Analysis II [Paperback]

The second volume of this introduction into analysis deals with the integration theory of functions of one variable, the multidimensional differential calculus and the theory of curves and line integrals. The modern and clear development that started in Volume I is continued. In this way a sustainable basis is created which allows the reader to deal with interesting applications that sometimes go beyond material represented in traditional textbooks. This applies, for instance, to the exploration of Nemytskii operators which enable a transparent introduction into the calculus of variations and the derivation of the Euler-Lagrange equations.

The second volume of this introduction into analysis deals with the integration theory of functions of one variable, the multidimensional differential calculus and the theory of curves and line integrals. It continues the modern and clear development that started in Volume I.

As with the ?rst, the secondvolume containssubstantially morematerialthancan be covered in a one-semester course. Such courses may omit many beautiful and well-grounded applications which connect broadly to many areas of mathematics. We of course hope that students will pursue this material independently; teachers may ?nd it useful for undergraduate seminars. For an overview of the material presented, consult the table of contents and the chapter introductions. As before, we stress that doing the numerous exercises is indispensable for understanding the subject matter, and they also round out and amplify the main text. In writing this volume, we are indebted to the help of many. We especially thank our friends and colleages Pavol Quittner and Gieri Simonett. They have not only meticulously reviewed the entire manuscript and assisted in weeding out errors but also, through their valuable suggestions for improvement, contributed essentially to the ?nal version. We also extend great thanks to our sta? for their careful perusal#”