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Continuous change is studied mathematically through calculus, a branch of mathematics focused on how quantities vary and accumulate. Its two main branches are differential calculus, which examines instantaneous rates of change and tangent slopes, and integral calculus, which measures accumulation, such as areas under curves and distance traveled. These branches are connected by the fundamental theorem of calculus, which establishes differentiation and integration as inverse processes. Calculus describes changing behavior using limits, derivatives, and integrals. Limits provide a rigorous way to analyze what happens as values approach a point, while derivatives quantify instantaneous change and integrals determine total accumulation. Developed independently by Isaac Newton and Gottfried Wilhelm Leibniz in the seventeenth century, calculus is widely used in science, engineering, economics, biology, and other fields to model continuous processes and solve differential equations.
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