幾何分析導論
Introduction to Geometric Analysis
| 節 | 週五 |
|---|---|
4 11:10–12:00 | 幾何分析導論 4 節連堂 |
N 12:20–13:10 | |
5 13:20–14:10 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
課程說明: 帶領學生研讀幾何分析的重要問題與其應用。 訓練學生思維能力. The main objective of this course is to introduce solutions to partial differential equations on manifolds. We will explore the general theory of elliptic differential operators in the context of Riemannian manifolds, along with their connections to topology and differential geometry. Additionally, we will study function-theoretic and spectral properties on Riemannian manifolds and complete non-compact smooth metric measure spaces. Our goal is to establish a connection between geometry and partial differential equations. Course keywords: Green's function, spectrum theory, Riemannian manfiolds
□ 具備發現問題、分析問題並解決問題的能力 Having ability to discover, analyze and solve problems. □ 培養運用數學作為發展其他學科的能力 Developing ability to interact mathematics with other subjects. □ 培養數學邏輯思考的能力 Developing ability of using mathematical logic to think. □ 學習進階數學的能力 Ability to learn advanced mathematical knowledge.
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L. Evans: Partial Differential Equations Jost: Riemannian Geometry and Geometric Analysis. Davies and Safrov:Spectral Theory and Geometry. Warner: Foundations of Differential Manifolds and Lie Groups. Do Carmo: Riemannian Geometry. P. Li: Lecture note on Geometric Analysis R. Courant and D. Hilbert: Methods of Mathematical Physics. Vol. I and II. E.B.Davies: Heat Kernels and spectral theory
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