Definition:Differential Increment of Position Vector
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Definition
Let $\map {\R^3} {x, y, z}$ denote the Cartesian $3$-space.
Let $\tuple {\mathbf i, \mathbf j, \mathbf k}$ be the standard ordered basis on $\R^3$.
Let $\mathbf r$ be the position vector of a point $P$ in $\R^3$:
- $\mathbf r = x \mathbf i + y \mathbf j + z \mathbf k$
The differential increment of $\mathbf r$ is denoted and defined as:
- $\d \mathbf r := \d x \mathbf i + \d y \mathbf j + \d z \mathbf k$
Sources
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {III}$: The Differentiation of Vectors: $3$. Partial Differentiation