Infinitesimal calculus is a branch of mathematics that focuses on the study of change and motion. It involves two main concepts: differentiation, which deals with rates of change and slopes of curves, and integration, which concerns the accumulation of quantities and areas under curves. These concepts help in understanding how things vary and how to calculate total quantities from their rates. Developed in the 17th century by mathematicians like Isaac Newton and Gottfried Wilhelm Leibniz, infinitesimal calculus has become essential in various fields, including physics, engineering, and economics. It provides tools for solving problems related to motion, growth, and optimization, making it a fundamental part of modern mathematics.