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## Ma108

### Classical Analysis (2013-2014)

Course websites:

http://www.math.caltech.edu/~2013-14/1term/ma108a/

http://www.math.caltech.edu/~2013-14/2term/ma108b/

Ma108a (first quarter) LaTeX'ed notes

Additional remarks/notes (i.e. not from lecture) are in parantheses and italics.

Assume all spaces are metric spaces unless otherwise stated.

(One notable omission is part of the proof of the implicit function theorem. The very last part was not covered in class, and it is unlikely I will get around to writing it up.)

Known typos: ch7-8notes.pdf: top of pg.7, M should be the union of balls with radius \delta_x/2 instead of \delta_x.

- Chapters 1-2 notes (pdf) [Lectures 1-4] (Calculus review, countable and uncountable sets, Cantor function)

- Chapters 3-6 notes (pdf) [Lectures 4-13] (Metric spaces, some point set topology)

- Chapters 7-8 notes + Implicit fcn theorem (pdf)
[Lectures 13-23] (Completeness, compactness, vector spaces + linear operators; differentiation, implicit fcn theorem)

- Chapters 9-12 notes (pdf)
[Lectures 23-29] (Baire category, some facts about uniformly convergent sequences, Arzela-Ascoli, Stone-Weierstrass)

All LaTeX'ed notes (concatenated) (pdf)

Scanned Ma108a notes (pdf) [bookmarked]

Scanned Ma108b notes (pdf)

Ma108c...

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