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Course11110409522 lectures

Curves and Surfaces

Prof. Sudipta Dutta · IIT Kanpur

Start with lecture 1 At NPTEL

Lectures

Module 1 Curves in R2 and R3

  1. Level curves and locus, definition of parametric curves, tangent, arc length, arc length parametrisation Video
  2. How much a curve is ‘curved’, signed unit normal and signed curvature, rigid motions, constant curvature Video
  3. Curves in R^3, principal normal and binormal, torsion Video
  4. Frenet-Serret formula Video
  5. Simple closed curve and isoperimetric inequality Video

Module II Surfaces-1: Smooth surfaces

  1. Surfaces and parametric surfaces, examples, regular surface and non-example of regular surface, transition maps. Video
  2. Transition maps of smooth surfaces, smooth function between surfaces, diffeomorphism Video
  3. Reparameterization Video
  4. Tangent, Normal Video
  5. Orientable surfaces Video

Module III Surfaces-2: First Fundamental Form

  1. Examples of Surfaces Video
  2. First Fundamental Form Video
  3. Conformal Mapping Video
  4. Curvature of Surfaces Video
  5. Euler's Theorem Video

Module IV Surfaces- 3: Curvature and Geodesics

  1. Regular Surfaces locally as Quadratic Surfaces Video
  2. Geodesics Video
  3. Existence of Geodesics, Geodesics on Surfaces of revolution Video
  4. Geodesics on surfaces of revolution; Clairaut's Theorem Video
  5. Pseudosphere Video
  6. Classification of Quadratic Surface Video
  7. Surface Area and Equiareal Map Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Mathematics
Teacher
Prof. Sudipta Dutta
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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