# Chapter 1 - Fundamentals

**The Calculus**

Calculus is a branch of mathematics which uses derivative to analyze the way in which the values of a function vary. Developed on 17th century, Calculus has now applications almost in all areas of human endeavor: engineering, physics, business, economics, astronomy, chemistry, biology, psychology, sociology, etc. Sir Isaac Newton (1642 – 1727) and Gottfried Wilhelm Leibniz (1646 – 1716), working independently from each other, developed the Calculus in connections with their work. Newton used Calculus in finding the velocity of a moving body, the work done by force and the centroid of mass of a body. Leibniz on the other hand focused on geometric calculation like finding the tangent and normal to a curve, area bounded by two or more curves, and volume of a solid. Leibniz is the one who initiated the modern notation of *dx* and ∫.

**Differential Calculus**

Calculus is divided into 5 major branches namely: Differential Calculus; Integral Calculus; Differential Equations; Calculus of Variations; and Calculus of Errors. As for this section, we are only concerned with the Differential Calculus. Differential Calculus is a branch of Calculus involving application such as the determination of maximum and minimum points and rate of change.