Mathematical Tools for Real-World Applications. A Gentle Introduction for Students and Practitioners

307 Pages·2022·7.771 MB·English

by  Alexandr Draganov

MathematicalToolsforReal-WorldApplications

MathematicalToolsforReal-WorldApplications
AGentleIntroductionforStudentsandPractitioners
AlexandrDraganov
TheMITPress
Cambridge,Massachusetts
London,England
©2022 Massachusetts Institute of Technology
All rights reserved. No part of this book may be reproduced in any form by any electronic or me-
chanical means (including photocopying, recording, or information storage and retrieval) without
permission in writing from the publisher.
The MIT Press would like to thank the anonymous peer reviewers who provided comments on drafts
of this book. The generous work of academic experts is essential for establishing the authority and
quality of our publications. We acknowledge with gratitude the contributions of these otherwise
uncredited readers.
This book was set in Times Roman by the author.
Library of Congress Cataloging-in-Publication Data
Names: Draganov, Alexandr, author.
Title: Mathematical tools for real-world applications : a gentle introduction for students and
practitioners / Alexandr Draganov.
Description: Cambridge, Massachusetts : The MIT Press, [2022] | Includes bibliographical
references and index.
Identifiers: LCCN 2021046200 | ISBN 9780262543965 (paperback)
Subjects: LCSH: Mathematics. | Problem solving—Mathematical models.
Classification: LCC QA39.3 .D73 2022 | DDC 510—dc23/eng/20211119
LC record available at https://lccn.loc.gov/2021046200
ToLuda

Thereaderwhofollowsmydriftwithsufficientattentionwilleasilyseethatnothingislessinmy
mind than ordinary Mathematics, and that I am expounding quite anotherscience, of which these
illustrationsarerathertheouterhuskthantheconstituents.Suchascienceshouldcontaintheprimary
rudimentsofhumanreason,anditsprovinceoughttoextendtotheelicitingoftrueresultsinevery
subject.
—Rene´Descartes,RulesfortheDirectionoftheMind
Indeed,Ihavefoundthatitisusuallyinunimportantmattersthatthereisafieldfortheobservation,
andforthequickanalysisofcauseandeffectwhichgivesthecharmtoaninvestigation.
—ArthurConanDoyle,TheAdventuresofSherlockHolmes

Contents
ListofFigures xv
ListofTables xix
Preface xxi
HowtoReadThisBook xxv
1 Units 1
1.1 UsingDimensionalAnalysistoSolveProblems 3
1.2 TheTwoHikersProblem 5
1.3 TheCircleandLineProblem 5
1.4 SatelliteCoverage 7
1.5 TheCubicFormula 8
1.6 Summary 10
Exercises 11
2 LimitingCases 19
2.1 TheProductofTwoLinearExpressions 21
2.2 TheTwoHikersProblem 22
2.3 TheRiverboatProblem 23
2.4 TheQuadraticEquation 25
2.5 TheIntersectionsbetweenaCircleandaStraightLine 27
2.6 TheSumofTwoRatios 30
2.7 TheSumofTwoScaledRatios 34
2.8 TheSumorDifferenceofTwoRadicals 36
2.9 ACircleInscribedinaRightTriangle 38
2.10 DrainingaPool 40
2.11 TheSumofanUnknownandItsReciprocal 44
2.12 DesigningSatelliteCoverage 46