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Calculus

The branch of mathematics devoted to the rigorous study of continuous change and accumulation — built on differentiation, which measures instantaneous rates of change, and integration, which computes accumulated quantities — is calculus.

Overview

Developed independently in the late seventeenth century by Isaac Newton and Gottfried Wilhelm Leibniz, calculus was one of the most consequential intellectual breakthroughs in the history of science. The Fundamental Theorem of Calculus, which establishes that differentiation and integration are inverse processes, unified fragmented geometric and algebraic techniques into a single coherent framework.

Why it matters

Newton applied calculus to formulate his laws of motion and universal gravitation, demonstrating that the same mathematical language could describe both a falling apple and a planetary orbit — fundamentally reshaping humanity's understanding of the natural world. Today calculus underlies classical mechanics, electromagnetism, thermodynamics, quantum theory, control systems, and models of population growth and drug absorption.

Where it leads

• Algebra
• Limit

Related concepts

• MathematicslogicalCalculus is a core subfield of mathematics built on the foundations of algebra and geometry
• PhysicsappliedClassical mechanics, electromagnetism, and quantum mechanics are all formulated in the language of calculus
• EconomicsappliedMarginal analysis, optimization, and dynamic modeling in economics all rely on calculus