polar

SearchAdvancedHelp

(0.001 seconds)

10 matching pages

1: 1.5 Calculus of Two or More Variables

… ►

Polar Coordinates

… ►

1.5.13 $${\nabla }^{2}f=\frac{{\partial }^{2}f}{{\partial x}^2}+\frac{{\partial }^{2}f}{{\partial y}^2}=\frac{{\partial }^{2}f}{{\partial r}^2}+\frac{1}{r}\frac{\partial f}{\partial r}+\frac{1}{r^2}\frac{{\partial }^{2}f}{{\partial \varphi }^2}.$$

ⓘ

Symbols:

$\frac{\partial f}{\partial x}$: partial derivative of $f$ with respect to $x$ , $\partial x$: partial differential of $x$ , $\varphi$: longitude and $r$: radius

Permalink:

http://dlmf.nist.gov/1.5.E13

Encodings:

pMML, png, TeX

See also:

Annotations for §1.5(ii), §1.5(ii), §1.5 and Ch.1

►

Cylindrical Coordinates

… ►

Spherical Coordinates

… ►

1.5.39 $$\frac{\partial (x,y)}{\partial (r,\varphi )}=r\text{(<span class="ltx\_text hilite">polar</span> coordinates)}.$$

ⓘ

Symbols:

$(a,b)$: open interval, $\frac{\partial f}{\partial x}$: partial derivative of $f$ with respect to $x$ , $\partial x$: partial differential of $x$ , $r$: radius and $\varphi$: angle

Permalink:

http://dlmf.nist.gov/1.5.E39

Encodings:

pMML, png, TeX

See also:

Annotations for §1.5(vi), §1.5(vi), §1.5 and Ch.1

…

2: 9.16 Physical Applications

… ►The use of Airy function and related uniform asymptotic techniques to calculate amplitudes of polarized rainbows can be found in Nussenzveig (1992) and Adam (2002). …

3: 36.13 Kelvin’s Ship-Wave Pattern

… ►In a reference frame where the ship is at rest we use polar coordinates $r$ and $\varphi$ with $\varphi =0$ in the direction of the velocity of the water relative to the ship. …

4: 22.18 Mathematical Applications

… ►In polar coordinates, $x=r\cos \varphi$, $y=r\sin \varphi$, the lemniscate is given by $r^2=\cos \left(2\varphi \right)$, $0\le \varphi \le 2\pi$. …

5: 1.9 Calculus of a Complex Variable

… ►

Polar Representation

… ►or in polar form (1.9.3) $u$ and $v$ satisfy …

6: 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 …

7: 18.39 Applications in the Physical Sciences

… ►By (1.5.17) the first term in (18.39.21), which is the quantum kinetic energy operator $T_e$, can be written in spherical coordinates $r,\theta ,\varphi$ as …

8: Bibliography S

… ►

The elliptical microstrip antenna with circular polarization. IEEE Trans. Antennas and Propagation 29 (1), pp. 90–94.

ⓘ

External Links:

FullText

Referenced by:

5th item.

Encodings:

BibTeX

…

9: 1.15 Summability Methods

… ► $A(r,\theta )$ is a harmonic function in polar coordinates (1.9.27), and …

10: 3.5 Quadrature

… ►The steepest descent path is given by $\mathrm{\Im }\left(t-2\sqrt{t}\right)=0$, or in polar coordinates $t=r{\mathrm{e}}^{\mathrm{i}\theta }$ we have $r={\sec }^2\left(\frac{1}{2}\theta \right)$. …