We have heard it a ton of times that Calculus is the study of change and we know that change is depicted by curves. So, can we safely conclude that Calculus is the study of curves?
But it appears that it is Geometry which is the study of curves. So, what exactly is the study of curves called?
No, it is inaccurate. The proposition that calculus is the study of curves would be more okay if the word "is" becomes "originates from". Still, the revised form only includes differential calculus; integral calculus thinking appeared early in the Archimede's time. The problem to find the slope of the tangent line at a point of a given curve would be an origin of differentiation.
Calculus has so many crazy unexpected developments and generalizations, theoretical and applied. Paul Halmos once said in some writing of his that (rephrased) there is no criterion to decide what material a calculus book should contain; for me this implies that "calculus" is an indefinite-to-a-certain-degree proper name.
I would say it would be even more to the point if one says instead that calculus is the study of limits; this at least contains much more modern sense.