Developments in Mathematical and Conceptual Physics Concepts and App
This book presents concepts of theoretical physics with engineering applications. The topics are of an intense mathematical nature involving tools like probability and random processes, ordinary and partial differential equations, linear algebra and infin
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Developments in Mathematical and Conceptual Physics Concepts and Applications for Engineers
Developments in Mathematical and Conceptual Physics
Harish Parthasarathy
Developments in Mathematical and Conceptual Physics Concepts and Applications for Engineers
123
Harish Parthasarathy Department of Electronics and Communication Engineering Netaji Subhas University of Technology Delhi, India
ISBN 978-981-15-5057-7 ISBN 978-981-15-5058-4 https://doi.org/10.1007/978-981-15-5058-4
(eBook)
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are solely and exclusively licensed 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 Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Preface
This book contains some special topics of recent research interest in most of the important topics in theoretical physics. It will be of value to the practising theoretical physicist as well as to applied mathematicians and engineers who wish to apply the techniques developed by physicists to engineering problems especially in nonlinear systems, signal processing and probabilistic analysis of systems. The chapter on classical mechanics talks about the Lagrangian formalism, then introduces the theory of the motion of particles in a potential subject to damping and random forces and sets up the Fokker–Planck equation that governs the evolution of the probability density of the particle or systems of particles in phase space using which the classical fluctuation–dissipation theorem of Kubo is derived as a condition for balance between the random fluctuating forces and dissipative forces so that at equilibrium the density is Gibbsian. Possible extensions to a quantum fluctuation–dissipat
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