Math 580: Mathematics of Fluid Mechanics

Synchronous Online Lecture Time on Zoom: M/W/F 1:00-1:50pm
Zoom Meeting ID: 708 026 5460
Instruction Method: The instructor will present lectures on a physical board.
Course Technology Requirements: personal computer or tablet, broadband Internet connection. You may contact ACCC (https://accc.uic.edu/services/teaching-learning/equipment-lending/acccell/) to request and borrow a laptop or be assigned a hotspot for the semester if you do not have the required hardware and internet capabilities.

Instructor:

Alexey Cheskidov
Office: 535 SEO
phone:
e-mail: acheskid@uic.edu
Office hours: MW 11am-12pm on Zoom (Meeting ID: 708 026 5460)

Course topics:

The Euler equations for an ideal incompressible fluid; vorticity equation; Bernoulli law.
Viscosity; Navier-Stokes equations; Reynolds number; vorticity diffusion; elementary examples.
Waves: capillary and gravity dispersive waves, dispersion relation, group velocity, wave packets and trains; shocks
Elements of vortex motion: Kelvin Circulation Theorem, Helmholtz Theorem, line vortices, method of images, von Karman street and other vortex configurations, stability.
Boundary layers; Prandtl's equations; Blasius profile; separation; Falkner-Skan equations.

Texts:

D. Acheson "Elementary Fluid Dynamics" (the main text)
A. Majda, A. Bertozzi "Vorticity and Incompressible Flow"

Grading:

Homework: 70%
Take-home final exam: 30%

Attendance

A basic requirement of the course is a serious commitment on your part to attend the lectures. Students that know ahead of time that they have an existing or potential conflict with the class must inform the instructor.

Academic Integrity Policy

As an academic community, UIC is committed to providing an environment in which research, learning, and scholarship can flourish and in which all endeavors are guided by academic and professional integrity. All members of the campus community - students, staff, faculty, and administrators - share the responsibility of insuring that these standards are upheld so that such an environment exists. Instances of academic misconduct by students will be handled pursuant to the Student Disciplinary Policy: https://dos.uic.edu/wp-content/uploads/sites/262/2020/01/DOS_Student-Disciplinary-Policy-2020.pdf

Academic Deadlines

Current academic calendar and the list of deadlines can be found here: https://catalog.uic.edu/ucat/\\academic-calendar/

Disability Policy

The University of Illinois at Chicago is committed to maintaining a barrier-free environment so that students with disabilities can fully access programs, courses, services, and activities at UIC. Students with disabilities who require accommodations for access to and/or participation in this course are welcome, but must be registered with the Disability Resource Center (DRC). You may contact DRC at 312-413-2183 (v) or 312-413-0123 (TTY) and consult the following: http://www.uic.edu/depts/oaa/\\ disability\_resources/faq/accommodations.html.

Religious Holidays

Students who wish to observe their religious holidays shall notify the faculty member by the tenth day of the semester of the date when they will be absent unless the religious holiday is observed on or before the tenth day of the semester. In such cases, the student shall notify the faculty member at least five days in advance of the date when he/she will be absent. The faculty member shall make every reasonable effort to honor the request, not penalize the student for missing the class, and if an examination or project is due during the absence, give the student an exam or assignment equivalent to the one completed by those students in attendance. If the student feels aggrieved, he/she may request remedy through the campus grievance procedure. http://oae.uic.edu/religious-calendar/

Grievance Procedures

UIC is committed to the most fundamental principles of academic freedom, equality of opportunity, and human dignity involving students and employees. Freedom from discrimination is a foundation for all decision making at UIC. Students are encouraged to study the University's ``Nondiscrimination Statement". Students are also urged to read the document ``Public Formal Grievance Procedures''. Information on these policies and procedures is available on the University web pages of the Office of Access and Equity: www.uic.edu/depts/oae.

COVID-19 Safety Protocols and Policies at UIC

UIC has built an infrastructure for COVID-19 testing and tracing of UIC community members. Please refer to the UIC website, Coronavirus Disease 2019 (COVID-19) (https://today.uic.edu/coronavirus), and the Circle Back to Campus Plan (https://today.uic.edu/circle-back-to-campus) and newsletter (https://today.uic.edu/coronavirus-recovery) for up-to-date campus policies and procedures. For information about what to do: UIC FAQs (https://today.uic.edu/frequently-asked-questions).
Students who think they have been exposed to COVID-19 or who have tested positive should inform Student Health Services at 312-996-2901, as soon as possible, so that the University can take action in accordance with University policies (https://today.uic.edu/coronavirus). Please do not hesitate to share a positive diagnosis; your identity will NOT be revealed to your classmates. UIC's utmost concern is for the students' welfare and trying to ensure that everyone can take the needed precautions to reduce the likelihood of additional infection. Arrangements will be made with students on an individual basis to accommodate missed classes or assignments due to illness.

Online Course Communication Guidelines (Netiquette)

Be mindful of different cultural and linguistic backgrounds, as well as different political ideologies and religious beliefs.
Use good judgment when composing your written responses. Swearing and profanity should be avoided. Also consider that slang terms can be misunderstood or misinterpreted.
Be respectful of others' views and opinions.
Be careful when using acronyms. If you use an acronym it is best to spell out its meaning first, then put the acronym in parentheses afterward, for example: Frequently Asked Questions (FAQs). After that you can use the acronym freely throughout your message.
Use good grammar and spelling in written communications.
In emails, always identify yourself and what class and section you are in. It is a good practice to put your course in the subject line. This helps your instructor identify course related emails.

Privacy Notification and Policy for Video Recording of Synchronous Class Sessions

We will be recording the class sessions, or portions of the class, for students who are unable to attend synchronously. The recording feature for others is disabled so that no one else will be able to record this session through Zoom, Blackboard Collaborate, Webex, or Echo360. Recording by other means is not permitted. The recorded class sessions will be posted on our Blackboard class website unless otherwise notified.
If you have privacy concerns and do not wish to appear in the recording, turn OFF your video and notify me in writing (via email) prior to the next class session. If you prefer to use a pseudonym instead of your name, please let me know what name you will be using, so that I can identify you during the class session. If you would like to ask a question, you may do so privately through the chat feature by addressing your question to me or your TA only (and not to ``everyone''), or you may contact me or your TA by another private method, which we will agree upon in advance of class. If you have questions or concerns about this video recording policy, please contact me before the end of the first week of class.
Students with disabilities must inform the instructor of the need for accommodations. Those who require accommodations for access and participation in this course must be registered with the Disability Resource Center. Please contact ODS at 312/413-2183 (voice) or 312/413-0123 (TTY).

Homework assignments:

HW 1 due Sep. 18

HW 2:
4.3, 4.5, 4.8

HW 3:
5.1, 5.2, 5.8

HW 4:
3.1, 3.3, 3.4, 3.18