What do the integral, nabla, and contour integral symbols mean?

[The riddler]

1. Hi, I am learning calculus off the interenet so that i may learn more advanced physics equations, but sadly I am being held back because i cannot find the meaning of the symbols without the explanation being based around some seemingly random equation like
∫ab x2 dx = b3/3 − a3/3 + blah blah Blah. So below I am going to post a few symbols that i want to learn and i don't understand, also can someone to explain to me on this youtube
what this guy is talking about in from 1:42 too 4:40. Please post the meaning of whichever one you can and thank you in advance .



2. ∫
∇
∮

 

[jgens]

Well, we can certainly explain what each of these symbols mean but unless you have the requisite mathematical knowledge, it won't help you very much. I would recommend getting a good calculus book to learn these things - if you want to do advanced physics, you need to know calculus very well.

∫ is called the integral sign and there are a lot of ways to define it. Perhaps the most common way is by Riemann or Darboux sums (the latter are easier to understand). You can find a fairly superficial treatment of the concept here:

http://en.wikipedia.org/wiki/Integral

∇ is called the del operator (it's a differential opperator). However, I you haven't encountered integrals before, you probably shouldn't be working with the del operator. If you're really inclined a definition is given here:

http://en.wikipedia.org/wiki/Del

From the video, it sounds like you're having difficulty with the limit concept. Intuitively, the limit of a function as x -> a is the value that the function approaches for x arbitrarily near a. For example, if f(x) = x/x, f(0) is undefined while lim (x -> 0) f(x) = 1.

It sounds like you really do need to get a good calculus book and learn these things. It won't do you much good to only get a superficial understanding of the concepts, especially if you want to pursue upper level physics.

 

[The riddler]

Yeah your probably right, when i first saw calculus i tried to relate it to the algebra I've learned but Calculus seems to have something to it that seems quite alien to me that i have not come across it before. Thanks jgens.

 

[queenofbabes]

Yes, I think you need a good calculus book for beginners, starting with differentiation and integration. If you're seeing del operators in the same place it's probably too difficult for you...for now.