One of the reasons why I hate, generally speaking, popular histories especially on the West vs. East dichotomy (*cough* Tom Holland, even if I own some of his works as a good historian should/would) is that it often reiterates bad history from 100 years ago and presents an "us" vs. "them" narrative. Yeah, until the rise of new studies in Islamic History, starting in the 1970s, the old caricature was that of an Orientalist flavor -- The Muslims were a dead civilization, brutal and oppressive, mischievous, but clever. That last 40 years of scholarship has completely overturned this mode of scholarship, hell, it wasn't until the 1970s when historians finally realized the Muslims were a very enlightened, tolerant, and not overly oppressive civilization that very rarely conquered through the old "Convert or Die" motto.
The rediscovery of Abu Ali al-Hasan ibn al-Haytham, a great Muslim mathematician during the Abbasid "Golden Age", really was the first to create the systems and foundations for modern calculus.
Here is a brief college/university oriented paper on him (not academic, but it gets the point across of who he was and his contributions). If you have access to JSTOR you can access a very good academic article by Dr. Victor J. Katz, "Ideas of Calculus in Islam and India,"
Mathematics Magazine, Vol. 68, No. 3 (Jun., 1995), pp. 163-174.
Since I will naturally cover the Golden Age after I discuss having fought a civil war (in-game, I know, a rare in-game post) I was setting the stage for a more modest overview of Islamic accomplishments in art, science, and mathematics. As a historian, I generally like to give credit where credit is due. Islamic mathematicians created 'modern' calculus before Leibniz or Newton.