Calculus (Differentiation and Integration)

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Maths revision course by Miriam Hanks 1 Differentiation and Integration Differentiation and Integration together are called Calculus .

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This is very useful for beginners.

Transcript of Calculus (Differentiation and Integration)

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