What is Calculus? A Physics Perspective
The geometry of curves obsessed mathematicians long before Newton hid from the plague at Woolsthrope Manor, where the seeds of the calculus took root. Before the late seventeenth century, finding slopes, areas, and volumes under curves was an entirely ad hoc affair. Unlike the lines of squares, triangles, rectangles, and cubes, height and/or depth doesn’t remain constant over any measurable length of curved lines, making calculations difficult. Although Newton and many others have conceptualized the foundations of calculus in more physics-like terms, it became a formalized system so effective in geometric analysis that it’s easy to mistake the study of mathematical change (calculus) and the geometry of curves as one in the same. This is not the case. Calculus is the study of continuously changing mathematical functions. A function, as you should know, is an expression of a variable(s) in terms of one or more others—e.g., Y=X ^2, Z=CV^2dx (^ means raised to some power). Cont...