Questions and answers
Questions concerned integrability of discontinuous functions, notions of improper integrals (how and when they can be defined), topological properties (equivalent definitions of compactness, connectedness etc.)
Here are some textbooks that I recommend for preparing when working on the exam. Keep them on your virtual bookshelf: they cover much more that I explained in the course, but who knows what questions related to analysis you might have.
- V. Zorich, vol. 1: Chapters 1-6, pp.1-371.
- V. Zorich, vol. 2: Parts of Chapter 9 (continuous maps) and the first part of Chapter 18 on Fourier series.
- W. Rudin: Chapters 1-6, pp.1-165.
The problems for exam will be posted on February 1st (at least the English version).