Unformatted text preview: y ( x )] 2 are both solutions of y 00 + p ( x ) y +2 y = 0. Find y ( x ) and the values of p ( x ) for which this is possible. 6. We will show that Z ∞∞ δ ( xa ) f ( x ) dx = f ( a ) . Let us assume that f has a Taylor series expansion about the point x = a . Consider two continuous sequences that approach the δ function: δ ± = 1 √ π± e( xa ) 2 /± δ ± = ± 1 / (2 ± )  xa  < ±  xa  ≥ ± . In both cases, if you compute Z ∞∞ δ ± ( xa ) f ( x ) dx for ± 6 = 0 the result is not f ( a ) but instead f ( a ) with some corrections. Estimate the ﬁrst nonvanishing correction for each form of δ ± ....
View
Full
Document
This note was uploaded on 03/16/2010 for the course MAE 294b taught by Professor Young,w during the Fall '08 term at UCSD.
 Fall '08
 Young,W

Click to edit the document details