T. W. Körner: A Companion to Analysis, 2004. American Mathematical Society. ISBN: 0-8218-3447-9. The author's web page, with sketched answers to some exercises, and a list of corrections.
The course curriculum (= pensum) will be chapters 1 through 13 of the textbook, minus section 11.5 and the heart-marked sections. This amounts to:
- Chapters 1, 3, 4, 6 and 7;
- Chapter 8, sections 1, 2, 3 and 5;
- Chapter 10, sections 3 and 4;
- Chapter 11, sections 1, 2, 3 and 4;
- Chapter 12, sections 1 and 2;
- Chapter 13, section 1.