Course: Math 6523 Numerical Solution of ODE & PDE
Semester: Spring 2021;
Time: 01/11/2021-04/29/2021, Tue&Thu 4:45pm-6:00pm (EST);
Location: Online course (Find the Zoom link in Blackboard under the Tab of Syllabus)
Instructor: Yanxiang Zhao, Phillips Hall 709
Phone: 202-994-0606
Email: yxzhao at email dot gwu dot edu
Office Hour: Tue&Thu 06:00pm--07:00pm (EST) or by appointment
Course Description
Initial and boundary value problems for ordinary differential equations. Error propagation, convergence and stability. Finite difference and finite element methods for partial differential equations.
Prerequisites
- Math 3342: Partial Differential Equations and knowledge of a programming language.
Textbook
- Finite Difference Method for Ordinary and Partial Differential Equations: steady-state and time-dependent problems by R. J. LeVeque, SIAM 2007.
Learning Outcomes
As a result of completing this course, the students will be able to:
- Apply finite difference method to initial value problem for ODEs;
- Apply finite difference method to boundary value problem for ODEs;
- Apply finite difference method to PDEs;
- Apply finite element method to PDEs.
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. 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
| Week | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| 01 | Jan11 | Jan12 | Jan13 | Jan14 | Jan15 |
| 02 | Jan18 | Jan19 | Jan20 | Jan21 | Jan22 |
| 03 | Jan25 | Jan26 | Jan27 | Jan28 | Jan29 |
| 04 | Feb01 | Feb02 | Feb03 | Feb04 | Feb05 |
| 05 | Feb08 | Feb09 | Feb10 | Feb11 | Feb12 |
| 06 | Feb15 | Feb16 | Feb17 | Feb18 | Feb19 |
| 07 | Feb22 | Feb23 | Feb24 | Feb25: in-class midterm | Feb26 |
| 08 | Mar01 | Mar02 | Mar03 | Mar04 | Mar05 |
| 09 | Mar08 | Mar09 | Mar10 | Mar11 | Mar12 |
| 10 | Mar15 | Mar16: Spring Break | Mar17 | Mar18: Spring Break | Mar19 |
| 11 | Mar22 | Mar23 | Mar24 | Mar25 | Mar26 |
| 12 | Mar29 | Mar30 | Mar31 | Apr01 | Apr02 |
| 13 | Apr05 | Apr06 | Apr07 | Apr08 | Apr09 |
| 14 | Apr12 | Apr13 | Apr14 | Apr15 | Apr16 |
| 15 | Apr19 | Apr20 | Apr21 | Apr22 | Apr23 |
| 16 | Apr26 | Apr27 | Apr28 | Apr29 | Apr30 |
| 16 | May03 | May04 | May05 | May06 | May07 |
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.
Exams
There will be one in-class midterm exam on Feb 25, and a final exam (or a final project, which will be decided later) in the final exam week (the exact date will be announced later).
- No makeup midterm exam for any excuse.
- The final exam is cumulative and is scheduled by the Registrar's Office. 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, etc.) is strictly banned during exams. Using the work of others on exams is strictly prohibited.
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- |
| 95% | 90% | 87% | 83% | 80% | 77% | 73% | 70% | 67% | 63% | 60% |
Your cumulative average will be the following weighted average:
| in-class performance | Midterm | Final | |
| Scheme | 30% | 30% | 40% |
If you missed the midterm exam due to personal emergence (with offical supported document), the final exam will weight 70% in the cumulative average.
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.
