An introduction to smooth manifolds F1VG1JAWDW

URI	`m2://res/F1VG1JAWDW`
Kind	course
Creators	Harish Seshadri (instructor)
Date	2020-01-20
Scope	in
Ids	course 04dese585:111108134

Expressions

e1: edition

Language	en
Date	2020-01-20

m1: page, IISc Bangalore (record). nptel 111108134
m2: page, 2020-01-20 (record). nptel 111108134

Contents

part 1: Week 1 Review of linear algebra and multivariable calculus
session 1: Basic linear algebra
session 2: Multivariable calculus - 1
session 3: Multivariable calculus - 2
session 4: The derivative map
session 5: Inverse Function Theorem
session 6: Constant Rank Theorem
session 7: Smooth functions with compact support
part 2: Week 2 Smooth manifolds and Smooth maps
session 8: Smooth manifold
session 9: Examples of smooth manifolds
session 10: Higher dimensional spheres as smooth manifolds
session 11: Smooth maps
session 12: Examples of smooth maps
part 3: Week 3 Tangent spaces
session 13: Tangent spaces - I
session 14: Tangent spaces - 2
session 15: Derivatives of smooth maps
session 16: Chain rule on manifolds
part 4: Week 4 Tangent Spaces (Contd.)
session 17: Dimension of tangent space - 1
session 18: Dimension of tangent space - 2
session 19: Derivative of inclusion map
session 20: Basis of tangent space
part 5: Week 5 Submanifolds
session 21: Inverse Function Theorem for manifolds
session 22: Submanifolds
session 23: Tangent space of a submanifold
session 24: Regular Value Theorem
session 25: Special linear group as a submanifold of the set of all square matrices
session 26: Hypersurfaces
session 27: Tangent spaces to level sets
part 6: Week 6 Vector Fields and Lie Groups
session 28: Vector fields - 1
session 29: Vector fields - 2
session 30: Vector fields - 3
session 31: Lie groups - 1
session 32: Lie groups - 2
part 7: Week 7 Flows of vector fields
session 33: Integral curve and flows - 1
session 34: Integral curve and flows - 2
session 35: Integral curve and flows - 3
session 36: Complete vector fields
session 37: Vector fields and smooth maps
part 8: Week 8 Lie Brackets and Lie Algebras
session 38: Lie Brackets - 1
session 39: Lie brackets - 2
session 40: Lie brackets - 3
session 41: Lie algebras of matrix groups - 1
session 42: Lie algebras of matrix groups - 2
session 43: Exponential map
session 44: Frobenius theorems
part 9: Week 9 Differential forms and Symmetric tensors.
session 45: Tensors and differential forms
session 46: Tensors and differential forms - 2
session 47: Pull-back form
session 48: Symmetric Tensors
part 10: Week 10 Alternating tensors
session 49: Alternating Tensors - 1
session 50: Alternating Tensors - 2
session 51: Alternating Tensors -3
session 52: Alternating Tensors - 4
session 53: Alternating Tensors - 5
session 54: Alternating Tensors - 6
session 55: Alternating Tensors - 7
session 56: Alternating Tensors - 8
session 57: Alternating Tensors - 9
part 11: Week 11 Differential Forms
session 58: Differential forms on manifolds-1
session 59: Differential forms on manifolds-2
session 60: The Exterior derivative - 1
session 61: The Exterior derivative - 2
session 62: The Exterior derivative - 3
session 63: The Exterior derivative - 4
session 64: The Exterior derivative - 5
part 12: Week 12 Orientation on manifolds.
session 65: Special classes of forms
session 66: Orientation on manifolds-1
session 67: Orientation on manifolds-2
session 68: Orientation on manifolds-3

Catalogue records

nptel: 111108134 (manifestation)
nptel_video: 111108134 (manifestation)