daviddoji/CalculusWithJuliaNotes.jl
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jverzani
2025-07-27 15:26:00 -04:00
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quarto/integral_vector_calculus/review.qmd
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# Quick Review of Vector Calculus
# Quick review of vector calculus
{{< include ../_common_code.qmd >}}
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$$
The generalization to $n>2$ is clear - the partial derivative in $x_i$ is the derivative of $f$ when the *other* $x_j$ are held constant.
The generalization to $n>2$ is clear---the partial derivative in $x_i$ is the derivative of $f$ when the *other* $x_j$ are held constant.
This may be viewed as the derivative of the univariate function $(f\circ\vec{r})(t)$ where $\vec{r}(t) = p + t \hat{e}_i$, $\hat{e}_i$ being the unit vector of all $0$s except a $1$ in the $i$th component.