2022 Fall Course Syllabus - Mathematics 9200.001

Course: Mathematics 9200.001.

Course Title: Topics in Numerical Analysis I: Computational Methods for Flow Problems.

Credits: 3.

How this course will be taught: In person.

Time: TR 2:00-3:20.

Place: Wachman Hall 617.

Instructor: Benjamin Seibold.

Instructor Office: Wachman Hall 518.

Instructor Email: benjamin.seibold@temple.edu

Instructor Phone: 215-204-1656.

Course Web Page: https://www.math.temple.edu/~seibold/teaching/2022_9200/

Office Hours: TR 3:30-4:30.

Prerequisites: -.

Course Materials: Recommended literature for further reading: Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations - Steady State and Time Dependent Problems, SIAM, 2007. Randall J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002. Alexandre J. Chorin, Jerrold E. Marsden, A Mathematical Introduction to Fluid Mechanics, 3rd ed., Springer 1993. C.A.J. Fletcher, Computational Techniques for Fluid Dynamics I, Springer.

Course Goals: The goal of this course is provide a broad perspective on these important types of flow problems, their connections, and how to tackle them computationally. This course provides the needed familiarity with each topic to enable the participants to engage into further studies via literature.

Topics Covered: This course provides an overview of numerical methods for many important types of flow problems, ranging from incompressible fluids (Navier-Stokes equations), over shock problems (such as the compressible Euler equations), front propagation problems (such as multiphase flows), kinetic equations (Boltzmann equation, radiative transfer), to network flows (such as traffic on roads). One third of the course will be devoted to the modeling, derivation, and mathematical/physical properties of the equations and their solutions; and two thirds to the design of efficient and robust numerical methods for their solution. The computational approaches include: finite volume methods, finite difference methods, meshfree and particle methods, level set methods, immersed interface and phase field models, moment methods.

Course Grading: The final grade consists of two parts, each counting 50%: homework problem sets and final examination.

Exam Dates: 04/28/2022.

Attendance Policy: Students are expected to attend every class. If a student cannot attend a class for some justifiable reason, he or she is expected to contact the instructor before class.

Attendance and Your Health: To achieve course learning goals, students must attend and participate in classes, according to your instructors' requirements. However, if you feel unwell or if you are under quarantine or in isolation because you have been exposed to the virus or tested positive for it, you should not come to campus or attend in-person classes or activities. Students have the responsibility to contact their instructors to create a plan for participation and engagement in the course as soon as they are able to do so and to make a plan to complete all assignments in a timely fashion when illness delays their completion.

Disability Statement: Any student who has a need for accommodations based on the impact of a documented disability or medical condition should contact Disability Resources and Services (DRS) in Howard Gittis Student Center South, Rm 420 (drs@temple.edu; 215-204-1280) to request accommodations and learn more about the resources available to you. If you have a DRS accommodation letter to share with me, or you would like to discuss your accommodations, please contact me as soon as practical. I will work with you and with DRS to coordinate reasonable accommodations for all students with documented disabilities. All discussions related to your accommodations will be confidential.

Academic Freedom: Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here (opens in new tab/window).

Add/Drop Policy: Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar (opens in new tab/window) for exact dates.

During the Drop/Add period, students may drop a course with no record of the class appearing on their transcript. Students are not financially responsible for any courses dropped during this period. In the following weeks prior to or on the withdrawal date students may withdraw from a course with the grade of "W" appearing on their transcript. After the withdrawal date students may not withdraw from courses. Check the University Calendar (opens in new tab/window) for exact dates. See the full policy by clicking here (opens in new tab/window).

Incomplete Policy: The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here (opens in new tab/window).

Student Support Services: The following academic support services are available to students (all links open in a new tab/window):
    The Math Consulting Center
    Student Success Center
    University Libraries
    Undergraduate Research Support
    Career Center
    Tuttleman Counseling Services
    Disability Resources and Services
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