# InfoCoBuild

## Curves and Surfaces

Curves and Surfaces. Instructor: Prof. Sudipta Dutta, Department of Mathematics and Statistics, IIT Kanpur. This course is intended for undergraduate students in Indian Universities with a background in Differential Calculus of Several Variables. Such a course was broadcasted in March 2016 under MOOC (NPTEL- IV) and that background will be enough to follow that course. It is kind of a threshold level compilation of lectures to Differential Geometry on which there is hardly any standard course at under graduate level in most universities. (from nptel.ac.in)

 Level Curves and Locus, Definition of Parametric Curves

 Module I. Curves in R2 and R3 Lecture 01 - Level Curves and Locus, Definition of Parametric Curves, Tangent, Arc Length, Arc Length Parameterization Lecture 02 - How Much a Curve Is Curved, Signed Unit Normal and Signed Curvature, Rigid Motions, Constant Curvature Lecture 03 - Curves in R3, Principal Normal and Binormal, Torsion Lecture 04 - Frenet-Serret Formula Lecture 05 - Simple Closed Curve and Isoperimetric Inequality Module II. Surfaces 1: Smooth Surfaces Lecture 06 - Surfaces and Parametric Surfaces, Regular Surface and Non-example of Regular Surface, Transition Maps Lecture 07 - Transition Maps Of Smooth Surfaces, Smooth Function Between Surfaces, Diffeomorphism Lecture 08 - Reparameterization Lecture 09 - Tangent, Normal Lecture 10 - Orientable Surfaces, An Example of Non-orientable Surface Module III. Surfaces 2: First Fundamental Form Lecture 11 - Examples of Surfaces: Ruling Surfaces, Surfaces of Revolution Lecture 12 - First Fundamental Form Lecture 13 - Stereographic Projection, Conformal Mapping Lecture 14 - Curvature of Surfaces Lecture 15 - Euler's Theorem Module IV. Surface 3: Curvature and Geodesics Lecture 16 - Regular Surfaces Locally as Quadratic Surfaces, Gaussian Curvature, Mean Curvature Lecture 17 - Geodesics, Geodesic Equations Lecture 18 - Existence of Geodesics, Geodesics on Surfaces of Revolution Lecture 19 - Geodesics on Surfaces of Revolution, Clairaut's Theorem Lecture 20 - Pseudosphere, Geodesics on Pseudosphere Lecture 21 - Classification of Quadratic Surface Lecture 22 - Surface Area and Equiareal Map

 References Curves and Surfaces Instructor: Prof. Sudipta Dutta, Department of Mathematics and Statistics, IIT Kanpur. This course is intended for students with a background in Differential Calculus of Several Variables.