MATH: P-11 Differential Geometry(e-PGP) (English)

   Friday, January 20, 2023   

Starting a new Lecture Notes Series on MATH: P-11 Differential Geometry(e-PGP)

 

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MATH: P-11 Differential Geometry(e-PGP)
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Lecture Description of this above Topic:

Lecture 1: Introduction of tensors: contravariant and covariant vectors (MAT)

Lecture 2: Algebra of tensors: algebraic operations on tensors (MAT)

Lecture 3: Introduction of tensors: higher order tensors (MAT)

Lecture 4: Algebra of tensors: symmetricness of tensors and quotient law (MAT)

Lecture 5: Riemannian space: fundamental metric tensor (MAT)

Lecture 6: Riemannian space: applications of fundamental metric tensors (MAT)

Lecture 7: Derivatives of tensors: christoffel symbols (MAT)

Lecture 8: Derivatives of tensors: covariant differentiation (MAT)

Lecture 9: Geometry of space curve: intrinsic derivative and curvilinear coordinate system in space (MAT)

Lecture 10: Geometry of space curve: serret-frenet formulii for space curve (MAT)

Lecture 11: Geometry of space curve: some particular type of space curves (MAT)

Lecture 12: Geometry of space curve: fundamental theorem for space curve (MAT)

Lecture 13: Surface: parametric representation of surfaces and first fundamental form (MAT)

Lecture 14: Surface: geodesic on a surface (MAT)

Lecture 15: Curvature on surface: parallel vector field and gaussian curvature (MAT)

Lecture 16: Curvature on surface: intrinsic geometry of curves on surface-2 (MAT)

Lecture 17: Surface embedded in space: second fundamental form and its applications (MAT)

Lecture 18: Surface embedded in space: gauss and weingarten formulas and third fundamental form (MAT)

Lecture 19: Surface embedded in space: gauss and Codazzi- Mainardi equations (MAT)

Lecture 20: Chap 9 Mod 2

Lecture 21: Chap 9 Mod 3

Lecture 22: Chap 9 Mod 4

Lecture 23: Chap 9 Mod 5

Lecture 24: Chap 9 Mod 6

Lecture 25: Chap 9 Mod 8

Lecture 26: Chap 9 Mod 9

Lecture 27: Chap 10 Mod 1

Lecture 28: Chap 10 Mod 2

Lecture 29: Chap 9 mod 7

Lecture 30: Chap 10 Mod 3

Lecture 31: Chap 10 Mod 4

Lecture 32: Chap 10 Mod 5

Lecture 33: Chap 10 Mod 6

Lecture 34: Chap 10 Mod 7