Analysis 2 (Q5917919)

The book is the second part of two-volume textbook on analysis which is a special edition for students preparing themselves for a work as mathematics teachers in secondary schools. It is also useful for experienced mathematics teachers. The first volume was published in 2011 [the author, Analysis 1. Berlin: Springer (2011; Zbl 1242.00003)]. Because of the target audience of this book, its main aim is to describe general ideas which are part of the curriculum of mathematics courses at secondary schools. These ideas are well-described and good illustrated by numerous examples and figures. Six main conceptions are in the discussion in this volume, namely integration, basic topology, multidimensional differentiation, Fourier series, introductory parts of the theory of ordinary differential equation, and introductory parts of multidimensional integration. Mainly, three questions are answered: what is the nature of one or the other concepts, how are they developed (principal moments are discussed); and how one can teach mathematics taking into account these concepts? Surely such discussion could be helpful for mathematics teachers as an additional source to standard textbooks.