M334Lec20

# M334Lec20 - Math 334 Lecture #20 5.1: Power Series Once a...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

## This note was uploaded on 11/29/2011 for the course MATH 334 taught by Professor Dallon during the Fall '08 term at BYU.

### Page1 / 3

M334Lec20 - Math 334 Lecture #20 5.1: Power Series Once a...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online