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.

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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