A strong foundation on vector calculus (divergence theorem) and rigorous analysis at the level comparable to that in Baby Rudin.
This is the first half of the year-long introductory graduate course on PDE. PDE is an enormously vast field, and provides essential tools for students interested in analysis, applied analysis, geometry, and mathematical physics. For students entering this field, it is probably more important to learn the methods and techniques through studying many prototype equations ---to build up experience and intuition--- than to learn the most general theories. This first semester course will be more basic, emphasizing the study of constructions and properties of solutions to a variety of prototype problems using relatively elementary tools; but the approaches that we will take will motivate and naturally lead to more sophisticated generalizations in more advanced treatment.
Schedule of Sections:
Some information about the Fall 2017 semester's offering is posted at here.