Week01. Aug28-Sep01 Aug 28 Aug30

Week02. Sep04-Sep08 Labor Day Sep06: quiz01

Week03. Sep11-Sep15 Sep11 Sep13

Week04. Sep18-Sep22 Sep18 Sep20: quiz02

Week05. Sep25-Sep29 Sep25 Sep27

Week06. Oct02-Oct06 Oct02 Oct04: quiz03

Week07. Oct09-Oct13 Oct 09 Oct11 (midterm)

Week08. Oct16-Oct20 Oct16 Oct18

Week09. Oct23-Oct27 Oct23 Oct25: quiz04

Week10. Oct30-Nov03 Oct30 Nov01

Week11. Nov06-Nov10 Nov06 Nov08: quiz05

Week12. Nov13-Nov17 Nov13 Nov15

Week13. Nov20-Nov24 Thanksgiving Thanksgiving

Week14. Nov27-Dec01 Nov27 Nov29: quiz06

Week15. Dec04-Dec08 Dec04 Dec06

Week16. Dec11-Dec15 Dec11 (last day) Final (announced later)

NOTE: In accordance with university policy, the final exam will be given during the final exam period (Dec 13-19). There will be no accommodation for Christmas flight before scheduled final exam.

Homework

Homework will NOT be collected and will NOT be graded. The main purpose of the homework assignment is for you to prepare for the bi-weekly quizzes and the exams.

Homework 01 (PDF); Solution (PDF);
Homework 02 (PDF); Solution (PDF);
Homework 03 (PDF); Solution (PDF);
Homework 04 (PDF); Solution (PDF, PDF2);
Homework 05 (PDF); Solution (PDF);
Homework 06 (PDF); Solution (PDF);
Homework 07 (PDF); Solution (PDF);
Homework 08 (PDF); Solution (PDF);
Homework 09 (PDF); Solution (PDF);
Homework 10 (PDF); Solution (PDF);
Homework 11 (PDF); Solution (PDF);
Homework 12 (PDF); Solution (PDF);
Homework 13 (PDF); Solution (PDF);

Notes

Lecture Notes (PDF);
Topic summary (PDF);
Frobenius matrix (PDF);
Gauss elimination and LU decomposition (PDF);
Cholesky decomposition (PDF);
Orthogonal Polynomials and Gauss Quadrature (PDF);

Quizzes

There are 6 10-minute biweekly quizzes, each out of 25 points, on Wednesday's classes. Each quiz will cover the the lecture of the same Monday, lectures of the previous Monday and Wednesday, and the lecture of the Wednesday before the previous week. The first quiz will only cover the lectures from Aug 28&30. 4 highest quizzes count for the final grade. NO MAKEUP QUIZZES for any excuses.

Quiz solutions: 1. 2. 3. 4. 5. 6.

Exams

There will be an in-class midterm exam on Oct 11, and a final exam in final exam period of Dec 13-19.

No makeup midterm exam for any excuse. If you have to miss the midterm exam due to some personal emergency, you can choose to excuse the midterm, and count your final exam score in the weight of 70%. See the Scheme I & II below for the details.
The final exam is cumulative. It is your responsibility to ensure that you do not have a schedule conflict involving the final exam.
Assistance of any type (notes in any form, books, AI, ChatGPT etc.) is strictly banned during exams. Using the work of others on exams is strictly prohibited.

Exam Solutions

Midterm [PDF];
Final Exam [PDF];

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 higher one of the following two weighted averages:

	HW	Quiz	Midterm	Final
Scheme I	0%	30%	30%	40%
Scheme II	0%	30%	0%	70%

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 permission 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).