Analysis III

The third and last volume of this series deals with the theory of integration and the foundations of global analysis. Again a modern and clear construction is emphasized which not only provides a well-structured and beautiful theory, but also equips the reader with powerful tools for his further work in mathematics. On this account, for instance, the Bochner-Lebesgue integral is presented which is an indispensable resource for the modern theory of partial differential equations. Likewise a version of Stoke's theorem is proven that meets the practical needs of mathematics and theoretical physics as far as possible. In the same way as in the previous volumes numerous prospects of continuative theories also will be given, and this will convey an impression of the importance and the strength of the presented theories to the reader. Additionally these parts will be used to practice and to deepen the provided material.Numerous examples, real calculations, a large number of exercises and many figures make this book a reliable escort for the whole course of studies.