大学の数学で，「微分幾何学」オンライン講義のYoutube動画
ニューサウスウェールズ大学の，「微分幾何学」の講義の動画。
前半
- 1. DiffGeom1: Classical curves
- 2. DiffGeom2: Introduction to GeoGebra
- 3. DiffGeom3: Parametrized curves and algebraic curves
- 4. DiffGeom4: The differential calculus for curves, via Lagrange!
- 5. DiffGeom5: Tangent conics and tangent quadrics
- 6. DiffGeom6: Visualizing the folium surface with GeoGebra
- 7. DiffGeom7: Differential geometry with finite fields
- 8. DiffGeom8: The differential calculus for curves (II)
- 9. DiffGeom9: Projective view of conics and quadrics
- 10. DiffGeom10: Duality, polarity and projective linear algebra
- 11. DiffGeom11: Duality, polarity and projective linear algebra (II)
- 12. DiffGeom12: Metrical structure and curvature of a parabola
- 13. DiffGeom13: Curvature for the general parabola
- 14. DiffGeom14: Quadratic curvature for algebraic curves
- 15. DiffGeom15: Quadratic curvature for algebraic curves (cont)
- 16. DiffGeom16: Curvature, turning numbers and winding numbers
- 17. DiffGeom17: Curvature, turning numbers and winding numbers (cont)
後半
- 18. DiffGeom18: The Frenet Serret equations
- 19. DiffGeom19: The Frenet Serret equations (example)
- 20. DiffGeom20: Geometric and algebraic aspects of space curves
- 21. DiffGeom21: An introduction to surfaces
- 22. DiffGeom21b: A tutorial: some differential geometry problems
- 23. DiffGeom22: More general surfaces
- 24. DiffGeom23: Paraboloids and associated quadratic forms
- 25. DiffGeom24: Topological spaces and manifolds
- 26. DiffGeom25: Manifolds, classification of surfaces and Euler characteristic
- 27. DiffGeom26: Classification of 2-manifolds and Euler characteristic
- 28. DiffGeom28: Curvature for the general paraboloid
- 29. DiffGeom29: Curvature for general algebraic surfaces
- 30. DiffGeom30: Examples of curvatures of surfaces
- 31. DiffGeom31: Meusnier, Monge and Dupin I
- 32. DiffGeom32: Meusnier, Monge and Dupin II
- 33. DiffGeom33: Meusnier, Monge and Dupin III
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