DiffEq PE2

# DiffEq PE2 - Name Section No 1 2 3 4 5 6 7 II 10 10 20 10...

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Name: Section No. 110.302 Diferential Equations December 10, 2007 Practice Final Exam One sheet (2 sides, 8 1 2 × 11) of handwritten notes may be used during this exam. No books, calculators or other materials are permitted. This exam contains 9pages and has a total of 140 points .T im e :3hou r s . Please put your name on the top of each page. 1 10 2 10 3 20 4 10 5 20 6 20 7 20 II 30 Express all answers using real numbers and real functions only. (You may use complex numbers in your work, but 1 should not appear in your answer.) To receive full credit you must show all o± your work and write your answers in the indicated places.

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Name: page 2 1. (20 points) Consider the matrix A = ab b a (a) (5) Calculate A 1 Answer: (b) (5) Find the eigenvalues and eigenvectors of A . Answer: (c) (5) Find a matrix T and a diagonal matrix D so that T 1 AT = D . Answer: (d) (5) Calculate e A . Answer:
Name: page 3 2. (10 points) Consider the system dx 1 dt = ax + by dx 2 dt = bx ay (a) (5 pts)

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• Spring '06
• Zelditch
• Eigenvalue, eigenvector and eigenspace, Recurrence relation, Complex differential equation, Frobenius method, Bessel function

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DiffEq PE2 - Name Section No 1 2 3 4 5 6 7 II 10 10 20 10...

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