NE 217- Midterm Exam Guide - Comprehensive Notes for the exam ( 400 pages long!)

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Step 3: evaluate x x with taylor series expansion x x x. Classification of 2nd order pdes ua xx ub xy uc yy uuuyxf x. Determine eigenvalues and eigenfunctions: > 0 complex roots, = 0 repeated roots, < 0 real roots. Use chain rule to evaluate partial derivations r x u x u t u s s t u r r t u r u s s x. Example find displacement u(x,t) for a string with fixed ends released from rest with c = 1 and l = 1 xf. 1 n ea n n x eb n n x sin n y. Sturm liouville eigenvalue problem xp d dx d dx xq x. Step 2 express eigenvalue problem in slp form xp d dx d dx xq x. 0 x x a. Step 3 check sign of using rayleigh quotient d p dx b a. 0 x x xq x a.

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