General Course Information

Prerequisites	Advanced calculus and linear algebra. Note: Math 231A is not part of prerequisites.
Textbook	L. C. Evans, Partial Differential Equations, 2nd ed., Amer. Math. Soc., 2010.
Lectures	10:00 - 10:50, Mondays, Wednesdays, and Fridays, AP&M 7421.
Instructor	Bo Li Office: AP&M 5723. Office phone: (858) 534-6932. E-mail: bli@math.ucsd.edu. Office hours: 11:00 am - 11:30 am Mondays and Fridays, or by appointment.
Class web page	http://www.math.ucsd.edu/~bli/teaching/math231Bw15/
Homework	Homework will be assigned, collected, and partially graded.
Exams	There will be no exams.
Grading	The final course grade will be determined mainly based on the class participation and homework.

Topics (Referring to the textbook)

• Chapter 5: Sobolev Spaces
• Chapter 6: Second-Order Elliptic Equations
• Chapter 7: Linear Evolution Equations
• Chapter 8: The Calculus of Variations

Homework Assignment

• Exercises on Sobolev Spaces (Part 1) (PDF)
• Exercises on Sobolev Spaces (Part 2) (PDF)
• Exercises on Linear Second-Order Elliptic Problems (Part 1) (PDF)
• Exercises on Linear Second-Order Elliptic Problems (Part 2) (PDF)
• Exercises on Linear Second-Order Parabolic Problems (PDF)
• Exercises on the Calculus of Variations (PDF)

Some References

• R. Adams and J. J. F. Fournier, Sobolev Spaces, 2nd ed., Academic Press, 2003.
• R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. II, Wiley, 1989.
• A. Friedman, Partial Differential Equations of Parabolic Type, Dover, 2008.
• D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer-Verlag, 1998.
• F. John, Partial Differential Equations, 4th ed., Springer-Verlag, 1982.
• J. Jost, Partial Differential Equations, Springer-Verlag, 2002.
• R. C. McOwen, Partial Differential Equations, Methods and Applications, 2nd ed., Prentice Hall, 2003.
• J. Smoller, Shock Waves and Reaction-Diffusion Equations, 2nd ed., Springer-Verlag, 1994.