Mathematical Background
This chapter focuses on the basic concepts and algebra of sets as well as a brief introduction to the theory of functions and the well known principle of mathematical induction. All this background will be needed as a tool to understand the theory of line
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Rafael Martínez-Guerra Oscar Martínez-Fuentes Juan Javier Montesinos-García
Algebraic and Differential Methods for Nonlinear Control Theory Elements of Commutative Algebra and Algebraic Geometry
Mathematical and Analytical Techniques with Applications to Engineering
The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, in all areas of today’s Physical Sciences and Engineering, is well established. The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems in modern Physical Sciences and Engineering would otherwise have been impossible. The purpose of the series is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume in the series will provide a detailed introduction to a specific subject area of current importance, and then will go beyond this by reviewing recent contributions, thereby serving as a valuable reference source.
More information about this series at http://www.springer.com/series/7311
Rafael Martínez-Guerra Oscar Martínez-Fuentes Juan Javier Montesinos-García •
•
Algebraic and Differential Methods for Nonlinear Control Theory Elements of Commutative Algebra and Algebraic Geometry
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Rafael Martínez-Guerra Departamento de Control Automático CINVESTAV-IPN Mexico City, Distrito Federal, Mexico
Oscar Martínez-Fuentes Departamento de Control Automático CINVESTAV-IPN Mexico City, Distrito Federal, Mexico
Juan Javier Montesinos-García Departamento de Control Automático CINVESTAV-IPN Mexico City, Distrito Federal, Mexico
ISSN 1559-7458 ISSN 1559-7466 (electronic) Mathematical and Analytical Techniques with Applications to Engineering ISBN 978-3-030-12024-5 ISBN 978-3-030-12025-2 (eBook) https://doi.org/10.1007/978-3-030-12025-2 Library of Congress Control Number: 2018968389 © Springer Nature Switzerland AG 2019 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 advi
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