Lectures
Monday 11-11:50 AM, Tuesday 11-11:50 AM, Thursday 10:00-10:50 AM
Tutorials
On alternate Thursdays
Weekly homework problems will be uploaded here.
Assignments
Assignment I (To be submitted by 18th February 2025)
Office Hours
Tuesdays 5:00-6:00 PM
TA details:
Dr Sahil Joshi
Roo No 459 (Main Building)
Office hours: Tuesday 5:00-6:00 PM
Course Contents
Curves: Parametrized curves, regular curves, arc length, local theory of curves, global properties of plane curves.
Surfaces: Review of the inverse and implicit function theorems, regular surfaces, smooth functions on surfaces, tangent plane, derivative of a map, the first fundamental form, area, and orientation of surfaces.
Curvature: The Gauss map, the second fundamental form, normal curvature, principal curvature, Gaussian curvature, mean curvature, Gauss theorema egregium.
Geodesics: Parallel transport, geodesics, geodesic curvature, the Gauss-Bonnet theorem and its applications.
References
1. Alfred Gray, Elsa Abbena, Simon Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica
2. M. P. do Carmo, Differential Geometry of Curves and Surfaces
3. A. Pressley, Elementary Differential Geometry
4. Gregory V. Bard, Sage for undergraduate
Evaluation
End-sem 35%
Mid-sem 35%
Quizzes 20%.
Others: 10%