For example, Maxwell’s equations contain upside down triangles. What exactly do they represent?
How does it apply to the real world?
In: 34
The upside triangle (called ‘del’) indicates the gradient.
When you follow del with a dot, it means divergence. When you follow del with an ‘x’, it means curl.
These are all concepts in multi-dimensional calculus. The gradient is simply a list (also called a ‘vector’) of all the partial derivatives of a functions – essentially the slope of the function in the direction of one of the variables. So if you have a function in x, y, z, the gradient would be a list containing the slope of the function in the x direction, the slope of the function in the y direction and the slope of the function in the z direction.
For divergence, think of water gushing out of a faucet. If you imagine a plane through which that water is passing, you want to know how fast/much is passing through that plane. For this, you need to calculate the ‘flux’ of the water stream through the plane and you use the divergence for that.
Curl is similar except it deals in rotation. You’re looking to find out whether the water is rotating – if you were to toss a cork into the water, would it just go one direction or would it spin around?. This is what the curl tells us.
However, because we’re dealing with complicated phenomenon, we’re not representing that water flow as a single number but rather a function which tells us what every bit of water is doing at any given time. Thus, the curl and divergence are themselves functions that tell us what is happening at every point in space.
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