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Analysis II Video Lectures

Analysis II Video Lectures

Arthur Parzygnat via YouTube Direct link

Analysis II Lecture 15 Part 4 Poincare Hopf theorem and hairy ball theorem

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Analysis II Lecture 15 Part 4 Poincare Hopf theorem and hairy ball theorem

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Analysis II Video Lectures

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  1. 1 Introduction to LaTeX and TikZ
  2. 2 Analysis II Lecture 01 Part 1 diagrams
  3. 3 Analysis II Lecture 01 Part 2 products
  4. 4 Analysis II Lecture 01 Part 3 existence and uniqueness of products
  5. 5 Analysis II Lecture 01 Part 4 determinants
  6. 6 Analysis II Lecture 02 Part 1 basic topology of euclidean space
  7. 7 Analysis II Lecture 02 Part 2 nested rectangles
  8. 8 Analysis II Lecture 02 Part 3 Compactness
  9. 9 Analysis II Lecture 02 Part 4 connected and convex subsets
  10. 10 Analysis II Lecture 03 Part 1 functions
  11. 11 Analysis II Lecture 03 Part 2 limits
  12. 12 Analysis II Lecture 03 Part 3 continuity
  13. 13 Analysis II Lecture 03 Part 4 continuity theorems
  14. 14 Analysis II Lecture 03 Part 5 continuous paths
  15. 15 Analysis II Lecture 04 Part 1 intuition for derivatives
  16. 16 Analysis II Lecture 04 Part 2 the differential
  17. 17 Analysis II Lecture 04 Part 3 the chain rule
  18. 18 Analysis II Lecture 04 Part 4 example applying the chain rule
  19. 19 Analysis II Lecture 05 Part 1 partial derivatives
  20. 20 Analysis II Lecture 05 Part 2 continuously differentiable functions
  21. 21 Analysis II Lecture 06 Part 1 The derivative functor
  22. 22 Analysis II Lecture 06 Part 2 vector fields as derivations
  23. 23 Analysis II Lecture 06 Part 3 when partial derivatives commute
  24. 24 Analysis II Lecture 06 Part 4 continuously differentiable versus differentiable
  25. 25 Analysis II Lecture 07 Part 1 integral curves of vector fields
  26. 26 Analysis II Lecture 07 Part 2 dynamical systems
  27. 27 Analysis II Lecture 07 Part 3 integrals/constants of the motion
  28. 28 Analysis II Lecture 08 Part 1 inverse differential
  29. 29 Analysis II Lecture 08 Part 2 motivation for the inverse function theorem
  30. 30 Analysis II Lecture 08 Part 3 sketch of proof of inverse function theorem I
  31. 31 Analysis II Lecture 08 Part 4 sketch of proof of inverse function theorem II
  32. 32 Analysis II Lecture 09 Part 1 (review) example computing the differential of a function
  33. 33 Analysis II Lecture 10 Part 1 height functions and level sets
  34. 34 Analysis II Lecture 10 Part 2 Lemma for the implicit function theorem
  35. 35 Analysis II Lecture 10 Part 3 proof of lemma for the implicit function theorem
  36. 36 Analysis II Lecture 10 Part 4 statement and example of implicit function theorem
  37. 37 Analysis II Lecture 11 Part 1 manifolds
  38. 38 Analysis II Lecture 11 Part 2 alternative definition of manifold and non-examples
  39. 39 Analysis II Lecture 11 Part 3 implicitly defined manifolds
  40. 40 Analysis II Lecture 12 Part 1 the tangent space
  41. 41 Analysis II Lecture 12 Part 2 tangent space using curves
  42. 42 Analysis II Lecture 12 Part 3 associative algebras and derivations
  43. 43 Analysis II Lecture 12 Part 4 Hadamard's Lemma
  44. 44 Analysis II Lecture 13 Part 1 the differential for functions on manifolds
  45. 45 Analysis II Lecture 13 Part 2 Jacobians for differentiable functions on manifold
  46. 46 Analysis II Lecture 13 Part 3 familiar theorems for manifolds
  47. 47 Analysis II Lecture 13 Part 4 submanifolds and normal vectors
  48. 48 Analysis II Lecture 14 Part 1 orientations
  49. 49 Analysis II Lecture 14 Part 2 the degree and index
  50. 50 Analysis II Lecture 14 Part 3 examples of the index for vector fields
  51. 51 Analysis II Lecture 14 Part 4 the index is well-defined
  52. 52 Analysis II Lecture 15 Part 1 vector fields on manifolds
  53. 53 Analysis II Lecture 15 Part 2 flows on manifolds
  54. 54 Analysis II Lecture 15 Part 3 Triangulations and the Euler characteristic
  55. 55 Analysis II Lecture 15 Part 4 Poincare Hopf theorem and hairy ball theorem
  56. 56 Analysis II Lecture 16 Part 1 metric spaces
  57. 57 Analysis II Lecture 16 Part 2 Cauchy sequences in metric spaces
  58. 58 Analysis II Lecture 16 Part 3 point set topology and types of functions
  59. 59 Analysis II Lecture 16 Part 4 the completion of a metric space
  60. 60 Analysis II Lecture 17 Part 1 the method of successive approximations
  61. 61 Analysis II Lecture 17 Part 2 contraction mapping theorem I
  62. 62 Analysis II Lecture 17 Part 3 contraction mapping theorem II
  63. 63 Analysis II Lecture 17 Part 4 weaker fixed point theorem for compact subsets
  64. 64 Analysis II Lecture 18 Part 1 the matrix exponential
  65. 65 Analysis II Lecture 18 Part 2 damped harmonic oscillator
  66. 66 Analysis II Lecture 18 Part 3 non-autonomous linear ordinary differential equations
  67. 67 Analysis II Lecture 19 Part 1 integral equations
  68. 68 Analysis II Lecture 19 Part 2 existence and uniqueness of solutions to ODEs

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