A collection of problems on mathematical analysis. Vol. 2. Integrals. Series. 2nd revised and enlarged ed. (Сборник задач по математическому анализу. Том 2. Интегралы. Ряды.) (Russian) Zbl 1080.00001

Moskva: Fizmatlit (ISBN 5-9221-0307-5/hbk). 502 p. (2003).
This is the joint review for Vols. 2 and 3 (see Zbl 1080.00002 below) of this problem collection.
Collections of exercises and problems are always useful in mathematics, especially those for fresh(wo)men, since the ‘learning by doing’ principle is the only possible method for aquainting mathematical knowledge (You cannot learn to play the piano either by just watching a pianist.) The topics covered in these two volumes are: indefinite integrals; definite integrals; improper integrals; numerical sequences and series; function sequences and series; differential calculus for functions of several variables; multiple, contour and surface integrals; parameter-dependent integrals; Fourier integrals and transforms; introduction to functional analysis. At the end of each chapter, the authors give very briefly the solutions, but fortunately not in all details. In fact, it is well known that looking for the solution after some unsuccessful attempts, for lack of Sitzfleisch, is always a great temptation, but, as the nice French saying goes: ‘Solution lue – exercice foutu!’.


00A07 Problem books
26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
40-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to sequences, series, summability