Learn · Geometry of Curves and Surfaces
Lecture 24 of 45Week 7
Lecture 24 : Tangent Plane and Tangent Vectors
Prof. Abhijit Pal · IIT Kanpur
Credits and licence
- From
- Geometry of Curves and Surfaces, IIT Kanpur (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- Lecture 1 : Parametrized Curves and Differentiable Curves
- Lecture 2 : Length of a Curve
- Lecture 3 : Regular Curve, Arc-length, Re-parametrization of a Curve
- Lecture 4 : Unit Speed Re-parametrization, Curvature of a Curve
- Lecture 5 : Curvature of a regular curve & Curvature formulas
- Lecture 6 : Level curves, Implicit function theorem
- Lecture 7 : Orientation of a curve, Signed curvature, Tangent & Normal vectors
- Lecture 8 : Turning Angle
- Lecture 9 : Curve determined by curvature, Total Curvature
- Lecture 10 : Hopf's Rotation Index Theorem
- Lecture 11 : Four Vertex Theorem
- Lecture 12 : Isoperimetric Inequality
- Lecture 13 : Space Curves & Principal Vectors
- Lecture 14 : Frenet-Serret Equations
- Lecture 15 : Curve determined by curvature and torsion
- Lecture 16 :Several variable calculus
- Lecture 17 : Regular surfaces in real three dimensional space
- Lecture 18 : Examples of regular surfaces
- Lecture 19 : Regular Value, Critical Value of a differentiable map
- Lecture 20 : Regular surface locally graph of a differentiable function
- Lecture 21 : Change of parametrizations in regular surfaces
- Lecture 22 : Differentiable function on surfaces
- Lecture 23 : Surface of Revolution, Torus, Higher genus surfaces
- Lecture 24 : Tangent Plane and Tangent Vectors
- Lecture 25 : Examples of Tangent Planes
- Lecture 26 : Differential Map between Tangent Spaces
- Lecture 27 : Orientation of Surfaces and Normal Vector Field
- Lecture 28 : First Fundamental Form on Surfaces
- Lecture 29 : Change of Parametrization in First Fundamental Form and Area
- Lecture 30 : Area of Some Surfaces and Gradient on Surfaces
- Lecture 31 : Isometries, local isometries, conformal maps
- Lecture 32 : Gauss Map and its Fundamental Properties
- Lecture 33 : Self Adjoint Operator
- Lecture 34 : Second Fundamental Form and normal Curvature
- Lecture 35 : Examples for second fundamental form
- Lecture 36 : Principal curvatures and Principal Directions
- Lecture 37 : Examples for principal curvatures and principal directions
- Lecture 38 : Gaussian Curvature and Mean Curvature
- Lecture 39 : Christoffel Symbols and The Gauss's Remarkable Theorem
- Lecture 40 : Invariance of Gaussian Curvature and Examples of Christoffel Symbols
- Lecture 41 : Vector Field and Covariant Derivative
- Lecture 42 : Vector Field along a curve, parallel vector field and geodesics
- Lecture 43 : Geodesics and its equations
- Lecture 44 : Simplicial Complex, Triangulation and Euler Characteristics
- Lecture 45 : Gauss Bonnet Theorem