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課程名稱 |
幾何學導論
Introduction to Geometry |
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開課學期 |
110-1 |
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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 |
MATH5356 |
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課程識別碼 |
221 U6580 |
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班次 |
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學分 |
4.0 |
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全/半年 |
半年 |
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必/選修 |
必帶 |
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上課時間 |
星期三3,4(10:20~12:10)星期五3,4(10:20~12:10) |
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上課地點 |
普503普503 |
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備註 |
此課程研究生選修不算學分。
限學士班學生
總人數上限：70人
外系人數限制：30人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1101MATH5356_IoG |
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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 |
We are going to apply basic calculus and linear algebra concepts to study the surfaces inside 3 dimensional space. This gives fruitful and essential results which form the basis of modern differential geometry, which, in turns, provide the framework of general relativity and quantum field theory.
The course would concentrate on the local concept of "curvature", global concept of "surface", and the interplay between them. We shall conduct a course from the local behavior of a surface to the global property of it. |
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課程目標 |
1. Curvature of Curves as a preliminary case study.
2. Curvature of Surfaces.
3. Intrinsic Curvature.
4. Curvature and Global Property of Surfaces |
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課程要求 |
Calculus; Linear Algebra; Inverse (also Implicit) function theorem; Experience in solving ODE. |
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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 |
M.P. do Carmo, Differential geometry of curves and surfaces, 1976.
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參考書目 |
B. O'Neill, Elementary Differential Geometry, 2006
J. Oprea, Differential Geometry and its Applications, 2nd edition, 2007. |
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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. |
習題 |
40% |
含習題課 |
2. |
期中考 |
30% |
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3. |
期末考 |
30% |
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