Basic Information
Course: Math 3553.80 Numerical Analysis
Semester: Fall 2024
Time: 08/22/2024-12/09/2024, Mon&Wed 12:45pm-02:00pm;
Location: Duques 251
Instructor: Yanxiang Zhao, Phillips Hall 702
Phone: 202-994-0606
Email: username at email dot gwu dot edu username equals yxzhao
Office Hour: Mon&Wed 02:00pm-03:00pm 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);
- Programming language (Matlab, Python, C, etc.);
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. Aug26-Aug30 Aug 26 Aug28
Week02. Sep02-Sep06 Labor Day Sep04: quiz01
Week03. Sep09-Sep13 Sep09 Sep11
Week04. Sep16-Sep20 Sep16 Sep18: quiz02
Week05. Sep23-Sep27 Sep23 Sep25
Week06. Sep30-Oct04 Sep30 Oct02: quiz03
Week07. Oct07-Oct11 Oct 07 Oct09 (midterm)
Week08. Oct14-Oct18 Oct14 Oct16
Week09. Oct21-Oct25 Oct21 Oct23: quiz04
Week10. Oct28-Nov01 Oct28 Oct30
Week11. Nov04-Nov08 Nov04 Nov06: quiz05
Week12. Nov11-Nov15 Nov11 Nov13
Week13. Nov18-Nov22 Nov18 Nov20: quiz06
Week14. Nov25-Nov29 Thanksgiving Thanksgiving
Week15. Dec02-Dec06 Dec02 Dec04
Week16. Dec09-Dec13 Dec09 (last day)
Week 17. Dec 16-Dec20 Dec 16(Final exam, 12:40-2:40pm)
NOTE: In accordance with university policy, the final exam will be given during the final exam period (Dec 12-17). 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 from this semester (PDF);
- Lecture Notes from previous year (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 26&28. 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 09, and a final exam will be on Dec 16th, 12:40-2:40pm in Duques 251 (our classroom).
- 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% |
Academic Integrity Code
Academic integrity is an essential part of the educational process, and all members of the GW community take these matters very seriously. As the instructor of record for this course, my role is to provide clear expectations and uphold them in all assessments. Violations of academic integrity occur when students fail to cite research sources properly, engage in unauthorized collaboration, falsify data, and otherwise violate the Code of Academic Integrity. If you have any questions about whether particular academic practices or resources are permitted, you should ask me for clarification. If you are reported for an academic integrity violation, you should contact Conflict Education and Student Accountability (CESA), formerly known as Student Rights and Responsibilities (SRR), to learn more about your rights and options in the process. Consequences can range from failure of assignment to expulsion from the University and may include a transcript notation. For more information, refer to the CESA website at students.gwu.edu/code-academic-integrity or contact CESA by email cesa@gwu.edu or phone 202-994-6757.
University policy on observance of religious holidays
Students must notify faculty during the first week of the semester in which they are enrolled in the course, or as early as possible, but no later than three weeks prior to the absence, of their intention to be absent from class on their day(s) of religious observance. If the holiday falls within the first three weeks of class, the student must inform faculty in the first week of the semester. For details and policy, see provost.gwu.edu/policies-procedures-and-guidelines.
Use of Electronic Course Materials and Class Recordings
Students are encouraged to use electronic course materials, including recorded class sessions, for private personal use in connection with their academic program of study. Electronic course materials and recorded class sessions should not be shared or used for non-course related purposes unless express permission has been granted by the instructor. Students who impermissibly share any electronic course materials are subject to discipline under the Student Code of Conduct. Contact the instructor if you have questions regarding what constitutes permissible or impermissible use of electronic course materials and/or recorded class sessions. Contact Disability Support Services at disabilitysupport.gwu.edu if you have questions or need assistance in accessing electronic course materials.
Academic Commons
Academic Commons is the central location for academic support resources for GW students. To schedule a peer tutoring session for a variety of courses visit go.gwu.edu/tutoring. Visit academiccommons.gwu.edu for study skills tips, finding help with research, and connecting with other campus resources. For questions email academiccommons@gwu.edu.
GW Writing Center
GW Writing Center cultivates confident writers in the University community by facilitating collaborative, critical, and inclusive conversations at all stages of the writing process. Working alongside peer mentors, writers develop strategies to write independently in academic and public settings. Appointments can be booked online at gwu.mywconline.
Support for students in and outside the classroom
- Disability Support Services (DSS) 202-994-8250: Any student who may need an accommodation based on the potential impact of a disability should contact Disability Support Services at disabilitysupport.gwu.edu to establish eligibility and to coordinate reasonable accommodations.
- Student Health Center 202-994-5300, 24/7: The Student Health Center (SHC) offers medical, counseling/psychological, and psychiatric services to GW students. More information about the SHC is available at healthcenter.gwu.edu. Students experiencing a medical or mental health emergency on campus should contact GW Emergency Services at 202-994-6111, or off campus at 911.
GW Campus Emergency Information
GW Emergency Services: 202-994-6111
For situation-specific instructions, refer to GW’s Emergency Procedures guide.
GW Alert
GW Alert is an emergency notification system that sends alerts to the GW community. GW requests students, faculty, and staff maintain current contact information by logging on to alert.gwu.edu. Alerts are sent via email, text, social media, and other means, including the Guardian app. The Guardian app is a safety app that allows you to communicate quickly with GW Emergency Services, 911, and other resources. Learn more at safety.gwu.edu.
Protective Actions
GW prescribes four protective actions that can be issued by university officials depending on the type of emergency. All GW community members are expected to follow directions according to the specified protective action. The protective actions are Shelter, Evacuate, Secure, and Lockdown (details below). Learn more at safety.gwu.edu/gw-standard-emergency-statuses.
- Shelter: Protection from a specific hazard; The hazard could be a tornado, earthquake, hazardous material spill, or other environmental emergency; Specific safety guidance will be shared on a case-by-case basis. Action: Follow safety guidance for the hazard.
- Evacuate: Need to move people from one location to another; Students and staff should be prepared to follow specific instructions given by first responders and University officials. Action: Evacuate to a designated location; Leave belongings behind; Follow additional instructions from first responders.
- Secure: Threat or hazard outside of buildings or around campus; Increased security, secured building perimeter, increased situational awareness, and restricted access to entry doors. Action: Go inside and stay inside; Activities inside may continue.
- Lockdown: Threat or hazard with the potential to impact individuals inside buildings; Room-based protocol that requires locking interior doors, turning off lights, and staying out of sight of corridor window. Action: Locks, lights, out of sight; Consider Run, Hide, Fight.
- Classroom emergency lockdown buttons: Some classrooms have been equipped with classroom emergency lockdown buttons. If the button is pushed, GWorld Card access to the room will be disabled, and GW Dispatch will be alerted. The door must be manually closed if it is not closed when the button is pushed. Anyone in the classroom will be able to exit, but no one will be able to get in.
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).
