What Is the Physical Meaning of These Vector Calculus Concepts?

[shermaine80]

Hi,

May i know the physical meaning of the following:

(1) Curl of a vector field A(x,y,z)
(2) divergence of a vector field A(x,y,z)
(3) directional deriative of G(x,y,z)
(4) gradient of a scalar field G(x,y,z)

 

[Tac-Tics]

http://www.math.umn.edu/~nykamp/m2374/readings/divcurl/

 

[HallsofIvy]

Tac-Tics gives possible interpretations of those in a particular application. There is NO general "physical meaning" of a mathematical concept- mathematics is not physics.

 

[maze]

These concepts were originally developed because of physics, and even the purest mathematics student should develop the physical intuition of it, while simultaneously developing the topic rigorously.

If you get a computer with a killer graphics card that can do floating point matrix computations really fast, then it would be stupid to write a program that uses the CPU instead. As humans, we have a killer "graphics card" and "physics card" built into our mind - it would be stupid not to use it.