LECTURES: Tuesday and Thursday   10:10AM-11:25AM
<br>
<br>課程說明(Course Desc<x>ription)：
<br>
<br>帶領學生研讀幾何分析的重要問題與其應用。 
<br>訓練學生思維能力.
<br>
<br>The main goal of this course is to introduce the existence of solutions to partial 
<br>differential equations over manifolds. We will study the general theory of 
<br>elliptic differential operators over Riemannian manifolds and some connections 
<br>with topology and differential geometry. In this course we will study functions 
<br>theoretic and spectral properties on Riemannian Manifolds and complete noncompact 
<br>smooth metric measure spaces. We will build a connection between geometry and PDE 
<br>on graduate level.  
<br>
<br>
<br>References:
<br>
<br>L. Evans: Partial Differential Equations
<br>Jost: Riemannian Geometry and Geometric Analysis.
<br>Davies and Safrov:Spectral Theory and Geometry. 
<br>Warner: Foundations of Differential Manifolds and Lie Groups. 
<br>Do Carmo: Riemannian Geometry. 
<br>P. Li: Lecture note on Geometric Analysis
<br>R. Courant and D. Hilbert: Methods of Mathematical Physics. Vol. I and II. 
<br>E.B.Davies: Heat Kernels and spectral theory 
<br>
<br>