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Analysis by its history
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2019-02-22
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This book presents first-year calculus roughly in the order in which it first was discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.
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Undergraduate Texts in Mathematics
Readings in Mathematics
Editors
S. Axler
K.A. Ribet
![](https://csdnimg.cn/release/download_crawler_static/10969703/bg3.jpg)
Graduate Texts in Mathematics
Readings in Mathematics
Ebbinghaus/Hermes/Hirzebruch/Koecher/Mainzer/Neukirch/Prestel/Remmert: Numbers
Fulton/Harris: Representation Theory: A First Course
Undergraduate Texts in Mathematics
Readings in Mathematics
Anglin: Mathematics: A Concise History and Philosophy
Anglin/Lambek: The Heritage of Thales
Bressoud: Second Year Calculus
Hairer/Wanner: Analysis by Its History
Hämmerlin/Hoffmann: Numerical Mathematics
Isaac: The Pleasures of Probability
Murty: Problems in Analytic Number Theory
Remmert: Theory of Complex Functions
Walter: Ordinary Differential Equations
Knoebel/Laubenbacher/Lodder/Pengelley: Mathematical Masterpieces: Further Chronicles
Laubenbacher/Pengelley: Mathematical Expeditions: Chronicles by the Explorers
Samuel: Projective Geometry
Stillwell: Numbers and Geometry
by the Explorers
Toth: Glimpses of Algebra and Geometry, Second Edition
![](https://csdnimg.cn/release/download_crawler_static/10969703/bg4.jpg)
E. Hairer G. Wanner
Analysis by
Its History
![](https://csdnimg.cn/release/download_crawler_static/10969703/bg5.jpg)
Editorial Board
S. Axler
K.A. Ribet
Mathematics Department
Mathematics Department
San Francisco State
University of California
University
at Berkeley
San Francisco, CA 94132
Berkeley, CA 94720-3840
E. Hairer
G. Wanner
Department of Mathematics
University of Geneva
Geneva, Switzerland
USA
USA
© 2008 Springer Science+Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,
in connection with any form of information storage and retrieval, electronic adaptation, computer
software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even if they
are not identified as such, is not to be taken as an expression of opinion as to whether or not they are
subject to proprietary rights.
Printed on acid-free paper
springer.com
Library of Congress Control Number: 2008925883
Editors
NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use
e-ISBN: 978-0-387-77036-9
9 8 7 6 5 4 3 2 1
ISBN: 978-0-387-77031-4
ribet@math.berkeley.edu
axler@sfsu.edu
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