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Course Archives Theoretical Statistics and Mathematics Unit |
Course: Curves and Surfaces
Instructor: Ramesh Sreekantan
Room: G24
Level: Undergraduate
Time: Currently offered
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Syllabus
Past Exams
Syllabus:
Curves in two and three dimensions, Curvature and torsion for space curves, Existence theorem for space curves, Serret-Frenet formula for space curves, Inverse and
implicit function theorems, Jacobian theorem, Surfaces in R3 as two dimensional
manifolds, Tangent space and derivative of maps between manifolds, First fundamental form, Orientation of a surface, Second fundamental form and the Gauss map,
Mean curvature and scalar curvature, Integration on surfaces, Stokes formula, GaussBonnet theorem.
Reference Texts:
(a) M.P. do Carmo: Differential Geometry of Curves and Surfaces.
(b) A. Pressley: Elementary Differential Geometry.
(c) J.Thorpe: Elementary Topics in Differential Geometry.
Evaluation:
| Mid-term | 30 marks |
Assignment | 20 marks |
Final Exam | 50 marks |
Total | 100 marks |
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Past Exams
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[ Semester Schedule ][ Statmath Unit ]
[Indian Statistical Institute] |