According to Wikipedia, the Circle of Confusion is this:
Not sure about your intent, if it is a question about CoC or not? It is not calculus, but it is math (mostly multiplication and division), which is often used to describe how the physical world works. Note the Wikipedia article on Circle of Confusion has several references back into the 1800s (basically, regarding camera lenses, it has always been known). It is how knowledgeable people have learned to discuss and predict what happens. Engineers and medical doctors and plumbers all have their own terms for things.
Circle of Confusion is how large the tiniest theoretical point source (of zero dimension) actually appears to us when it is not in good focus. Like perhaps a photo of a star in the night sky, but it is a theoretical concept. The star is so far away, so it should be infinitesimal size in our image, but if not in good focus, it appears as a larger blob, of size called CoC. How large is a measure of misfocus.
CoC is NOT the size of any misfocused blob in our photo. CoC is specifically the size of a misfocused point source, which otherwise should be of zero dimension.
CoC is important detail when discussing math of focus, esp including Depth of Field. In cameras, how much this CoC is actually visible to our eye depends also on the degree of print enlargement, so film size or sensor size affects what CoC diameter our eye is likely to see (to see it larger than the tiniest zero point size).
In Depth of Field, focus is of course only at one exact point. At greater or lesser distance than exact focus, focus error grows. Depth of Field computes near and far limits where we finally see and object to the degree of out of focus. Depth of Field is NOT a hard limit, it just computes where CoC becomes visible to our normal eyesight, in a standard print size (considered 8x10 inches viewed at 10 inches). Different enlargements of course computes different numbers and different CoC and different DOF numbers. And of course, there is no actual difference in a bit farther or a bit closer than the DOF number. Misfocus just gradually grows larger.
Carl Zeiss was an extremely important lens maker in Germany before WWII. His notion was CoC of 1/1730 of the film diagonal was the visible CoC limit (takes into account the standard print enlargement). Today, for 35mm film or full frame sensors, for DOF calculations, we call CoC to be 0.03 mm (for full frame. For DX, we call it 0.02 mm, because smaller DX has to be enlarged 1.5x more). This means that at the standard print enlargement (8x10 inches viewed at 10 inches), our eye can recognize a 0.03mm or 0.02mm blob to be larger than the tiniest zero point size. We then declare that to NOT be in good focus.
The purpose of the DOF charts is so we don't have do this math ourself. But for best use, we do still need to know that DOF certainly also depends on degree of print enlargement. In practice, we eagerly learn how (what factors) to increase or decrease DOF, more so than trying to assign specific DOF distance numbers.