1

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?

ankit
  • 2,381

1 Answers1

1

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.

Yes
  • 20,719
  • I would not say calculus is the study of limits. That I would call real analysis. You can do real analysis without calculus and calculus without real analysis. People were doing calculus for over a century before real analysis came along, and there are a variety of modern approaches that aren't based on real analysis (some of which are more similar to how calculus was done before it was "founded" on real analysis). For example, algebraic approaches, non-standard analysis, and synthetic differential geometry. – Derek Elkins left SE May 14 '17 at 10:23
  • @DerekElkins, It makes a point. For me, when I was writing the words I was thinking of that the concept of limit is usually the first introduced major concept in a calculus book. Note that from context my answer should not imply I see calculus as the study of limits. I was just saying this would be better than the original one. – Yes May 14 '17 at 12:03