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Jincheng Yang

Johns Hopkins University

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Research Blog

EN.553.798.01 Partial Differential Equations for Applied Mathematicians

EN.553.798.01 Partial Differential Equations for Applied Mathematicians

Contact

Instructor: Dr. Jincheng Yang

Office: Wyman N418

E-mail: jincheng@jhu.edu

Canvas message is preferred.

Schedule

Regular in-person class: TTh 4:30 PM - 5:45 PM @ Latrobe 107

Office Hour: by appointment

Course description

This Ph.D.-level course introduces the ordinary and partial differential equations theories from an applied mathematician’s viewpoint. The course starts with concepts widely used in applied mathematics and functional analysis, including Banach spaces, Hilbert spaces, distributions, Fourier transform, and Sobolev spaces. Then we discuss existence and uniqueness theory for weak solutions and viscosity solutions to ordinary and partial differential equations, with an emphasis on those that arise in mathematical physics, calculus of variations, or deterministic and stochastic control theory.

Textbook

The textbook for the course is Functional Analysis for the Applied Mathematician, by Todd Arbogast and Jerry L. Bona (1st edition). This book will be helpful to you as a reference and also as a source of practice problems. It is available electronically via JHU library.

Policies

Grading

The course will be graded based on homework and class attendance.

Homework

You can collaborate with your classmates in small study groups of up to 3 members. If you do so, please mark at the beginning of each assignment the full name of your collaborators. Each member still needs to submit their own solution. Homework submission will be via canvas. You are responsible for submitting a legible scan of your written solutions.

Zoom protocols

There is an expectation that students in this course will be actively engaged and on camera while on Zoom. If a student requires an exception, they will need to reach out to the instructor directly.

Recording and Deletion Policies

Do not record, share, or disseminate any course sessions, videos, transcripts, audio, or chats. Do not share links for the course to those not currently enrolled. Any Zoom cloud recordings will be automatically deleted 90 days after the completion of the recording.

Ethics

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Report any violations you witness to the instructor. You can also contact:

  • For undergraduates: the director of student conduct (or designee) by calling the Office of Student Conduct at (410) 516-2509 or via email at studentconduct@jhu.edu
  • For KSAS Graduate Students; rseitz5@jh.edu
  • For WSE Graduate Students: christinekavanagh@jhu.edu

Johns Hopkins takes academic honesty very seriously. Students are expected to be independently familiar with the university policy and to understand that their work in the course must be their own original work. Violations of the policy are taken seriously.

Using Generative Artificial Intelligence

You can use generative artificial intelligence tools (ChatGPT, New Bing, Gemini, etc.) to help you study. Find the learning strategy that best suits you. However, you have to complete your homework by yourself. This means you can never copy and paste (by keyboard or by hand) any answers from Chatbot or Copilot to your homework. You should learn, understand, internalize, and create your own solution. Grammar and spelling check tools are allowed.

Personal Wellbeing

  • Because of ongoing COVID-19 concerns, special requirements may be in effect this term, and these may vary during the term. Please keep updated with these at the following sites:
  • COVID-19 vaccination a required unless an exception has been granted by the university for health or religious reasons.
  • If you are sick please notify me by email so that we can make appropriate accommodations should this affect your ability to attend class, complete assignments, or participate in assessments. The Student Health and Wellness Center is open and operational for primary care needs. If you would like to speak with a medical provider, please call (410) 516-8270, and staff will determine an appropriate course of action. See also student affair website.
  • Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions, and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements. For further information or to start the process of requesting accommodations, please contact Student Disability Services at Homewood Campus, Shaffer Hall 101, call: (410) 516-4720 and email: studentdisabilityservices@jhu.edu or visit the website.
  • If you are struggling with anxiety, stress, depression, or other mental health related concerns, please consider visiting the JHU Counseling Center. If you are concerned about a friend, please encourage that person to seek out their services. The Counseling Center is located at 3003 North Charles Street in Suite S-200 and can be reached at (410) 516-8278 and online.
  • Student Outreach & Support helps students manage physical and mental health concerns, personal and family emergencies, financial issues, and other obstacles that may arise during their college experience. Students can self-refer or refer a friend who may need extra support or help getting connected to resources. To connect with SOS, please visit this website or email deanofstudents@jhu.edu, call (410) 516-7857, or students can schedule to meet with a Case Manager by visiting the Student Outreach & Support website and filling out a referral form online.

Policy on Incomplete Grades

The full policy is available here.

The significant component of this policy is that there is an Incomplete Grade Contract available to students in SIS to request an incomplete grade. This is how all incomplete grades must be initiated. Another significant component is the timeline for completion of an incomplete grade for undergraduate students, which is 45 calendar days after the last day of classes. For graduate students, the deadline is the end of the third week of classes of the following semester. See the full catalogue entry for considerations for students on academic probation and graduating students.

Deadlines for Adding, Dropping and Withdrawing from Courses can be found here.

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