# Toronto Math Forum

## APM346-2015F => APM346--Home Assignments => HA7 => Topic started by: Victor Ivrii on November 01, 2015, 05:10:06 PM

Title: HA7-P4
Post by: Victor Ivrii on November 01, 2015, 05:10:06 PM
Problem 4

http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter5/S5.2.P.html#problem-5.2.P.4 (http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter5/S5.2.P.html#problem-5.2.P.4)
Title: Re: HA7-P4
Post by: Yumeng Wang on November 04, 2015, 04:46:40 PM
Solution for a(i) is attached. Please correct me if I am wrong.
Title: Re: HA7-P4
Post by: Yumeng Wang on November 04, 2015, 04:54:46 PM
a(ii)
Title: Re: HA7-P4
Post by: Yumeng Wang on November 04, 2015, 05:05:43 PM
Whole solution for part b is attached.
Title: Re: HA7-P4
Post by: Yeming Wen on November 05, 2015, 04:20:34 PM
Solution for a(i) is attached. Please correct me if I am wrong.

Maybe the transform for $e^{-\frac{ax^2}{2}}$ should be $\sqrt{\frac{2\pi}{a}}e^{-\frac{k^2}{2a}}$ instead of $\sqrt{\frac{2\pi}{a}}e^{-\frac{ak^2}{2}}$?
Title: Re: HA7-P4
Post by: Victor Ivrii on November 05, 2015, 04:25:43 PM
Maybe the transform for $e^{-\frac{ax^2}{2}}$ should be $\sqrt{\frac{2\pi}{a}}e^{-\frac{k^2}{2a}}$ instead of $\sqrt{\frac{2\pi}{a}}e^{-\frac{ak^2}{2}}$?
Indeed
Title: Re: HA7-P4
Post by: Yumeng Wang on November 05, 2015, 04:49:45 PM
I think I am also wrong for part d. But general formula is right, just do derivative to get final answer. ;)