Analysis II

Joachim Escher

ISBN 10: 3764374721 / ISBN 13: 9783764374723

Published by Springer International Publishing, Birkhäuser Basel Mai 2008, 2008

About this Item

Neuware -As with the first, the second volume contains substantially more material than can 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 find 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 colleagues 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 final version. We also extend great thanks to our staff for their careful perusal of the entire manuscript and for tracking errata and inaccuracies. Our most heartfelt thank extends again to our ¿typesetting perfectionist¿, 1 without whose tireless effort this book would not look nearly so nice. We also thank Andreas for helping resolve hardware and software problems. Finally, we extend thanks to Thomas Hintermann and to Birkhauser for the good working relationship and their understanding of our desired deadlines.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 416 pp. Englisch.

Seller Inventory # 9783764374723

Bibliographic Details

• Title: Analysis II
• Publisher: Springer International Publishing, Birkhäuser Basel Mai 2008
• Publication Date: 2008
• Language: English
• ISBN 10: 3764374721
• ISBN 13: 9783764374723
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 240W x 168H x 23D millimeters 240 millimeters width by 168 millimeters height by 23 millimeters depth
• Weight: 695 grams

About this title

Synopsis

As with the first, the second volume contains substantially more material than can 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 find 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 colleagues 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 final version. We also extend great thanks to our staff for their careful perusal of the entire manuscript and for tracking errata and inaccuracies. Our most heartfelt thank extends again to our “typesetting perfectionist”, 1 without whose tireless effort this book would not look nearly so nice. We also thank Andreas for helping resolve hardware and software problems. Finally, we extend thanks to Thomas Hintermann and to Birkhauser for the good working relationship and their understanding of our desired deadlines.

From the Back Cover

Der zweite Band dieser Einführung in die Analysis behandelt die Integrationstheorie von Funktionen einer Variablen, die mehrdimensionale Differentialrechnung und die Theorie der Kurven und Kurvenintegrale. Der im ersten Band begonnene moderne und klare Aufbau wird konsequent fortgesetzt. Dadurch wird ein tragfähiges Fundament geschaffen, das es erlaubt, interessante Anwendungen zu behandeln, die zum Teil weit über den in der üblichen Lehrbuchliteratur behandelten Stoff hinausgehen.

Dies betrifft beispielsweise die Behandlung von Nemytskiioperatoren, welche eine transparente Einführung in die Variationsrechnung und Herleitung der Euler-Lagrangeschen Gleichungen ermöglicht. Ein weiteres Beispiel stellt die Darstellung der lokalen Theorie der Untermannigfaltigkeiten des Rn dar.

Als Anwendungen der Theorie der Kurvenintegrale werden die Cauchyschen Integralsätze und die Theorie der holomorphen Funktionen bis einschließlich der Homologieversion des Residuensatzes entwickelt. Neben der Berechnung wichtiger bestimmter Integrale der Mathematik und der Physik, werden funktionentheoretische Eigenschaften der Gamma- und der Riemannschen Zetafunktionen besprochen.

Zahlreiche Übungsaufgaben von unterschiedlichem Schwierigkeitsgrad und viele informative Abbildungen runden dieses Lehrbuch ab.