In the first half of this book, we study various mathematical functions and the process of mathematical modeling by creating models for diverse data sets, both large and small. Throughout MMAC, the study of mathematical ideas takes place in real-world contexts. These students often have di↵erent needs than just a simplified version of a traditional Calculus I course, and this book is designed to meet these needs. However, students who intend to major in other disciplines, such as biology, economics, psychology, or sociology, genuinely benefit from an introduction to the process of mathematical modeling and to the tools of calculus as a means to analyze models. Many traditional introductory courses in mathematics are oriented toward supporting students who intend to major in mathematics, engineering, physics, or chemistry. Our driving motivation for writing this book is to create a learning experience that introduces the mathematical content students need for allied disciplines in the contexts they will encounter in those disciplines. This book, Mathematical Modeling and Applied Calculus (MMAC), explores some of the most important elements of such mathematics by introducing the reader to mathematical modeling and provides a set of tools for analyzing these mathematical models by means of calculus. For millenia now, humans have recognized that mathematics serves as an impressively e↵ective tool for understanding many aspects of reality. From the moment we are born, we touch, we listen, we look, we taste, we smell, and we process this sensory information in an e↵ort to make sense of our world. A Answers to Questions 677 B Answers to Odd-Numbered Exercises 703 C Getting Started with RStudio 770 D Sources 773 Index 791 Preface Human beings have an innate desire to understand reality. 6.4 Second Fundamental Theorem 6.5 The Method of Substitution. 5.4 Newton’s Method and Optimization 5.5 Multivariable Optimization. ![]() 4.3 Derivatives of Modeling Functions 4.4 Product and Quotient Rules. Existence of Linear Combinations Vector Projection. Method of Least Squares Vectors and Vector Operations. 2.2 Modeling with Exponential Functions 2.3 Modeling with Power Functions. 1 2 19 36 52 71 89 105 2 Mathematical Modeling 2.1 Modeling with Linear Functions. For Alexander and Harrison and For Benjamin, Daniel, and Ella Contents Preface ix 1 Functions for Modeling Data 1.1 Functions. ![]() Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2018940139 ISBN 978–0–19–882472–5 (hbk.) ISBN 978–0–19–882473–2 (pbk.) Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. McAllister 2018 The moral rights of the authors have been asserted First Edition published in 2018 Impression: 1 All rights reserved. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Joel Kilty and Alex M. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. M C A LLISTER 1 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. Mathematical modeling and applied calculus Mathematical Modeling and Applied Calculus J O E L KI LT Y A N D A L E X M.
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