SYLLABUS for Partial differential equation on manifolds
TEXT:Partial differential equation on manifolds
INSTRUCTOR: C.J. Anna Sung
OFFICE: Math. Building 525 ; Tel: ext 62308; Email: cjsung@math.nthu.edu.tw
OFFICE HOURS:To be annouced.
LECTURES: Friday 11:10AM-12:30PM and 1:20PM-2:30PM
Contents:
The main goal of this course is to introduce the existence of solutions to partial differential equations over manifolds. We will study the general theory of elliptic differential operators over Riemannian manifolds and some connections with topology and differential geometry. This course will study function theory and spectral properties on Riemannian manifolds and complete noncompact smooth metric measure spaces. We will build a connection between geometry and PDE at the graduate level. Depending on student interests, more topics will be covered at the instructor's discretion.

***Please check your email account frequently so you do not miss responding to any time-sensitive requests from an instructor or other part of NTHU.***

References:
Jurgen Jost, Riemannian Geometry and Geometric Analysis, Springer 2011.
Peter Li, Geometric Analysis, Cambridge Univ. Press 2012.
E.B.Davies: Heat Kernels and spectral theory.
Peter Petersen, Riemannian Geometry, Springer 2006.
F. John: Partial Differential Equations. 4th Edition.
L. Evans: Partial Differential Equaitons.
Warner: Foundations of Differential Manifolds and Lie Groups.
Do Carmo: Riemannian Geometry.
S. Gallot, D. Hulin and J. Lafontaine, Riemannian Geometry, Universitext, Springer.

REMARKS:
(1) Evaluation: Homework and Oral presentation(or Exam)(to be scheduled)
There is homework that must be handed in. The homework will be due in class on the designated day. You can discuss the homework with others in the class, but you must write up your homework solution by yourself. Thus, you should understand the solution and be able to reproduce it yourself.
(2) No late home-works and make-up for Exam.
(3) You have to show your work to receive any credit.
(4) Any student missing an exam without providing a
legitimate excuse is given a grade of zero on that exam.
(5) Any student who wants to be excused from any of the
scheduled exams must discuss the situation with me at least
one week before the exam.
***'Turn off' the cellular phone in the class***

All the above information is subject to change, based on in-class announcement