Ilyin V.A., Poznyak E.G. Fundamentals of Mathematical Analysis. Part 2

Translated into English from the 4th Russian edition by I. Aleksanova. — Moscow: Mir Publishers, 1982. — 438 p.The book is based on the lectures delivered by the authors at the Physics Department of Moscow University.
In the course of systematic exposition of the material, the authors gave prominence to the most important concepts and theorems, the most significant of the latter being called fundamental theorems. The authors tried to give the formulations of new concepts and theorems not long before their direct application.
The sequence of presentation of the material corresponds to that accepted at the Physics Department of Moscow University. The chapter “Preliminary Information on the Main Concepts of Mathematical Analysis”, in particular, comes before the exposition of the systematic course because this chapter deals with some very important physical problems and discusses mathematical means for their solution. Thus it becomes clear from the very beginning what problems and concepts constitute the subject matter of mathematical analysis. Our lecturing experience shows that such a preliminary elucidation of the range of problems treated in the course of the analysis makes it appreciably easier for the students to understand the basic mathematical concepts.