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

From Wikiversity
Jump to navigation Jump to search

problem 2: Solution of the Logistic equation[edit]


Statement[edit]

P.39-1

Solution[edit]

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


     

Author[edit]


problem 7[edit]


Statement[edit]

Solution[edit]

Author[edit]


problem 14: Constants of the Cosine Series[edit]


Statement[edit]

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


Solution[edit]

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,


Author[edit]

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