Stream 3A: Scalar Calculus
Stream 3 is \(\infty \) , a concept that typically means unbounded (immeasurably large), but in the case of calculus, \(\infty \) means infinitesimal (immeasurably small), since taking a limit requires small numbers.
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An Invitation to Mathematical Physics and Its History
An Invitation to Mathematical Physics and Its History
Jont Allen
An Invitation to Mathematical Physics and Its History
123
Jont Allen Electrical & Computer Engineering University of Illinois at Urbana Champaign Urbana, IL, USA
ISBN 978-3-030-53758-6 ISBN 978-3-030-53759-3 https://doi.org/10.1007/978-3-030-53759-3
(eBook)
© Springer Nature Switzerland AG 2020 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, even in the absence of a specific statement, that such names are exempt from the relevant 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 believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for 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 Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
Science has evolved over thousands of years. It began out of curiosity about how the world around us works as well as a need to know how to make things work better. From water management to space travel, science is essential for success. The evolution of science is layered: Early science depended mostly on critical observation, thus the early scientist was considered a philosopher, who created a theory. Soon experiments were designed to test these theories. This process is successful when a new principle is established, leading to a deeper and reproducible experimental observation. This typically takes years. A key component of science is making and testing models that are designed to evaluate the results of experiments quantitatively in a mathematical framework. Good science is observation and experimentation. Great science is the art of making models that explain experimental results. This always results in a deeper question, suggesting new experiments. Each generation has its geniuses. One of these was Galileo, who was a philosopher, experimentalist, and mathematician. An understanding of physics requires a knowledge of mathematics. The converse is not true. By definition, pure mathematics contains no physics. Yet hist
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