Can You Master Basic Index Notation in a Weekend?

[synkk]

A week or two ago we went through index notation in class, however I didn't understand it when the lecturer was going through it thus I need to go through it now. I have this weekend to go through it along with other material. Is it possible to go over basic index notation in this short period of time and if so what resources should I use as I have no direct textbook that my lecturers follow

please help, thanks.

edit: I'm talking about vector calculus index notation

 

[jedishrfu]

can you be more specific by showing an example that doesn't seem to make sense?

 

[synkk]

can you be more specific by showing an example that doesn't seem to make sense?

http://en.wikipedia.org/wiki/Levi-Civita_symbol

if you scroll down to "properties" we're doing similar stuff like that, e.g. the identity when n = 3 with the 4 delta symbols, we were asked to prove that and I was baffed :s.

we also are doing some 2d vector index notation

 

[FeDeX_LaTeX]

http://en.wikipedia.org/wiki/Levi-Civita_symbol

if you scroll down to "properties" we're doing similar stuff like that, e.g. the identity when n = 3 with the 4 delta symbols, we were asked to prove that and I was baffed :s.

we also are doing some 2d vector index notation

Are you asking for the proof of this identity?

 

[jedishrfu]

Well some people get confused by the subscript vs superscript notation. In the case of the LeviCivita symbol (a psuedo-tensor) there is no distinction between sub and superscripts so you can use them as needed.

The Einstein notation convention is that when a subscript and a superscript index are the same letter then it is understood that you sum them to get the result:y_j = Aⁱ_jx_i

y₁ = A¹₁ * x₁ + A²₁ * x₂ + A³₁ * x₃

y₂ = A¹₂ * x₁ + A²₂ * x₂ + A³₂ * x₃

y₃ = A¹₃ * x₁ + A²₃ * x₂ + A³₃ * x₃

Check Google for more info on the Levi-Civita symbol...

 

[Jorriss]

Just search for every post by WannabeNewton.

 

[FeDeX_LaTeX]

Just search for every post by WannabeNewton.

Haha, agree with this. He's posted a lot of interesting stuff in the Differential Geometry and SR/GR forums -- his profile is on my friend list if you can't find it.

 

[raxAdaam]

Vector Calculus by P.C. Matthews has an awesome chapter on index notation. I struggled with the notation enormously when it was tangentially introduced during and E&M course because neither the teacher nor the textbook provided sufficient information (for me) or any basic practice problems. Matthews is thorough, concise and has a bunch of problems with solutions at the back. After 2 days playing with it I was able to prove most standard identities. Wish I had had it during that class …