**A New Take on Infinitesimal Calculus with the Limit of Discontinuous Function**

Infinitesimal calculus, developed in the late 17^{th} century, is the key to much of modern science, economics and engineering. Calculus is the mathematical study of change, and since we’re surrounded by change in the natural world, the development of calculus was nothing short of a breakthrough! Until recently, the use of infinitesimals was largely neglected for reasons of mathematical rigor; mathematicians hadn’t discovered the correct treatment of infinitesimals.

This book opens a new way to discontinuous calculus. The author succeeds to generalize limits for arbitrary discontinuous functions and proceeds to define non-differentiable solutions of differential equations. The book, “Limit of discontinuous function” not only discusses the foundations of infinitesimal calculus, but also simplifies the students’ grasp of the central concepts of discontinuity and mathematical nondifferentiable analysis. It starts with concepts of basic math, benefitting even novice students to do such things as to find simple solutions of calculations of infinite sums using author’s concept of generalized limit of discontinuous.

The author opens a door to a new world where functions aren’t just functions or analytical expressions; they illustrate profound concepts at a low level of complexity.

No root of -1? No limit of discontinuous function?

Like as once roots were generalized for negative numbers, I succeeded to generalize limits for arbitrary discontinuous functions. Generalized limit allows for example to define derivative of an arbitrary function and integral of an arbitrary function.