MATH723 Differential Equations I Fall 2019

Course Information

Instructor Dr. Changhui Tan
Lectures M W 2:20pm - 3:35pm, at LeConte 401
Office LeConte 422
Office Hours M 10:00am - 12:00pm, or by appointment
Textbooks Lawrence C. Evans, Partial Differential Equations. (ISBN: 978-0821849743)


Course Description

  • The official course description for the MATH 723/724 sequence:
  • Elliptic equations: fundamental solutions, maximum principles, Green’s function, energy method and Dirichlet principle; Sobolev spaces: weak derivatives, extension and trace theorems; weak solutions and Fredholm alternative, regularity, eigenvalues and eigenfunctions.
  • Detailed study of the following topics: method of characteristics; Hamilton-Jacobi equations; conservation laws; heat equation; wave equation; linear parabolic equations; linear hyperbolic equations.
  • List of Topics (for MATH 723):


Homework Assignments

  • Homework assignments will be assigned and collected each week. The tentative due date is on Monday in class.
  • The homework is not pledged. You are encouraged to discuss the problems. However, each student is responsible for the final preparation of his/her own homework papers.
  • Last update: 11/6, Homework 8 is available. It is due on Monday 11/11 in class.
  •  Download Homework Assignments.



  • A final take-home exam will be given at the end of the semester. The exam will take 3 hours. You can use the textbook, your own lecture notes and your own homework assignments during the exam. Other communications and helps are not allowed. You should spend no more than 3 consecutive hours on the exam.
  • Exams are under the honor code. Be sure and hand in all the work you do on each problem. Good luck! 
  • Last update: 12/6, the final exam is available.
  •  Download the Final Exam.



  • Your grade are distributed as below:
  • Class Participation » 10%
    Homework » 50%
    Final exam » 40%


Contact Information

  • Contact me at This email address is being protected from spambots. You need JavaScript enabled to view it. if you have any questions.