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noc20 ma01 lec13 Tangent spaces I
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Classroom Contents
An Introduction to Smooth Manifolds
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- 1 Intro An introduction to smooth manifolds
- 2 noc20 ma01 lec01 Basic linear algebra
- 3 noc20 ma01 lec02 Multivariable calculus 1
- 4 noc20 ma01 lec03 Multivariable calculus 2
- 5 noc20 ma01 lec04 The derivative map
- 6 noc20 ma01 lec05 Inverse Function Theorem
- 7 noc20 ma01 lec06 Constant Rank Theorem
- 8 noc20 ma01 lec07 Smooth functions with compact support
- 9 noc20 ma01 lec08 Smooth manifold
- 10 noc20 ma01 lec09 Examples of smooth manifolds
- 11 noc20 ma01 lec10 Higher dimensional spheres as smooth manifolds
- 12 noc20 ma01 lec11 Smooth maps
- 13 noc20 ma01 lec12 Examples of smooth maps
- 14 noc20 ma01 lec13 Tangent spaces I
- 15 noc20 ma01 lec14 Tangent spaces 2
- 16 noc20 ma01 lec15 Derivatives of smooth maps
- 17 noc20 ma01 lec16 Chain rule on manifolds
- 18 noc20 ma01 lec17 Dimension of tangent space 1
- 19 noc20 ma01 lec18 Dimension of tangent space 2
- 20 noc20 ma01 lec19 Derivative of inclusion map
- 21 noc20 ma01 lec20 Basis of tangent space
- 22 noc20 ma01 lec21 Inverse Function Theorem for manifolds
- 23 noc20 ma01 lec22 Submanifolds
- 24 noc20 ma01 lec23 Tangent space of a submanifold
- 25 noc20 ma01 lec24 Regular Value Theorem
- 26 noc20 ma01 lec25 Special linear group as a submanifold of the set of all square matrices
- 27 noc20 ma01 lec26 Hypersurfaces
- 28 noc20 ma01 lec27 Tangent spaces to level sets
- 29 noc20 ma01 lec28 Vector fields 1
- 30 noc20 ma01 lec29 Vector fields 2
- 31 noc20 ma01 lec30 Vector fields 3
- 32 noc20 ma01 lec31 Lie groups 1
- 33 noc20 ma01 lec32 Lie groups 2
- 34 noc20 ma01 lec33 Integral curve and flows 1
- 35 noc20 ma01 lec34 Integral curve and flows 2
- 36 noc20 ma01 lec35 Integral curve and flows 3
- 37 noc20 ma01 lec36 Complete vector fields
- 38 noc20 ma01 lec37 Vector fields and smooth maps
- 39 noc20 ma01 lec38 Lie Brackets 1
- 40 noc20 ma01 lec39 Lie brackets 2
- 41 noc20 ma01 lec40 Lie brackets 3
- 42 noc20 ma01 lec41 Lie algebras of matrix groups 1
- 43 noc20 ma01 lec42 Lie algebras of matrix groups 2
- 44 noc20 ma01 lec43 Exponential map
- 45 noc20 ma01 lec44 Frobenius theorems
- 46 noc20 ma01 lec45 Tensors and differential forms
- 47 noc20 ma01 lec46 Tensors and differential forms 2
- 48 noc20 ma01 lec47 Pull back form
- 49 noc20 ma01 lec48 Symmetric Tensors
- 50 noc20 ma01 lec49 Alternating Tensors 1
- 51 noc20 ma01 lec50 Alternating Tensors 2
- 52 noc20 ma01 lec51 Alternating Tensors 3
- 53 noc20 ma01 lec52 Alternating Tensors 4
- 54 noc20 ma01 lec53 Alternating Tensors 5
- 55 noc20 ma01 lec54 Alternating Tensors 6
- 56 noc20 ma01 lec55 Alternating Tensors 7
- 57 noc20 ma01 lec56 Alternating Tensors 8
- 58 noc20 ma01 lec57 Alternating Tensors 9
- 59 noc20 ma01 lec58 Differential forms on manifolds 1
- 60 noc20 ma01 lec59 Differential forms on manifolds 2
- 61 noc20 ma01 lec60 The Exterior derivative 1
- 62 noc20 ma01 lec61 The Exterior derivative 2
- 63 noc20 ma01 lec62 The Exterior derivative 3
- 64 noc20 ma01 lec63 The Exterior derivative 4
- 65 noc20 ma01 lec64 The Exterior derivative 5
- 66 noc20 ma01 lec65 Special classes of forms
- 67 noc20 ma01 lec66 Orientation on manifolds 1
- 68 noc20 ma01 lec67 Orientation on manifolds 2
- 69 noc20 ma01 lec68 Orientation on manifolds 3
