Differentiable Functions on Surface 第七週 The Tangent Plane

Text: Differential Geometry of Curves and Surfaces, revised & updated second edition, by Manfredo P. Do Carmo, Dover Publications, Inc.

Prerequisite: Linear Algebra and Advanced Calculus Course Website: http://www.math.ncku.edu.tw/~rchen/

第一週 2/23, 2/25

1-3 Regular Curves; Arc Length

Chapter 1 Curves

1-4 The Vector Product in R³

1-5 The Local Theory of Curves Parametrized by Arc Length 第二週

3/2, 3/4 1-6 The Local Canonical Form 第三週

3/9, 3/11 1-7 Global Properties of Plane Curves

Chapter 2 Regular Surfaces

第四週

3/16, 3/18 2-2 Regular Surfaces; Inverse Images of Regular Values 第五週

3/23, 3/25 2-2 Regular Surfaces; Inverse Images of Regular Values 第六週

3/30, 4/1 2-3 Change of Parameters; Differentiable Functions on Surface 第七週

4/6, 4/8 2-4 The Tangent Plane; The Differential of a Map 第八週

4/13, 4/15 2-5 The First Fundamental Form; Area 第九週

4/20, 4/22

Midterm Exam

(考試時間及範圍將依據實際課程之進度調整) Chapter 3

The Geometry

of the Gauss Map

第十週

4/27, 4/29 3-2 The Definition of the Gauss Map and Its Fundamental Properties

第十一週

5/4, 5/6 3-2 The Definition of the Gauss Map and Its Fundamental Properties

第十二週

5/11, 5/13 3-3 The Gauss Map in Local Coordinates

Chapter 4 The Intrinsic Geometry of Surfaces

第十三週

5/18, 5/20 4-2 Isometries; Conformal Maps 第十四週

5/25, 5/27 4-3 The Gauss Theorem and the Equations of Compatibility 第十五週

6/1, 6/3 4-4 Parallel Transport; Geodesics 第十六週

6/8, 6/10 4-5 The Gauss-Bonnet Theorem and Its Applications 第十七週

6/15, 6/17 4-5 The Gauss-Bonnet Theorem and Its Applications 第十八週

6/22, 6/24

Final Exam

(考試時間及範圍將依據實際課程之進度調整) Grading

期中考 40%

作業及平時表現 20%

期末考 40%

Course Lecture Hours : Tuesday 13:10-15:00; Thursday 14:10-15:00 in 數學系館 3174 Contact with Teacher

Email: rchen@mail.ncku.edu.tw Phone: 06-2757575 轉 65157 Office: 數學系 405

Contact with Tutors

應用數學研究所博士班：蔡誌軒 Office: 數學系 415

Email: L18071023@mail.ncku.edu.tw