HA7-P4

[Victor Ivrii]

Problem 4

http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter5/S5.2.P.html#problem-5.2.P.4

[Yumeng Wang]

Solution for a(i) is attached. Please correct me if I am wrong.

[Yumeng Wang]

a(ii)

[Yumeng Wang]

Whole solution for part b is attached.

[Yeming Wen]

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 $\sqrt{\frac{2\pi}{a}}e^{-\frac{ak^2}{2}}$?

[Victor Ivrii]

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

[Yumeng Wang]

I think I am also wrong for part d. But general formula is right, just do derivative to get final answer.