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This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.
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A Visual Introduction
to Differential
Forms and Calculus
on Manifolds
Jon Pierre Fortney
A Visual Introduction to Dif ferential Forms and Calculus on Manifolds
Jon Pierre Fortney
A Visual Introduction to Differential Forms
and Calculus on Manifolds
Jon Pierre Fortney
Department of Mathematics and Statistics
Zayed University
Dubai, United Arab Emirates
ISBN 978-3-319-96991-6 ISBN 978-3-319-96992-3 (eBook)
https://doi.org/10.1007/978-3-319-96992-3
Library of Congress Control Number: 2018952359
Mathematics Subject Classification (2010): 53-01, 57-01, 58-01, 53A45, 58C20, 58C35
© Springer Nature Switzerland AG 2018
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights
of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or
information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, ev en in the absence of a specific
statement, that such names are exempt from the rele vant protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this book are believ e d to be true and accurate at the date
of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained hereinorfor
any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional
affiliations.
This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To my parents, Daniel and Marlene Fortney, for all of their love and support.
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