For example, Maxwell’s equations contain upside down triangles. What exactly do they represent?
How does it apply to the real world?
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In Maxwell’s Equations, they tell you how electric and magnetic fields either push in/out or swirl. If the upside down triangle has a dot, that’s about how it pushes in/out, if it has multiplication symbol then that’s how it swirls. This constitutes complete information about how electromagnetic fields work.
Maxwell’s Equations are compact, abstract formulae that tells us how electromagnetism works at a fundamental scale (classically, at least). It’s like an intricate piece of origami that can be unfolded in innumerable ways. If you want to use them in real life, then you need to know how to unravel them for the specific concrete situation that you’re in. This is where multivariable calculus, partial differential equations, mechanics, statistics, and computer modelling help. With these, you can take the compactified instructions of the Maxwell equations and slowly unwrap them to conform to the constraints that you’re working in in order to deduce concrete conclusions.
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