"This seminal project will fundamentally change the way that we think about calculus in relation to differentials and integrals from the combined perspectives of the mind, nature, society, and culture, with enormous implications for the human future and what I originally called its post-human fate." - the author This is a milestone book on calculus, in which the author exposes the reader to the definition and history of calculus, branching into integrals and differentials, its diverse aspects, the debates, arguments and controversies surrounding it, and so on; he then selectively picks up the dialectic relationship between differentials and integrals; and goes on to synthesize an entirely new body of knowledge - The Conversional Theory of Calculus (TCTC). TCTC comprises forty-one major theses, encompassing the relationship between method, structure, process, agency and outcome. The author has dissected the dialectic contexts of differentials and integrals from the perspectives of the mind, nature, society and culture, which pave the way for further enquiry and the need to transcend them, finally leading to the eventual postulation of the TCTC theses. With the approach, focus and the subject matter, this book will attract those who have an interest in areas as diverse as science, engineering, economics, algebra, geometry, mathematical analysis, heuristics, population dynamics, finance, physics, non-standard analysis, differential ecology, medicine, topology, logic, and cosmology, as well as calculus.