Learn · An Introduction to Smooth Manifolds
Lecture 37 of 68Week 7 Flows of vector fields
Vector fields and smooth maps
Prof. Harish Seshadri · IISc Bangalore
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- From
- An Introduction to Smooth Manifolds, IISc Bangalore (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.
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- Tweens profiles and older. How courses are placed
All the lectures
- Basic linear algebra
- Multivariable calculus - 1
- Multivariable calculus - 2
- The derivative map
- Inverse Function Theorem
- Constant Rank Theorem
- Smooth functions with compact support
- Smooth manifold
- Examples of smooth manifolds
- Higher dimensional spheres as smooth manifolds
- Smooth maps
- Examples of smooth maps
- Tangent spaces - I
- Tangent spaces - 2
- Derivatives of smooth maps
- Chain rule on manifolds
- Dimension of tangent space - 1
- Dimension of tangent space - 2
- Derivative of inclusion map
- Basis of tangent space
- Inverse Function Theorem for manifolds
- Submanifolds
- Tangent space of a submanifold
- Regular Value Theorem
- Special linear group as a submanifold of the set of all square matrices
- Hypersurfaces
- Tangent spaces to level sets
- Vector fields - 1
- Vector fields - 2
- Vector fields - 3
- Lie groups - 1
- Lie groups - 2
- Integral curve and flows - 1
- Integral curve and flows - 2
- Integral curve and flows - 3
- Complete vector fields
- Vector fields and smooth maps
- Lie Brackets - 1
- Lie brackets - 2
- Lie brackets - 3
- Lie algebras of matrix groups - 1
- Lie algebras of matrix groups - 2
- Exponential map
- Frobenius theorems
- Tensors and differential forms
- Tensors and differential forms - 2
- Pull-back form
- Symmetric Tensors
- Alternating Tensors - 1
- Alternating Tensors - 2
- Alternating Tensors -3
- Alternating Tensors - 4
- Alternating Tensors - 5
- Alternating Tensors - 6
- Alternating Tensors - 7
- Alternating Tensors - 8
- Alternating Tensors - 9
- Differential forms on manifolds-1
- Differential forms on manifolds-2
- The Exterior derivative - 1
- The Exterior derivative - 2
- The Exterior derivative - 3
- The Exterior derivative - 4
- The Exterior derivative - 5
- Special classes of forms
- Orientation on manifolds-1
- Orientation on manifolds-2
- Orientation on manifolds-3