Toronto Math Forum
Welcome,
Guest
. Please
login
or
register
.
1 Hour
1 Day
1 Week
1 Month
Forever
Login with username, password and session length
News:
Home
Help
Search
Calendar
Login
Register
Toronto Math Forum
»
APM346-2016F
»
APM346--Lectures
»
Chapter 8
»
Typo
« previous
next »
Print
Pages: [
1
]
Author
Topic: Typo (Read 2428 times)
Luyu CEN
Jr. Member
Posts: 12
Karma: 0
Typo
«
on:
November 23, 2016, 04:26:33 PM »
http://www.math.toronto.edu/courses/apm346h1/20169/PDE-textbook/Chapter8/S8.1.html#mjx-eqn-eq-8.1.9
If we follow from equation(7)
http://www.math.toronto.edu/courses/apm346h1/20169/PDE-textbook/Chapter8/S8.1.html#mjx-eqn-eq-8.1.7
(9) should be
\begin{equation}
\sin^2(\phi)
\Phi'' +\sin(\phi)\cos(\phi)\Phi' = -\bigl(l(l+1)\sin^2(\phi) -m^2\bigr)\Phi,
\end{equation}
instead of
\begin{equation}
\sin^2(\phi)
\Phi'' +2\sin(\phi)\cos(\phi)\Phi' = -\bigl(l(l+1)\sin^2(\phi) -m^2\bigr)\Phi,
\end{equation}
There will be a coefficient 2 if we substitute $\Phi(\phi)=L(\cos(\phi))$ into the equation and use the chain rule to get its derivatives but I think not now.
Logged
Victor Ivrii
Administrator
Elder Member
Posts: 2607
Karma: 0
Re: Typo
«
Reply #1 on:
November 24, 2016, 06:00:41 AM »
Thanks. There are also more serious omissions. Corrected.
Logged
Print
Pages: [
1
]
« previous
next »
Toronto Math Forum
»
APM346-2016F
»
APM346--Lectures
»
Chapter 8
»
Typo