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MidtermA_98F

# MidtermA_98F - Midterm Examination 1998 Fall MEAM 501...

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Midterm Examination : 1998 Fall Midterm Examination : 1998 Fall MEAM 501 Analytical Methods in Mechanics and Mechanical Engineering Analytical Methods in Mechanics and Mechanical Engineering 1. (15 Points) Formulate the following boundary value problem () () () ( ) ( ) () () 0 0 , 0 , , 0 , v L dx du L a u u P b dx du b a b dx du b a L b b x x f u x k dx du x h dx du x a dx d = = = = + + + + by the weighted residual method and by applying the integration by parts rule, where () ( ) () ( ) ε + = = + b g b g b g b g 0 0 lim , lim , b in a point inside of the interval (0, L ), and P is a given number. () () () () ( ) ( ) () ()() () () () () () 0 0 . . , 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = + + = + + = + + + + + = + + + + + + = + = + + + + + + + + w t s w v L w P b w dx x wf dx wu x k dx du w x h dx du dx dw x a dx x wf dx wu x k dx du w x h dx du dx dw

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MidtermA_98F - Midterm Examination 1998 Fall MEAM 501...

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