I was looking for some material that could help me understand a real analysis course (1st year undergraduate). My teacher treated the following topics:

Partition of unity

Existence of regular functions on compact support

Dyadic covering and Paley Littlewood's partition of unit.

Morse's lemma.

Do you know any book or note where I can find a simple introduction to these topics?

Thank you!

  • 2
    $\begingroup$ Don't know what is "Dyadic covering and Paley Littlewood's partition of unit", but all the others are standard in differential geometry. You can take a look of the book "Introduction to smooth manifold" by John M. Lee and "Differential topology" by Hirsch. Also, the book "Morse theory" by John Milnor is one of the most beautiful introduction to Morse theory (Well of course Morse lemma is proved there). $\endgroup$
    – user99914
    Apr 1, 2014 at 5:32

1 Answer 1


Shifrin's differential geometry notes contain most of those and are free on the web. math.uga.edu/~shifrin/ShifrinDiffGeo.pdf


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