Syllabus
- 2/20: Introduction
- 2/21: Manifolds
- 2/27: No Classes (holiday)
- 2/28: No Classes (holiday)
- 3/5: Smooth Maps: submersion
- 3/6: Smooth Maps: immersion, embedding
- 3/12: Tangent vectors and Tangent spaces
- 3/13: Vector bundle and Tangent bundle
- 3/19: Vector fields
- 3/20: Lie bracket, integral curves, local flow
- 3/26: Lie derivative
- 3/27: Covector, cotangent bundle, differential 1-form
- 4/2: No Classes (holiday)
- 4/3: No Classes (holiday)
- 4/9: K-tensor
- 4/10: Differential K-forms and operators
- 4/16: Orientation
- 4/17: Orientation and Volume form
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(continue)
- 4/23: Manifold with boundary
- 4/24: Stokes' Theorem
- 4/30: Homotopy operator
- 5/1: Midterm (from the beginning to differential 1-form)
- 5/7: 換時間
- 5/8: 換時間
- 5/14: De Rham cohomology
- 5/15: De Rham cohomology, Hodge Star
- 5/21: Adjoint operator, Harmonic form
- 5/22: Hodge Theorem, Poincare duality (compact manifold)
- 5/28: Differential Complex
- 5/29: Mayer-Vietoris, Compactly supported cohomology
- 6/4: Finiteness of de Rham
- 6/5: Poincare duality (general)
- 6/11: Lie group
- 6/12: Group action on manifold
- 6/19: Final 10:00am 許 (application of de Rham) 10:30am 陳冠 (application of de Rham) 11:00 吳 (proof of homotopy invariance) 11:30 陳哲(Stokes' Thm) 1:00pm 韓 (application of de Rham) 1:30 翁 (TBA) 2:00pm 賴 (Lie group) 2:30 洪 (proof of de Rham or application of de Rham)
- 6/26: Final 1:00 翁(TBA) 2:00 林(Example of de Rham cohomology)
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