WorkSheet.Week5

# WorkSheet.Week5 - converge to 1 x 2 x 2 3 x 3 4 x 4(4 3...

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MATH 2930 Summer 2009 Worksheet For Discussion on 10th July Topics covered: EVPs, BVPs, Power Series Solutions Ashivni Shekhawat 1 BVPs And EVPs 1. Solve the following boundary value problem y 00 + 2 y 0 - 3 y = 0; y (0) = 0 ,y 0 (1) = 0 . (1) 2. Find the eigenvalues and eigenfunctions of y 00 - 4 λy 0 + 4 λ 2 y = 0; y (0) = 0 ,y (1) + y 0 (1) = 0 . (2) 2 Power Series 1. Does the following series converge? X n =0 (3 - 4 i ) n n ! (3) 2. Does the following series converge? If yes, then ﬁnd the radius of convergence. What does it
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Unformatted text preview: converge to? 1 + x + 2 x 2 + 3 x 3 + 4 x 4 + ... (4) 3. What are the singular points of the following equation? What is the guaranteed radius of convergence for solutions of the form Σ C n x n and Σ C n ( x-π ) n ? sin( x ) y 00 + cos( x ) y = 0 (5) 4. Solve the following for a n ∞ X n =2 n ( n-1) a n ( x + 2) n-2-x ∞ X n =0 a n ( x + 2) n = 0 (6) 1...
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