Maths revision course by Miriam Hanks1Differentiation and IntegrationDifferentiation and Integration together are called Calculus.Maths revision course by Miriam Hanks2DifferentiationDifferentiate if the question says:Derive Find the derivativeFind the rate of changeFindor f !"Ma!imise or minimiseHo# do you kno# #hen to differentiate$ d!dyMaths revision course by Miriam Hanks3DifferentiationChange to %et rid of fractions #ith ! on the bottom:eg Multi&ly out bracketsHo# do you &re&are for differentiation$21!!2233= !!Maths revision course by Miriam Hanks4DifferentiationHo# do you differentiate$'ring the &o#er to the front to multi&ly"(ubtract ) from the &o#erMaths revision course by Miriam Hanks5Differentiation in real life*hy #as differentiation develo&ed originally$In Isaac +e#ton,s day- shirecks occurred regularly because the shi& #as not #here the ca&tain thought it #as using only the stars for guidance.Calculus #as develo&ed to im&rove navigation techniques.Maths revision course by Miriam Hanks6Differentiation in real lifeDifferentiation is used in economics and business to find o&timum solutions. eg to use the minimum amount of material to make the &ackaging- or to ma!imise efficiency of &roducts or to minimise their costs.Maths revision course by Miriam Hanks7Differentiation and IntegrationClick for calculus videoMaths revision course by Miriam Hanks8%ra&hs of the derivativeIf you are asked to dra# the gra&h of the derivative- kee& in mind that this is a gra&h of the gradient.(tart by marking &oints on the a!es #here there are turning &oints on the original gra&h.+o# look at the gradient before and after each of these &oints: Is it u& in #hich case- dra# above the !. a!is" or do#n dra# belo# !.a!is"$Make sure you curve is smoothMaths revision course by Miriam Hanks9IntegrationIntegrate if the question says:Find the integralFind the area under a curveFind the area bet#een /curvesFind Find y #hen you are given Ho# do you kno# #hen to integrate$ d!d!dyMaths revision course by Miriam Hanks10IntegrationChange to %et rid of fractions #ith ! on the bottom:eg Multi&ly out bracketsHo# do you &re&are for integration$21!!2233= !!Maths revision course by Miriam Hanks11IntegrationHo# do you integrate$0dd ) to the &o#erDivide by the ne# &o#er1 cMaths revision course by Miriam Hanks12Integration in real lifeIntegration is used to analyse crash test data- to im&rove safety of cars.It is also used by engineers to find the force of #ater from the surface area of a reservoir- to design dams.Maths revision course by Miriam Hanks13Further Calculussin a!a cos a!cos a!.a sin a!sin a! .cos a!cos a!sin a!differentiates tointegrates toa1a12o differentiate or integrate a trig function-use the formula sheet:Maths revision course by Miriam Hanks14Further Calculus2o differentiate or integrate a bracket #ith a &o#er:). 2hink of the #hole bracket as an 3!4 anddifferentiate or integrate it as usual/. Multi&ly by the derivative of the bracketif differentiating"orDivide by the derivative of the bracketif integrating"Maths revision course by Miriam Hanks15IntegrationClick for an integration joke