History of Calculus: Newton & Leibnitz Discoveries & Controversies

[ynuo]

I am looking for books that can help me to answer the following questions.

1. How Newton and Leibnitz independently invent calculus.
2. What were the controversies that followed.
3. How did the two theories continue to evolve? Did one theory win over the other?

Can you please recommend any.

 

[HallsofIvy]

Try a "google" on "Leibniz + Newton". I found a number of sites.

 

[ynuo]

Is there a companion that I can use to complement "The origins of the infinitesimal Calculus" by Margaret Baron. I am having trouble following the ideas in Baron on the development of Calculus by Newton and Leibnitz.

Thanks a lot.

 

[arildno]

If you want a good rough idea of the difference in ideas,
Newton was EXPLICIT in stating that in differentiation, we were finding the limiting expression of a fraction, and not that the derivative should be regarded as a fraction between infinitesemal quantities (he regarded that as meaningless)

Leibniz, however, used infinitesemals freely.

Neither were particularly clear with what they meant by "limit"; the precise definition of this belongs to mathematicians from Cauchy, Bolzano and onwards 8in particular Weierstrass).

 

[ynuo]

Thank you very much for your reply and your help. Actually, there is a chapter devoted to the Mathematics of Newton and Leibniz in M. Baron's book the first edition. It is chapter 7. I was wondering if I can find another book to help me understand this chapter.