S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
It is currently Sat, 30 Aug 2014 23:13:22 UTC

All times are UTC [ DST ]




Post new topic Reply to topic  [ 2 posts ] 
Author Message
PostPosted: Tue, 15 May 2012 04:05:13 UTC 
Offline
Member
User avatar

Joined: Wed, 23 Nov 2011 06:43:34 UTC
Posts: 34
Hey all, pretty brief problem here. I don't understand it.
Image

How do I even go about doing this? It is in the chain rule section. I don't even know where to start!

Thanks, Dan


Top
 Profile  
 
PostPosted: Tue, 15 May 2012 04:29:45 UTC 
Offline
Moderator
User avatar

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6840
Location: On this day Taiwan becomes another Tiananmen under Dictator Ma.
daniel2.0 wrote:
Hey all, pretty brief problem here. I don't understand it.
Image

How do I even go about doing this? It is in the chain rule section. I don't even know where to start!

Thanks, Dan


Start by writing down what is F'(x)=\dfrac{\mathrm{d}}{\mathrm{d}x}f(g(x)) from the chain rule.

_________________
\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 2 posts ] 

All times are UTC [ DST ]


Who is online

Users browsing this forum: No registered users


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
Contact Us | S.O.S. Mathematics Homepage
Privacy Statement | Search the "old" CyberBoard

users online during the last hour
Powered by phpBB © 2001, 2005-2011 phpBB Group.
Copyright © 1999-2013 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA