國立清華大學 數學系 宋瓊珠
關鍵字： Geometry II The Sign of Gauss Curvature Geometric Interpretation of Gauss Curvature Vector Field Ruled Surface The Intrinsic Geometry of Surfaces: Fundamental Theorem of Surface Clairaut’s Theorem Hyperbolic Models
This is an introductory course on the theory of curves and surfaces in the three dimensional Euclidean space. After developing the theory of curves, we will study the geometry of a surface from both intrinsic and extrinsic point of view. Topics include first and second fundamental forms, various notions of curvature, and the famous Gauss-Bonnet theorem.
|Successful completion of Linear Algebra and Advanced Calculus|
|♠||Differential geometry of curves and surfaces, by Manfredo P. Do|
|Carmo. Prentice Hall.|
|♠||Elementary Differential Geometry, 2nd edition, A. Pressley, Springer, 2010.|
|♠||Elementary Differential Geometry, 2nd Edition, by Barrett O'Nell.|