What does 'dx' mean and how does it relate to calculus and physics?

[Dolton]

Hey guys. I've started studying Physics at home, but only the theory side with a little mathematics. So i would like to try, if i can, to introduce a little calculus to my work. But the problem is i find calculus a mind boggle, i understand All the GCSE math that i did. Could someone explain to me what "dx" means in this equation? displacement perhaps? i don't know. and possibly explain the equation please?

b
$$\int$$F(x) dx
a

 

[danago]

"dx" usually is a differential, an infinitesimal change in whatever x represents. The integral basically represents adding up heaps of these small quantities multiplied by the function F(x) over some interval [a,b].

Check out this link:

http://mathworld.wolfram.com/RiemannIntegral.html

It briefly explains how the riemann integral is defined.

In terms of actually carrying out the integration, the 'dx' just tells you what variable you need to integrate with respect to; it won't have any direct effect on the calculation itself.

Also, what you have written isn't an 'equation', since there is no equality involved.If you are just starting out with this, perhaps check out these notes:

http://tutorial.math.lamar.edu/Classes/CalcI/IndefiniteIntegrals.aspx

They are one of the best sets of online notes i have ever come across.

 

[Hootenanny]

Welcome to Physics Forums.

For a brief introduction, consider Kurdt's excellent https://www.physicsforums.com/showthread.php?t=213784".

 

[Dolton]

Wow, thanks a lot guys, this is a really helpful community :)

 

[slider142]

I found the following text to be a great introduction to both calculus and basic classical mechanics: Integrated Physics & Calculus by Rex/Jackson. The interrelations between the two subjects are well motivated by examples and you get a good feel for both calculus and physics as each author has his own specialty.