How a Multivariable Function Changes with Respect to the Cartesian Coordinates

Suppose $F(x,y,z) \equiv f(x) g(y) h(z)$. This post shows how to calculate a partial derivative of a multivariable function $F(x,y,z)$ with respect to each Cartesian coordinates. The resulting expressions are in spherical coordinates. In previous…

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The Polar Unit Vector

Consider a spherical coordinate system. Let a point be represented by $(r, \theta, \phi)$, in that order. Now that the order of the coordinates is established, I can define unit vectors that form…

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Defining Del in Terms of Cartesian Coordinates

What is Del? In math, the symbol $\vec{\nabla}$ is called “del.” This symbol is defined in terms of Cartesian coordinates. $\vec{\nabla} := \vec{e}_x\frac{\partial}{\partial x} + \vec{e}_y\frac{\partial}{\partial y} + \vec{e}_z\frac{\partial}{\partial z}$ The right side…

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How to Integrate in a Spherical Coordinate System

Review of Integration Integration with Cartesian coordinates is simple. The general form is $\int\int\int f(x,y,z)dxdydz$ in which $f(x,y,z)$ is an arbitrary function of the Cartesian coordinates. However, there may be cases in which integrating with…

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