For example, Maxwell’s equations contain upside down triangles. What exactly do they represent?
How does it apply to the real world?
In: 34
Its the nabla operator. An operator is just a thing that codes an operating.
For example if all you want is to multiply a number a by a number b then you can describe an operator that by definition does this a × b. You can have another number c and you use the operator on it which gives you a × c. Lets call this operator M_a for multiplication. So (M_a)b = a × b. Simple enough.
If your operating is a bit more complicated like take the partial derivitives of a scalar field its a bit painful to write down all the derivitives. We often use a gradient (nabla operator) when we have a force filled. You can often write your force filled up with just a scalar field thats only a number assigned to all points in usually 3D sapce. But a force field assigns vectors to all points in space. So how do we turn numbers into vectors. (It only works with conservative fields. Like gravity or the electricfield.)
So lets say we use an xyz coordinate system. Now our scalar or potential filed P is a function of xyz so P(x,y,z). What we do is this: (dP/dx, dP/dy, dP/dz) we build a vector out of the partial derivitive of P which is exactly the vector of the force at that point. This operation of take the partial derivitives of the function and plug them in a vector is often compressed into symbols like that upside-down triangle.
For a gradient like this grad(P) is often used. There are other useful operations you can do to a filed like a vector filed. Like divergence often used as div(v) or nabla • v or rotation used as rot(v) or nabla × v. They aren’t too difficult to understand but some visualisations are quite helpful. It you are interested look them up.
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