Basic Information
Course: Math 6523.10 Numerical Solution of ODEs & PDEs
Semester: Fall 2023
Time: 01/17/2024-04/29/2024, Mon&Wed 03:45pm-05:00pm;
Location: Phillips Hall 730
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: Numerical methods for ODEs (initial value problems, and boundary value problems); Finite difference for PDEs (elliptic equations and parabolic equations); Spectral methods for PDEs.
Prerequisites
- Calculus I & II;
- Linear Algebra (Matrix theory);
- Computing in Mathematics (Matlab);
Textbook
- Finite difference methods for ordinary and partial differential equations, by Randall J. LeVeque, SIAM 2007.
Learning Outcomes
As a result of completing this course, the students will be able to:
- solve ODEs (initial value problems and boundary value problems) using finite difference;
- solve PDEs (elliptic equations and parabolic equations) using finite difference;
- Spectral methods for PDEs;
- Numerical methods for optimal control problems.
AI and ChatGPT (University policies)
The use of AI and ChatGPT is completely forbidden for the homework assignments, quizzes and exams. On the other hand, the use of AI and ChatGPT is recommended for self-study of the course materials.
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. 01/15-01/19 01/15 01/17
Week02. 01/22-01/26 01/22 01/24
Week03. 01/29-02/02 01/29 01/31
Week04. 02/05-02/09 02/05 02/07
Week05. 02/12-02/16 02/12 02/14
Week06. 02/19-02/23 02/19 (No class) 02/23
Week07. 02/26-03/01 02/26 02/28
Week08. 03/04-03/08 03/04 03/06 (Midterm)
Week09. 03/11-03/15 03/11 (No class) 03/13 (No class)
Week10. 03/18-03/22 03/18 03/20
Week11. 03/25-03/29 03/25 03/27
Week12. 04/01-04/05 04/01 04/03
Week13. 04/08-04/12 04/08 04/10
Week14. 04/15-04/19 04/15 04/17
Week15. 04/22-04/26 04/22 04/24
Week16. 04/29-05/03 04/29 (Last day)
Homework
No homework assignments.
Quizzes
No quizzes.
Exams
There will be an in-class midterm exam on March 06, and a final exam on April 24.
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 based on the following scheme:
| In-class performance | Midterm | Final | |
| Scheme | 30% | 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 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).
