Calculus

The mathematical study of continuous change through differentiation and integration.

• Founders: Isaac Newton, Gottfried Leibniz
• limits formalize the concept of approaching a value, grounding both derivatives and integrals
• The fundamental theorem of calculus unifies differentiation and integration as inverse operations
• derivatives measure instantaneous rate of change; integrals accumulate quantities over intervals
• Multivariable calculus extends to gradients, divergence, and curl in higher dimensions
• Taylor series approximates functions as infinite polynomials around a point
• Foundation of differential equations, optimization, physics, and fourier transform
• Related: linear algebra, topology, probability, statistics, relativity