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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.
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Description
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)
Course content
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- Lecture 01 – Level Curves and Locus, Definition of Parametric Curves, Tangent, Arc Length Unlimited
- Lecture 02 – How Much a Curve Is Curved, Signed Unit Normal and Signed Curvature, Rigid Motions Unlimited
- Lecture 03 – Curves in R3, Principal Normal and Binormal, Torsion Unlimited
- Lecture 04 – Frenet-Serret Formula Unlimited
- Lecture 05 – Simple Closed Curve and Isoperimetric Inequality Unlimited
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- Lecture 06 – Surfaces and Parametric Surfaces, Regular Surface and Non-example of Regular Surface Unlimited
- Lecture 07 – Transition Maps Of Smooth Surfaces, Smooth Function Between Surfaces Unlimited
- Lecture 08 – Reparameterization Unlimited
- Lecture 09 – Tangent, Normal Unlimited
- Lecture 10 – Orientable Surfaces, An Example of Non-orientable Surface Unlimited
- Lecture 11 – Examples of Surfaces: Ruling Surfaces, Surfaces of Revolution Unlimited
- Lecture 12 – First Fundamental Form Unlimited
- Lecture 13 – Stereographic Projection, Conformal Mapping Unlimited
- Lecture 14 – Curvature of Surfaces Unlimited
- Lecture 15 – Euler’s Theorem Unlimited
Instructor
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