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Theorem

Gradient Theorem

Analysis

The gradient theorem, also known as the fundamental theorem of calculus for line integrals, states that a line integral through a gradient field can be evaluated simply by evaluating the original scalar field at the two endpoints of the curve. It generalizes the second fundamental theorem of calculus from the real line to curves in a plane or in space. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Classification
Statement Form
Identity or Equation 1
Connections

Has Statement Form

Equation, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Identity, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Source Gradient Theorem (Wikipedia)
Sources
1. Gradient Theorem (Wikipedia)
In Branch: Calculus, Lead sentence
Quote, In Branch: Calculus, Lead sentence
theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field
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