Geometry of Curves and Surfaces VWXS4D4KTM

URI	`m2://res/VWXS4D4KTM`
Kind	course
Creators	Abhijit Pal (instructor)
Date	2025-07-24
Scope	in
Ids	course 05pjsgx75:111104765

Expressions

e1: edition

Language	en
Date	2025-07-24

m1: page, IIT Kanpur (record). nptel 111104765
m2: page, 2025-07-24 (record). nptel 111104765

Contents

part 1: Week 1
session 1: Lecture 1 : Parametrized Curves and Differentiable Curves
session 2: Lecture 2 : Length of a Curve
session 3: Lecture 3 : Regular Curve, Arc-length, Re-parametrization of a Curve
session 4: Lecture 4 : Unit Speed Re-parametrization, Curvature of a Curve
part 2: Week 2
session 5: Lecture 5 : Curvature of a regular curve & Curvature formulas
session 6: Lecture 6 : Level curves, Implicit function theorem
session 7: Lecture 7 : Orientation of a curve, Signed curvature, Tangent & Normal vectors
session 8: Lecture 8 : Turning Angle
part 3: Week 3
session 9: Lecture 9 : Curve determined by curvature, Total Curvature
session 10: Lecture 10 : Hopf's Rotation Index Theorem
session 11: Lecture 11 : Four Vertex Theorem
session 12: Lecture 12 : Isoperimetric Inequality
part 4: Week 4
session 13: Lecture 13 : Space Curves & Principal Vectors
session 14: Lecture 14 : Frenet-Serret Equations
session 15: Lecture 15 : Curve determined by curvature and torsion
session 16: Lecture 16 :Several variable calculus
part 5: Week 5
session 17: Lecture 17 : Regular surfaces in real three dimensional space
session 18: Lecture 18 : Examples of regular surfaces
session 19: Lecture 19 : Regular Value, Critical Value of a differentiable map
session 20: Lecture 20 : Regular surface locally graph of a differentiable function
part 6: Week 6
session 21: Lecture 21 : Change of parametrizations in regular surfaces
session 22: Lecture 22 : Differentiable function on surfaces
session 23: Lecture 23 : Surface of Revolution, Torus, Higher genus surfaces
part 7: Week 7
session 24: Lecture 24 : Tangent Plane and Tangent Vectors
session 25: Lecture 25 : Examples of Tangent Planes
session 26: Lecture 26 : Differential Map between Tangent Spaces
session 27: Lecture 27 : Orientation of Surfaces and Normal Vector Field
part 8: Week 8
session 28: Lecture 28 : First Fundamental Form on Surfaces
session 29: Lecture 29 : Change of Parametrization in First Fundamental Form and Area
session 30: Lecture 30 : Area of Some Surfaces and Gradient on Surfaces
session 31: Lecture 31 : Isometries, local isometries, conformal maps
part 9: Week 9
session 32: Lecture 32 : Gauss Map and its Fundamental Properties
session 33: Lecture 33 : Self Adjoint Operator
session 34: Lecture 34 : Second Fundamental Form and normal Curvature
part 10: Week 10
session 35: Lecture 35 : Examples for second fundamental form
session 36: Lecture 36 : Principal curvatures and Principal Directions
session 37: Lecture 37 : Examples for principal curvatures and principal directions
part 11: Week 11
session 38: Lecture 38 : Gaussian Curvature and Mean Curvature
session 39: Lecture 39 : Christoffel Symbols and The Gauss's Remarkable Theorem
session 40: Lecture 40 : Invariance of Gaussian Curvature and Examples of Christoffel Symbols
session 41: Lecture 41 : Vector Field and Covariant Derivative
part 12: Week 12
session 42: Lecture 42 : Vector Field along a curve, parallel vector field and geodesics
session 43: Lecture 43 : Geodesics and its equations
session 44: Lecture 44 : Simplicial Complex, Triangulation and Euler Characteristics
session 45: Lecture 45 : Gauss Bonnet Theorem

Catalogue records

nptel: 111104765 (manifestation)
nptel_video: 111104765 (manifestation)