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課程名稱 |
流形導論
Introduction to Manifolds |
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開課學期 |
110-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
翁秉仁 |
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課號 |
MATH5418 |
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課程識別碼 |
221 U5130 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期二A,B(18:25~20:10)星期四8(15:30~16:20) |
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上課地點 |
天數302天數302 |
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備註 |
限學士班三年級以上
總人數上限：34人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1102MATH5418_mfd |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
1. Manifold in R^n
2. Differential form, calculus on manifold, and Stokes’Theorem
3. Application: Introduction to moving frame method on surface
4. Application:De Rham Cohomology.
5. Sard Theorem
6. Degree theory
7. Vector fields, Euler number and Poincare-Hopf Theorem
8. Pontryagin construction, framed Corbordism and Hopf Theorem
9. General Manifolds |
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課程目標 |
The course is the continuation for the Introduction of Geometry course in thefirst semester. We introduce the concept of smooth manifold and some related topics to pave the way for the courses like Riemannian Geometry or Differential Topology. |
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課程要求 |
Introduction to Geometry |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
Spivak, “Calculus on Manifolds”
Milnor, “Topology from Differential Viewpoint”
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參考書目 |
O’Neill “Elementary Differeantial Geometry”
Spivak, “A Comprehensive Introduction to Differential Geometry” Vol 1 chap1-chap6 |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
期中考 |
50% |
筆試 |
2. |
期末考 |
50% |
筆試或口試 |
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