Calculus for Cognitive Scientists Higher Order Models and Their Anal
This book offers a self-study program on how mathematics, computer science and science can be profitably and seamlessly intertwined. This book focuses on two variable ODE models, both linear and nonlinear, and highlights theoretical and computational tool
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James K. Peterson
Calculus for Cognitive Scientists Higher Order Models and Their Analysis
Cognitive Science and Technology Series editor David M.W. Powers, Adelaide, Australia
More information about this series at http://www.springer.com/series/11554
The seadragons were intrigued by calculus and flocked to the teacher
James K. Peterson
Calculus for Cognitive Scientists Higher Order Models and Their Analysis
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James K. Peterson Department of Mathematical Sciences Clemson University Clemson, SC USA
ISSN 2195-3988 ISSN 2195-3996 (electronic) Cognitive Science and Technology ISBN 978-981-287-875-5 ISBN 978-981-287-877-9 (eBook) DOI 10.1007/978-981-287-877-9 Library of Congress Control Number: 2015958343 © Springer Science+Business Media Singapore 2016 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, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by SpringerNature The registered company is Springer Science+Business Media Singapore Pte Ltd.
I dedicate this work to the biology students who have learned this material over the last 10 semesters, the practicing biologists, the immunologists, the cognitive scientists, and the computer scientists who have helped an outsider think much better and to my family who have listened to my ideas in the living room and over dinner for many years. I hope that this text helps inspire everyone who works in science to consider mathematics and computer science as indispensable tools in their own work in the biological sciences.
Acknowledgments
We would like to thank all the students who have used the various iterations of these notes as they have evolved from handwritten to the fourth fully typed version here. We particularly appreciate your interest as this course is required and uses mathematics; a combination that causes fear in many biological science majors. We have been pleased by the enthusiasm you have brought to this interesting combination of ideas from many disciplines. Finally, we gratefully acknowledge the
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