# 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)

 Lecture 20 - Pseudosphere, Geodesics on Pseudosphere

Go to the Course Home or watch other lectures:

 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