IST - Curves, Surfaces and Differential Forms (2024)

Speakers and Syllabus

  Detailed Syllabus:

Topic: Theory and Examples of Curves and Surfaces
Speaker: Dr. Taniya Srivastava, IIT Gandhinagar.
    • Curves in the Plane and in Space
    • How Much Does a Curve Curve?
    • Global Properties of Curves
    • Surfaces in Three Dimensions

Topic:Introduction to Differential Manifolds
 Speaker: Dr. Vivek Mallick, IISER, Pune.
    • The Volume of a Parallelopiped
    • Volume of a Parametrized-Manifold
    • Manifolds in
    • The Boundary of a Manifold
    • Integrating a Scalar Function over a Manifold

Topic: First and second fundamental forms, Gaussian, mean and principal curvatures of a surface
Speaker: Prof. Nitin Nitsure, Bhaskaracharya Pratishthana, Pune.
    • The First Fundamental Form
    • Curvature of Surfaces
    • Gaussian Curvature and the Gauss Map

Topic: Differential Forms and Vector Calculus
Speaker: Prof. V. M. Sholapurkar, Bhaskaracharya Pratishthana, Pune.
    • Multilinear Algebra
    • Tangent Vectors and Differential Forms
    • The Differential Operator
    • Application to Vector and Scalar Fields

Reference Books

    1. Elementary Differential Geometry, Andrew Pressley, Springer.
    2. Analysis on Manifolds, James R. Munkres, CRC Press. 

Course Associates:

1. Dr. Aman Jhinga (AJ)
2. Dr. Vinod Ghale (VG)

Time Table

First week: 
2^nd Dec 2024 to 14^th Dec 2024

Second week:
9^th Dec 2024 to 14^th Dec 2024