##### The Fundamental Theorem for Gradients
c.m.ic.ftg

\[ {\int_{\bf a}^{\bf b}}_{\cal P} ({\boldsymbol \nabla} T) \cdot d{\bf l} = T({\bf b}) - T({\bf a}). \label{Gr(1.55)} \]

Corollary 1: \(\int_{\bf a}^{\bf b} ({\boldsymbol \nabla} T) \cdot d{\bf l}\) is independent of the path taken from \({\bf a}\) to \({\bf b}\).

Corollary 2: \(\oint ({\boldsymbol \nabla} T) \cdot d{\bf l} = 0\) since the beginning and end points coincide.

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Author: Jean-Sébastien Caux

Created: 2022-03-24 Thu 08:42