Domain 06 · Mathematics Codex
Analysis & Calculus
The rigorous mathematics of limits, continuity, and change — from Newton and Leibniz to the foundations of modern physics.
Scope
Real analysis, complex analysis, functional analysis, measure theory, ordinary differential equations (ODEs), partial differential equations (PDEs), Fourier analysis, harmonic analysis, variational calculus.
Calculus is the language of change. Every differential equation describing physical law — from Newton's mechanics to Maxwell's electromagnetism to Schrödinger's quantum mechanics — is a product of analysis. The Kerala school (14th–16th century CE, India) developed infinite series expansions for sine, cosine, and π that precede Newton's and Leibniz's calculus by 250 years — a story this codex tells in full.
Entries in this domain
Build status: This domain is in active build. Live entries are marked below. All other entries are planned and pending — see build status for the full picture.
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Limit
Pending
The value that a function approaches as its input approaches some value — the foundational concept of calculus.
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Derivative
Pending
The instantaneous rate of change of a function — the central operation of differential calculus.
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Integral
Pending
The accumulation of quantities over a continuous range — the central operation of integral calculus, and the inverse of differentiation.
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Series
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The sum of a sequence of terms — convergent series underlie calculus, physics, and the Kerala school's discoveries 250 years before Newton.