MATH 4030 微分幾何學 Differential Geometry

 

Course Code	MATH 4030 MATH4030			科目名稱		Differential Geometry 微分幾何學
教員	Professor LI Man Chun [官方介紹及學術著作]			學　　分		3學分
課程性質				同科其他選擇
Workload	l   非PAPER類HOMEWORK l   MIDTERM l   FINAL EXAM								好重
									重
									平均	1
									輕
									極輕
評價教學內容	#1  教學內容非常有趣
評價教員教學	#1  佢講野非常之清楚有條理，上堂講比較多嗰個concept背後嘅intuition. 佢寫嘅白板字都好靚
CUSIS科目資料	Description： This course covers basic theory on curves, and surfaces in the Euclidean three space. Topics include: regular curves, Frenet formulas, local theory of curves, global properties of curves such as isoperimetric inequality, regular surfaces, 1st and 2nd fundamental form, Gaussian curvature and mean curvature, Gauss map, special surfaces such as ruled surfaces, surfaces of revolution, minimal surfaces, intrinsic geometry: geodesic, and Gauss-Bonnet Theorem. Students taking this course are expected to have knowledge in advanced calculus, linear algebra, and elementary differential equations.   Learning Outcome： - Students learn ways to describe curves and surfaces in space, by equations and parametrizations.   - Students learn the differential approach to regular geometric objects, using moving frames and searching for complete local invariants. In particular, they learn the Frenet frame, curvature and torsion of regular space curves.   - Students use integration techniques to study some global theorems on plane curves and methods of ordinary differential equations to obtain curves with prescribed curvature and torsion.   - Students learn the formulation of regular surfaces in 3 dimensions, their orientability, differentiable structure and metric structure.   - Students learn the Gauss map and its many important consequences.   - Students learn computations of various curvatures through examples and special surfaces.
其他資料	2025Sem1：學位 40|註冊 30|剩餘 10
同學推薦	高度推薦	1	推薦			有保留		極有保留