## Lecture Notes for Analysis I and II

by Jason Swanson

Theorem numbers that start with an "L" are unique to these notes. Other theorem numbers in Chapters 1-10 refer to Principles of Mathematical Analysis by Walter Rudin; in Chapters 11-15, they refer to Applied Analysis by John Hunter and Bruno Nachtergaele. Chapters 16 and 17 are supplemental material, and not part of the core content of the Analysis sequence.

1 Number systems (pp. 1-65)

2 Metric spaces (pp. 65-110)

3 Sequences and series (pp. 111-159)

4 Continuity (pp. 160-207)

5 Differentiation (pp. 207-242)

6 Riemann-Stieltjes integration (pp. 242-262)

7 Some special functions (pp. 262-278)

8 Linear transformations (pp. 279-314)

9 Functions of several variables (pp. 315-355)

10 Measure and integration (pp. 356-544)

11 Topological spaces (pp. 545-562)

12 Banach spaces (pp. 562-656)

13 Hilbert spaces (pp. 656-679)

14 Bounded linear operators (pp. 680-726)

15 Distributions and the Fourier transform (pp. 726-844)

16 Polar coordinates in R^{n} (pp. 845-852)

17 Signed measures and the Radon-Nikodym derivative (pp. 853-873)