課程說明(Course Desc<x>ription)：
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<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.
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<br>This course will study functions
<br>theoretic and spectral properties on Riemannian Manifolds.  The main goal is to 
<br>introduce partial differential equations on Riemannian manifolds.
<br>We will build a connection between geometry and PDE
<br>on the graduate level.
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<br>References:
<br>E.B.Davies: Heat Kernels and spectral theory 
<br>L. Evans: Partial Differential Equaitons
<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. 
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<br>Exam 50% + Homework 50%