# polar coordinates

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## 6 matching pages

##### 1: 1.5 Calculus of Two or More Variables
###### PolarCoordinates
1.5.13 $\nabla^{2}f=\frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{\partial}^{2}f}{{% \partial y}^{2}}=\frac{{\partial}^{2}f}{{\partial r}^{2}}+\frac{1}{r}\frac{% \partial f}{\partial r}+\frac{1}{r^{2}}\frac{{\partial}^{2}f}{{\partial\phi}^{% 2}}.$
###### Spherical Coordinates
1.5.39 $\frac{\partial(x,y)}{\partial(r,\phi)}=r\quad\text{(polar coordinates)}.$
##### 2: 36.13 Kelvin’s Ship-Wave Pattern
In a reference frame where the ship is at rest we use polar coordinates $r$ and $\phi$ with $\phi=0$ in the direction of the velocity of the water relative to the ship. …
##### 3: 22.18 Mathematical Applications
In polar coordinates, $x=r\cos\phi$, $y=r\sin\phi$, the lemniscate is given by $r^{2}=\cos\left(2\phi\right)$, $0\leq\phi\leq 2\pi$. …
##### 4: 36.7 Zeros
There are also three sets of zero lines in the plane $z=0$ related by $2\pi/3$ rotation; these are zeros of (36.2.20), whose asymptotic form in polar coordinates $(x=r\cos\theta,\;y=r\sin\theta)$ is given by …
##### 5: 1.15 Summability Methods
$A(r,\theta)$ is a harmonic function in polar coordinates ((1.9.27)), and …
The steepest descent path is given by $\Im\left(t-2\sqrt{t}\right)=0$, or in polar coordinates $t=re^{i\theta}$ we have $r={\sec}^{2}\left(\frac{1}{2}\theta\right)$. …