Course Information
Instructor  Dr. Changhui Tan 
Lectures  Tu Th 9:25am  10:40am, at HBH 227 
Office  HBH 426 
Office Hours  Th 11:00am  12:00pm, or by appointment 
Teaching Assistants  Chao Li 
TA Office Hours  M 2:30pm  3:30pm, at HBH 36 
Textbooks  Lawrence C. Evans, Partial Differential Equations. (ISBN: 9780821849743) 
References  Fritz John, Partial Differential Equations. (ISBN: 9780387906096) 
Walter A. Strauss, Partial Differential Equations: An Introduction. (ISBN: 9780470054567) 
Course Description
 The official course description on MATH 423 / CAAM 423 / MATH 513 / CAAM 523.
 List of Topics:

 An introduction to PDEs and associated applications.
 First order linear and nonlinear PDE:
 Transport equation, the method of characteristics, local existence theory.
 Burgers equation, weak solution, distribution theory.
 Hyperbolic conservation laws, Riemann problem, entropy solution.  Second order linear PDE, 3 basic equations:
 Wave equation: plane wave, traveling wave and solitons, Fourier analysis.
 Laplace equation: fundamental solution, Green's function, potential theory.
 Heat equation: maximum principle, regularity.  Second order elliptic equations (if time permits):
 Sobolev spaces, weak solution, and regularity.
Homework Assignments
 Homework assignments will be assigned and collected each week. The tentative due date is on Tuesday 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: 11/18, Homework 9 is available. It is due on Tuesday 11/28 in class.
Homework #  1  2  3  4  5  6  7  8  9 
Due  9/5  9/19  10/3  10/17  10/24  10/31  11/7  11/14  11/28 
Download  [H1]  [H2]  [H3]  [H4]  [H5]  [H6]  [H7]  [H8]  [H9] 
Exams
 A sample final exam is available HERE. (Update on problem 7c: M=maxf). The solution can be found HERE.
 The final exam is now available. You can download the exam HERE. For MATH423/CAAM423 student, the exam will take 200 minutes. For MATH513/CAAM523 students, the exam will take 4 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 200 consecutive minutes (or 4 consecutive hours) on the exam. Please submit your exam to my office on Wednesday December 13th, between 10am12pm, 2pm4pm.
 The solution of the final exam is available HERE.
 Exams are under the honor code. Be sure and hand in all the work you do on each problem. Good luck!
Grades
 Your grade are distributed as below:

Homeworks » 60% 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. Or you can leave a comment below.