Calculus is a branch of mathematics that focuses on the study of change and motion. Its foundation lies in the understanding and calculation of derivatives and integrals of functions. Divided into two main branches, differential calculus and integral calculus, it provides a framework for analyzing the dynamic behavior of functions and their applications in various fields of science and engineering.
Differential calculus concentrates on the concept of a derivative, which represents an instantaneous rate of change. It allows us to understand the behavior of function values and predict outcomes. Integral calculus, on the other hand, focuses on the accumulation of quantities and the computation of areas and volumes. The fundamental theorem of calculus connects these two branches, establishing a link between derivatives and integrals.
From understanding the motion of celestial bodies to predicting the behavior of electrical circuits, the applications of calculus are diverse and have shaped the progress of human knowledge for centuries.