May 09, 2013 Rate of Change U+Me=Calculus May 09, 2013 CALCULUS • Calculus (Latin, a small stone used for counting) is a branch in mathematics focused on limits, functions, derivatives, integrals, and infinite series. • This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus. • Calculus is the study of change. May 09, 2013 While some of the ideas of calculus were developed earlier in Egypt, Greece, China, India, Iraq, Persia, and Japan, the modern use of calculus began in Europe, during the 17th century, when Isaac Newton and Gottfried Wilhelm Leibniz built on the work of earlier mathematicians to introduce its basic principles. The development of calculus was built on earlier concepts of instantaneous motion and area underneath curves. May 09, 2013 While some of the ideas of calculus were developed earlier in Egypt, AGrpeepclei,c Cahtiionan, sI nodfia d, Iirfafqe, rPeenrstiaa, la cnda lJcaupalnu,s t hien mcloudderen use of caolcmulpuus tbaetgiaonn isn Einuvrooplev, idnugri nvge tlhoe c1i7ttyh acenndtu aryc, cwehleenr aIstaiaocn , the sNleowpteon o afn da Gcoutrtfvriee,d aWnidlh oelpmt iLmeiibznaizt ibounil.t Aonp tphel iwcaortkio onf se aorlfie r mathematicians to introduce its basic principles. The development of icnaltceuglursa wl casa blcuuiltl uons einarclileur dcoen cceopmts pouf itnasttiaonntasn eionuvs omlvotiinong aanrde a, varoealu umndee,r naeracth l ceunrvgetsh., center of mass, work, and pressure. Calculus can be used to compute the Applications of differential calculus include computations involving tvrealojecictyto arnyd aocfc eal esrahtuiotnt,l eth de oslcokpei nogf aa ctu arv se,p aancde o pstiamtizoanti oonr. the aAmppoliucantito onsf osfn iontweg rianl caa ldcuriluvse iwncaluyd.e computations involving area, volume, arc length, center of mass, work, and pressure. Calculus can Cbea ulsceudl tuos c oism apulsteo t hues terdaj etcoto grya oinf aa s hmutotlree d opcrkeicnigs aet a space station or the amount of snow in a driveway. understanding of the nature of space, time, and mCaolctuioluns .i sF aolsro cuesendt utor igeasin, am maothree pmreacitsiec iuanndesr satnandd ing of the pnahtuilroe soof psphaecres, tiwmree, santlde md owtioitnh. Fpoar rcaedntouxriess, minavthoelmvaitnicgia ns and philosophers wrestled with paradoxes involving division by zero or dsuimviss oifo inn fbinyit ezlye rmoa noyr nsuummbesr so. fC ianlcfuilnuist eprloyv imdeas ntoyo lns,u emspbeceirasll.y Tthhe elismei tq aunde sthtieo infsin aitrei seer iiens, twhhei csht uredsoyl voef t hme poatriaodno xaens.d area. Calculus provides tools, especially the limit and the infinite series, which resolve the paradoxes. May 09, 2013 Instaneous Rates of Change May 09, 2013 May 09, 2013 May 09, 2013 Interpreting the Derivative.