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 Rn (pp. 845-852)
17 Signed measures and the Radon-Nikodym derivative (pp. 853-873)