Cursive big f: "integration", which can be interpreted in two ways. One is "area under the curve" for some part of the curve. Other is "average value of a part of the curve multiplied by the size of that part of the curve". Curve being the function, the graph, f(x), however you wanna call it.
Normal d: "differentiation" (from difference), infinitely small change. Usually used in ratios: df/dx means how much does f(x) change relative to x when you change x a little bit.
Cursive d: "partial", same as normal d but used when working with higher dimensional data like 3D. Can also mean "boundary" of something. Example: boundary of a volume in 3D, like wrapping paper around a box. Or, boundary of such wrapping paper itself, if it's not perfectly connecting.
Omega: just a Greek letter used as a variable, in this case there's a history of it being used as a sort of "density" variable in the field of differential geometry. The college row in the meme is kind of translating the high school row from a function to a 3D volume.