daviddoji/CalculusWithJuliaNotes.jl
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jverzani
2026-06-03 14:34:02 -04:00
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quarto/integral_vector_calculus/line_integrals.qmd
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@@ -302,7 +302,7 @@ The main point above is that *if* the vector field is the gradient of a scalar f
::: {.callout-note icon=false}
## Conservative vector field
If $F$ is a vector field defined in an *open* region $R$; $A$ and $B$ are points in $R$ and *if* for *any* curve $C$ in $R$ connecting $A$ to $B$, the line integral of $F \cdot \vec{T}$ over $C$ depends *only* on the endpoint $A$ and $B$ and not the path, then the line integral is called *path indenpendent* and the field is called a *conservative field*.
If $F$ is a vector field defined in an *open* region $R$; $A$ and $B$ are points in $R$ and *if* for *any* curve $C$ in $R$ connecting $A$ to $B$, the line integral of $F \cdot \vec{T}$ over $C$ depends *only* on the endpoint $A$ and $B$ and not the path, then the line integral is called *path independent* and the field is called a *conservative field*.
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