Midterm1_Spring_2010_Solutions.doc

Midterm1_Spring_2010_Solutions.doc - 1 SDP Total points: 40...

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SDP 1 MAE 105 Introduction to Mathematical Physics MID-TERM EXAM April23,2010 Total points: 40 You are allowed the use of your class notes and textbook (Haberman) Please state any assumptions clearly r, ' u +l-c*/ ^ =&gbrc dr" 1. (5 points) Solve the following for y(x) f\SllttL U z 4 a eb* L*n4= a b = f iJ-z- a"Aeb* 2',?,J** dx ,,&(b) (EXTRA cREDIT) #.2ft.2v =o '/ t A*ebt + 3.^g gb( + L 6.e,bL 'o d aeb* Lu'n 3 b+z] =-o & - d, e-L t 4-L-'* n .rr) Cb -iz-) = o tb =.) b=-1,-L 2. (6 points) Mark as True or False (Justify very briefly): (D The method of separation of variables can only be used for solution, only if the PDE and the boundary conditions (BCs) are linear and homogeneous. This implies that the boundary conditions, say on the left and the right hand sides of a one-dimensional rcd must equal zero. l-a AE t Homotrlrc". BC,i ewLiv_ x I fr #,^ T(x,L) ' X /,,") Tdt) (ii) The solution of the differential "quxionQ t ay =0 are of the form sin d@and cos dxo d;)if a <0 and of the form sinh ddand
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Midterm1_Spring_2010_Solutions.doc - 1 SDP Total points: 40...

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