Class meets:MTH2, 10:20--11:40am in Hill-425.
Instructor: Dr. Zheng-Chao Han
Office Hours: M1-2pm, T11:00-noon. Hill 230.
Email: zchan at math dot rutgers dot edu (I prefer to answer math questions in person during office hours, not through emails; I try to process my emails once per day ).

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Course Description: This course will be a continuation of the PDE course, 517, offered in the fall semester. We will take a similar approach, i.e., we will emphasize the methods than the most general forms of the results. One main theme will be how to extend the results and methods for dealing with constant coefficients prototype equations to related variable coefficients and nonlinear equations. We will continue to use the text being used in 517, ``Partial Differential Equations" by Lawrence C. Evans. I am planning to focus my discussion around chapters 5--8, perhaps supplementing with some material not contained in the text. Students' input may affect my emphasis and order of presentation. Students should be prepared to do some reading and working of certain sections on their own.

• Graded homework: 50%.
• Midterm and Final Exam: 25% each.

Course Material: In addition to our main text "Partial Differential Equations" by Lawrence C. Evans, published by AMS, 2002, I will also suggest other references whenever I find them useful. The course page of Professor Safanov of the University of Minnesota provides another perspective on a graduate PDE course and many additional problems for students to try on. I have also requested to put some additional books on reserve in the math library, including:

• Emmanuele Dibenedetto, Partial Differential Equations, Springer Verlag; (April 1995), ISBN: 0817637087.
• D. Gilbarg and N Trudinger, Elliptic Partial Differential Equations of Second Order, Springer 2001, ISBN-10: 3540411607.
• F. John, Partial Differential Equations, 4th ed., Springer-Verlag, 1982, ISBN-10: 0387906096.
• N. V. Krylov, Lectures on Elliptic and Parabolic Equations in Holder Space, American Mathematical Society, 1996, ISBN: 0-8218-0569-X.
• Robert McOwen, Partial Differential Equations: Methods and Applications, Second Edition, 2003, ISBN 0130093351.
• Michael Renardy and Robert C. Rogers, An Introduction to Partial Differential Equations, Springer; 2 edition (January 8, 2004), ISBN: 0387004440.

Some Course Notes/Outlines/Assignments:

• Here are some introductory remarks on a 517 PDE course from an earlier semester. They may still be useful for setting our perspective in 518.
• Here are some openning remarks about our course and the first assignment, due February 7.
• Here is the second assignment, due February 21.
• Here is the midterm, due March 27.
• Here is the third assignment, due April 17.