Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Every text that I read starts by defining differentiation then integration... but does anyone know if there is one that goes the other way? Also is there any harm in taking this approach.... to me, the current approach is only done because it has always been this way. I say this because I believe that this approach would allow a neater flow of logic in teaching calculus.

share|cite|improve this question
I think the idea behind this is that differentiation is usually far easier than integration and allows the practical introduction of limits easier. – George V. Williams Jan 19 '13 at 21:12
How would you integrate by parts without differentiation? Too much trouble, I think. – Git Gud Jan 19 '13 at 21:13
Apostol's Calculus text books go through integration before differentiation. – Mike B Jan 19 '13 at 21:37
up vote 2 down vote accepted

Richard Courant's Differential and Integral Calculus discusses the integral before differentiation.

share|cite|improve this answer

as Mike noted: Apostol, Calculus (1967) begins with integration.

But then, later, derivatives are defined in the usual way, not somehow obtained as anti-integral.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.