Analysis

The book is written in the style of Analysis 1: everything is motivated and developed in great detail, and there was particularly intensive collaboration with students. In addition to the usual material of Analysis 2 (function spaces, integration, differential calculus for functions of several variables), the book contains a number of unique features that are not found in any other textbook. For example, it includes Liouville's theorem, which guarantees that certain simple functions cannot be integrated in a closed form. In the chapter 'Applications of Integral Calculus,' there is a section on number theory that presents transcendence proofs for specific numbers, including the number e; this chapter also covers the existence theorem of Picard-Lindelöf. Finally, there is a detailed appendix on the topic 'English for Mathematicians': what should one consider when discussing mathematics in English? In the second edition, the text has been corrected in many places, and a section in Chapter 6 (Integration) has been revised.