University of Florida/Egm6341/s10.team2.niki/HW7

problem 2: Solution of the Logistic equation

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Statement

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P.39-1

Solution

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We have Verhulst model or the Logistic equation as P.38-3


      


Separating variables and integrating we have


      


which can be written as


      


We get


      


      


Rearranging we have


      

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problem 7

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Statement

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Solution

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problem 14: Constants of the Cosine Series

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Statement

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We have the cosine series expressed as  , we need to express teh constants   as


 

Solution

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We have the given expression for the cosine series as


 

multiplying both sides by   where k is not the same as m and integrating we get,


 


Using the property of orthogonality we know that   exists only when k = m i.e


 

wkt,

  and


 

Thus we have by substituting and rearranging terms,


 

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--Egm6341.s10.team2.niki 14:43, 23 April 2010 (UTC)