From the probably unique position of (a)someone who's (supposed to be) writing a PhD on Deleuze and Mathematics and (b)someone who spent much of their life ignorant of what calculus was and why it might be important:

>1. Does my ignorance of calculus matter?

>For my understanding of Deleuze, for my

>understanding of philosophy, or for

>anything else?

Important for Deleuze: Yes, because from D&R onwards he bases his logic of difference and problems on concepts drawn directly from modern mathematical analysis (whose foundation is calculus). Without an understanding of analysis I think one can only achieve a vague discursive idea of Deleuze's argument (like most secondary texts). Implicitly Deleuze's -somewhat Badiousian- argument is that philosophical thought needs to take account of the conceptual manouevres contained in mathematical analysis, relating to universality, generality, singularity, if it is to escape various classical images - just as modern analysis finally escaped the long reign of aristotelianism, so must philosophy. The new mode of thought Deleuze is proposing bases itself on the historical thought-events of modern analysis. Briefly, to appreciate the mathematical side deepens your historical and philosophical understanding of what Deleuze is doing.

For an understanding of philosophy: Yes, because the more you look into this the more you will see that every major philosopher has something to say about calculus (even Engels!) - Why? (and this is the answer to the final question): because it is the single most important enabling conceptual mechanism for modern science. Put simply, it provides a mathematical handle on the large majority of physical phenomena which are not rectilinear. It constitutes a singular meeting-point of the problems of physics, mathematics and metaphysics (hence the interest in the 'esoteric history' - Whereas for Badiou mathematics eventually sloughs off all philosophical problematics clinging to it, Deleuze is interested in recovering these metaphysical problems and the relation of mathematics to philosophy and physics that they suggest.)

>2. Is Deleuze's use of calculus a Sokalian

>"intellectual imposture"? Is he right about

>the maths? And does that matter?

No, it's not simply a rhetorical misuse. But it is difficult to read and interpret. It's not an 'example' or an 'illustration' or a 'metaphor' either: deleuze's discussion is about the relationship between history, mathematics, physics and philosophy, from a (french philosophy of science) point of view which attempts to fathom the articulation of different orders (historical order, logical order, epistemological order. Obviously this is something Sokal can't understand. But obviously it doesn't matter if a wilfully myopic pigheaded scientist doesn't get it.

>3. What is calculus for or about anyways?

>Is there a good introduction somewhere that

>will explain it even to me?

It's used to give a formal treatment of problems which involve relationships between continuously varying quantities, ie. almost any physical, economical, astronomical, etc. problem you care to mention. (see Kline book, below, for simplest possible examples)

The problem I've found, as other comments suggest, is that pedagogical texts, even high school ones, never give any conceptual explanation that would be satisfying to a philosopher (which is rather shocking given the historical importance of calculus).

I would recommend firstly the calculus chapter in Kline's 'mathematics in western culture', which is the simplest account I have read of why calculus matters.

Secondly Boyer's 'The Concepts of the Calculus' is a fascinating book on the history (Deleuze read it).

More technically, Bruce Exner's book 'Inside Calculus' is the only academic maths book I have read which seems thoughtful on a conceptual level, and which gives discursive expositions before introducing massive equations; it describes very clearly the modern (epsilon-delta) form of calculus.