偏微分方程(一)

The purpose of this course is to introduce to our students the basic techniques of mordern partial differential equations. In this semester, we will first discuss the classical topics such as solutions to the Laplace equation and the heat equation in the Euclidean setting. By doing so, important techniques such as the maximum principle and the gradient type estimates will be introduced. Another important objective in this course is to introduce to our students the basic concept of weak derivatives of a function. Once the concept of weak (or distributional ) derivatives has been clarified, we will develop the essense of the theory of Sobolev space, which is the concerstone of the modern theory of PDE's.

A student taking this course should have a solid training in standard undergraduate analysis and linear algebra. In particular, a student should have a basic working knowledge of multi-varibale-Calculus, including the use of Stokes theorem.

Attendance 40% Homework 20% Final report (consisting of a written document and oral presentation ) 20% Take home final exam 20%