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 [email protected] cos dxo d;)if a <0 and of the form sinh ddand

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## This note was uploaded on 05/06/2010 for the course MAE MAE 105 taught by Professor Nemat-nasser during the Spring '09 term at UCSD.

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

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