Basic Information
Course: Math 6540 Topics in Numerical Analysis
Semester: Spring 2018;
Time: 01/16/2018-04/30/2018, Tuesday&Thursday 02:20pm-03:35pm;
Location: Phillips 640
Instructor: Yanxiang Zhao, Phillips Hall 709
Phone: 202-994-0606
Email: yxzhao at email dot gwu dot edu
Office Hour: Tuesday&Thursday 04:00pm--05:00pm or by appointment
Course Description
This course introduces numerical method for partial differential equations, particular focus will be numerical methods for advection-diffusion-reaction equations.
Textbook
- Numerical solutions of time-dependent advection-diffusion-reaction equations by Hundsdorfer, Springer Nature, 2003;
- A downloadable notes from Hundsdorfer [link];
- Finite difference schemes and partial differential equations by Strikwerda, SIAM, 2004;
- Finite difference methods for ordinary and partial differential equations by LeVeque, SIAM, 2007.
- Scientific computing with ordinary different equations by Deuflhard and Bornemann, Springer, 2000.
Learning Outcomes
As a result of completing this course, the students will be able to:
- Apply simple numerical schemes to solve advection-diffusion-reaction equations;
- Perform numerical analysis (error estimate, stability analysis) on the advection-diffusion-reaction equations;
- Apply the numerical schemes to other related partial differential equations such as Schrodinger equations.
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.
Homeworks and Exams
- Some reading homeworks are assigned weekly.
- There will be no exams. A final project will be assigned in the final week.
Grading
Your course grade will be determined by in-class performance (50%) and a final project (50%).
A A- B+ B B- C+ C C- D+ D D-
95% 90% 87% 83% 80% 77% 73% 70% 67% 63% 60%
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).
