Calculus on Manifolds

Effective immediately, I’m self-studying out of Spivak’s Calculus on Manifolds (it’s about time). Here’s a tentative outline of which sections I’ll be covering when. If time permits, I’m thinking of creating a full lecture series based off the book (such a thing doesn’t really seem to exist at the time), although it’s unlikely I could finish by the end of the term.

May 1 — May 7: p. 1-15. Finish first chapter, Functions on Euclidean Space.
May 8 — May 14: p. 15-30. Basic definitions, basic theorems, partial derivatives.
May 15 — May 21: p. 30-43. Derivatives, inverse functions, implicit functions.
May 22 — May 28: p. 44-56. Notation, basic definitions, measure zero, integrable functions.
May 29 — June 4: p. 56-67. Fubini’s theorem, partitions of unity.
June 5 — June 11: p. 67-80. Change of variable, algebraic preliminaries.
June 12 — June 18: p. 80-97. Algebraic preliminaries, fields and forms.
June 19 — June 25: p. 97-109. Geometric preliminaries, fundamental theorem of calculus.
June 26 — July 2: p. 109-115. Manifolds.
July 3 — July 9: p. 115-122. Fields and forms on manifolds.
July 10 — July 16: p. 122-126. Stokes’ theorem on manifolds.
July 17 — July 23: p. 126-134. The volume element.
July 24 — July 30: p. 134-137. The classical theorems.

Extra references:

  1. C.H. Edwards Jr., Advanced Calculus of Several Variables.
  2. W. Rudin, Principles of Mathematical Analysis.
  3. V. Runde, Math 217 Lecture Notes.
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About mlbaker

just another guy trying to make the diagrams commute.
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3 Responses to Calculus on Manifolds

  1. Garrett says:

    Oh my God if you made a full lecture series I would be freaking ecstatic. I’ve always wanted to read that text but if it was explained as well as you cover other topics that would be stellar!

  2. Brian says:

    So, are there still any plans for video lectures?

    • mlbaker says:

      Unfortunately, as I plan to start graduate school in under a year, I have to make judicious use of my time. That being said, expository projects like this will likely have to wait while I prove to the world that I can actually do math…

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