Calculus

Definition

Branch of mathematics studying continuous change through derivatives (rates of change) and integrals (accumulation of quantities)

Examples

• Differential calculus finds the rate of change: if position s(t) = t², then velocity v(t) = ds/dt = 2t. Integral calculus reverses this: ∫2t dt = t² + C.
• Engineers use calculus to design roller coasters, calculating the exact curvatures needed for safe G-forces, optimal speeds at each point, and structural load requirements.

Case Study

Newton and Leibniz independently developed calculus in the late 17th century. Today, calculus underpins GPS navigation, weather prediction, medical imaging, and virtually every engineering discipline.

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Related Terms

Derivative, Integral, Differential Equation, Limit

Antonyms

Arithmetic, Algebra