Analysis 2. Textbook and exercise book. With free demo-access: MyMathLab. Transl. from the English and edited by Daniel Rost. 12th updated ed. (Analysis 2. Lehr- und Übungsbuch.) (German) Zbl 1296.26005

Thomas, George B.; Weir, Maurice D.; Hass, Joel

Always Learning. München: Pearson Studium (ISBN 978-3-86894-172-2/hbk). 624 p. (2014).

This is a German translation of the second part of the text book in analysis (for the first part see [the authors, Analysis 1. Textbook and exercise book. München: Pearson Studium (2013; Zbl 1270.00022)]).
Several features of the book are very helpful for any auditorium of the book. Among them are attractive and instructive color illustrations, prepared by using facilities of the MyMathLab package, carefully calculated and discussed examples, in particular those related to certain physical models, and a big collection of exercises.
The book consists of 7 chapters and a short appendix. Its content can be characterized as vector- and multi-dimensional analysis.
Chapter 11 “Parametric representation and polar coordinates” describes properties of plane curves. Here one can find a large number of geometrical problems which nowadays are presented in a textbook quite seldom.
In Chapter 12 “Vectors and geometry in space” the authors study 3-dimensional objects, vectors, planes, figures, basing on the coordinate point of view.
Only in Chapter 13 “Vector-valued functions and movement in space” a “purely” mathematical analysis is started. Such an analysis is not formal and relates question of physical models and analysis itself. The mathematical analysis is presented in the remaining Chapters as well (Chapter 14 “Partial derivatives”, Chapter 15 “Multi-dimensional integrals”, Chapter 16 “Integration in vector fields”, Chapter 17 “Differential equations of the second order”). Two questions are discussed in the Appendix, namely, a distribution law for the vector product and the Schwarz theorem for mixed derivatives of the second order.
The book is well-organized and surely a very good example of modern textbooks in mathematics.

Reviewer: Sergei V. Rogosin (Minsk)

MSC:

26-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
00A35	Methodology of mathematics
00A07	Problem books

Keywords:

real analysis; textbook; exercises

Citations:

Zbl 1283.26001; Zbl 1270.00022

Software:

MyMathLab