Everyday Calculus: Discovering the Hidden Math All Around Us

167 Pages·2014·1.63 MB·English

by  Oscar E. Fernandez

EVERYDAY CALCULUS

EVERYDAY CALCULUS
DiscoveringtheHiddenMathAllaroundUs
OSCARE.FERNANDEZ
Withanewprefacebytheauthor
PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD
Copyright(cid:1)c 2014byPrincetonUniversityPress
PublishedbyPrincetonUniversityPress,41WilliamStreet,
Princeton,NewJersey08540
IntheUnitedKingdom:PrincetonUniversityPress,
6OxfordStreet,Woodstock,OxfordshireOX201TR
press.princeton.edu
AllRightsReserved
Fourthprinting,firstpaperbackprinting,2017
PaperbackISBN:978-0-691-17575-1
TheLibraryofCongresshascatalogedtheclotheditionasfollows:
Fernandez,OscarE.(OscarEdward)
Everydaycalculus:discoveringthehiddenmathallaroundus/OscarE.Fernandez.
pagescm
Includesbibliographicalreferencesandindex.
ISBN978-0-691-15755-9(hardcover:acid-freepaper)
1. Calculus–Popularworks. I. Title.
QA303.2.F472014515—dc232013033097
BritishLibraryCataloging-in-PublicationDataisavailable
ThisbookhasbeencomposedinMinionPro
Printedonacid-freepaper.∞
TypesetbySRNovaPvtLtd,Bangalore,India
PrintedintheUnitedStatesofAmerica
5 7 9 10 8 6 4
DedicadoaZoraida,
ereslabellezademivida
ytambiénanuestrahija
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yporsupuestoamimamá
sintuamoraquínoestuviera

CONTENTS
PrefacetothePaperbackEdition ix
Preface xi
CalculusTopicsDiscussedbyChapter xiii
CHAPTER1 WakeUpandSmelltheFunctions 1
What’sTrigGottoDowithYourMorning? 2
HowaRationalFunctionDefeatedThomasEdison,and
WhyInductionPowerstheWorld 5
TheLogarithmsHiddenintheAir 10
TheFrequencyofTrigFunctions 14
Galileo’sParabolicThinking 17
CHAPTER2 BreakfastatNewton’s 21
IntroducingCalculus,theCNBCWay 21
CoffeeHasItsLimits 25
AMultivitaminaDayKeepstheDoctorAway 30
DerivativesAreaboutChange 34
CHAPTER3 DrivenbyDerivatives 35
WhyDoWeSurviveRainyDays? 36
PoliticsinDerivatives,orDerivativesinPolitics? 39
WhattheUnemploymentRateTeachesUsaboutthe
CurvatureofGraphs 41
America’sBallooningPopulation 44
FeelingDerivatives 46
TheCalculusofTimeTravel 47
CHAPTER4 ConnectedbyCalculus 51
E-Mails,Texts,Tweets,Ah! 51
TheCalculusofColds 53
WhatDoesSustainabilityHavetoDowithCatchinga
Cold? 56
WhatDoesYourRetirementIncomeHavetoDowith
Traffic? 58
TheCalculusoftheSweetTooth 61
viii CONTENTS
CHAPTER5 TakeaDerivativeandYou’llFeelBetter 65
I“Heart”Differentials 65
HowLife(andNature)UsesCalculus 67
TheCostlyDownsideofCalculus 73
TheOptimalDriveBackHome 75
CatchingSpeedersEfficientlywithCalculus 77
CHAPTER6 AddingThingsUp,theCalculusWay 81
TheLittleEngineThatCould...Integrate 82
TheFundamentalTheoremofCalculus 90
UsingIntegralstoEstimateWaitTimes 93
CHAPTER7 Derivatives Integrals:TheDreamTeam 97
IntegrationatWork—TandooriChicken 98
FindingtheBestSeatintheHouse 101
KeepingtheTRunningwithCalculus 104
LookUptoLookBackinTime 108
TheUltimateFateoftheUniverse 109
TheAgeoftheUniverse 113
Epilogue 116
AppendixA FunctionsandGraphs 119
Appendices1–7 125
Notes 147
Index 149
PREFACE TO THE PAPERBACK EDITION
WHEN IT WAS PUBLISHED IN2014,EverydayCalculuspromisedtohelp
readerslearnthebasicsofcalculusbyusingtheireverydayexperiences
to reveal the hidden calculus around them. It also promised to do
thatinjustover100pages,andassumingaminimalmathbackground
fromthereader.Sincethen,Ihaveheardpositivereviewsfromdozens
of readers of all ages and backgrounds, and I could not be happier.
However, there is always room for improvement. For example, some
carefulreadersalertedme to severalsmalltypos throughout the book.
Others wrote detailed reviews with suggestions for the next edition
of the book. I am indebted to these readers for their input, and this
feedback,inpart,inspiredthereleaseofthispaperbackedition.
Hereisabriefdescriptionoftheupdatestotheoriginaledition.
1. Allknowntyposhavebeencorrected.
2. Some graphs now have a computer icon next to them in
the margin. This signals that there is an online interac-
tive demonstration that I have created to complement that
graph. Please visit the Everyday Calculus section of my website
www.surroundedbymath.com/bookstoaccessthem.
3. EverydayCalculuswasnotwrittentoreplaceacalculustextbook.
However, several readers have suggested that having all of the
calculus math discussed in one place might help summarize the
calculus the book discusses (and also serve as a quick refresher
forthosewhohavealreadystudiedcalculus).Inresponsetothis,
Ihavewrittenashortintroductiontothemathematicsbehindthe
calculuscoveredinthebook.Pleasevisitmywebsite(linkabove)
todownloadthatdocument.