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Unformatted text preview: Math 334 Lecture #20 § 5.1: Power Series Once a fundamental set of solutions of the associated homogeneous ODE for a linear ODE with nonconstant coefficients like y 00 + xy + 2 y = g ( x ) is found, then a particular solution is found by Variation of Parameters. How are solutions of homogeneous linear ODEs with nonconstant coefficients found? By power series. Review of Power Series. A power series in x with center x is the infinite sum ∞ X n =0 a n ( x x ) n where the a n ’s are real (or complex) numbers. Whenever infinitely many numbers are added together, there is always the question of whether the sum makes sense or not as a number. A power series converges (or makes sense as a number) at x if the sequence of partial sums has a limit: lim m →∞ m X n =0 a n ( x x ) n exists . [Each partial sum is a finite sum which always makes sense.] A power series converges absolutely at x if lim m →∞ m X n =0  a n ( x x ) n  exists ....
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This note was uploaded on 03/08/2011 for the course MATH 334 taught by Professor Smith during the Spring '11 term at Vanderbilt.
 Spring '11
 Smith
 Power Series

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