Discrete exterior calculus

Discrete exterior calculus is a way to understand and calculate complicated things called "differential forms" using simple shapes like triangles and squares.

Imagine you have a flat sheet of paper, and you want to measure how much it bends or curves. You can do this by using differential forms, which give you a way to measure these changes. But differential forms can be hard to work with, especially when the surface is curved in multiple directions at once.

That's where discrete exterior calculus comes in. Instead of trying to measure the surface using the whole sheet of paper, we break it up into smaller shapes like triangles and squares that we can easily work with. We can then use these shapes to approximate the differential forms and make calculations.

For example, if we have a curved surface with a dip in the middle, we can use a triangle to measure how much it dips. We can then use these measurements to figure out other important things about the surface, like its area or how much it bends in different directions.

Discrete exterior calculus is useful in many fields, like physics and engineering, where we need to understand and work with complicated shapes and surfaces. By breaking them down into smaller, simpler parts, we can make calculations and solve problems that would otherwise be very difficult.