Review1_98F

# Review1_98F - Review Problems for Midterm Examination MEAM...

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MEAM 501, Fall 1998 1. Formulate the following boundary value problem () () () () ( ) () 0 0 , 0 , u u L x x f u x k dx du x u dx du x a dx d = = + + by the weighted residual method. 2. Formulate the following boundary value problem () () () ( ) ( ) () () () () () 0 0 , , 0 , 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 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. After obtaining the weighted residual formulation, approximate it by () () () () = = = = n i i i n j j j x w x w x u x u 1 1 , ψ φ where w is an arbitrary weighting function, and obtain a discrete problem f Ku = in terms of a , k , f , , φ j , ψ , and L. That is, find the i-j component of K and i component of f.

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Review1_98F - Review Problems for Midterm Examination MEAM...

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