Transcription of community project mathcentre community project
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community project mathcentre community project
Mathcentrecommunityprojectencouragingaca demicstosharemathssupportresourcesAllmcc presourcesarereleasedunderaCreativeCommo nslicencecommunity projectSecond order Ordinary differential Equationsmccp-richard-2 IntroductionPrerequisites:Inordertomaket hemostofthisresource,youneedtoknowaboutt rigonometry,di erentiation, (x),its rstderivativeandsecondderivative:ad2ydx2 + bdydx+ cy = f(x)(1)Wewillonlylookatequationswherethe coe cientsa,bandcareconstant;wewillnottreati nthishandoutthecaseofcoe EquationsIff(x) = ,welookatthecharacteristicequation,obtai nedbyreplacingd2ydx2,dydxandybyr2,rand1i ntheODE:ar2+ br + c = 0 Wedistinguishbetween3cases:thecasewhenth erootsofthecharacteristicequationaredist inctandreal, :realanddistinctro otsr1andr2 Thenthesolutionsofthehomogeneousequation areoftheform:y(x) = Aer1x+ , (x0) = andy (x0) = ,thenAandBwillbeuniquelyde nedby:Aer1x0+ Ber2x0= Ar1er1x0+ Br2er2x0= Exampled2ydx2+ 5dydx+ 6y = 0 Thecharacteristicequationis:r2+ 5r + 6 = 0andtherootsare 5 25 4 62= 3or :y(x) = Ae 3x+ Be MorgianeRichardUniversityofAberdeenShazi aAhmedUniversityofGlasgowmathcentrecommu nityprojectencouragingacademicstosharema thssupportresourcesAllmccpresourcesarere leasedunderaCreativeCommonslicenceCase2.
mathcentre community project encouraging academics to share maths support resources ... Second Order Ordinary Differential Equations mccp-richard-2 Introduction Prerequisites: In order to make the most of this resource, you need to know about trigonometry, di …
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