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polar coordinates

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1: 1.5 Calculus of Two or More Variables
Polar Coordinates
1.5.13 2 f = 2 f x 2 + 2 f y 2 = 2 f r 2 + 1 r f r + 1 r 2 2 f ϕ 2 .
Cylindrical Coordinates
Spherical Coordinates
1.5.39 ( x , y ) ( r , ϕ ) = r (polarcoordinates) .
2: 36.13 Kelvin’s Ship-Wave Pattern
In a reference frame where the ship is at rest we use polar coordinates r and ϕ with ϕ = 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 ϕ , y = r sin ϕ , the lemniscate is given by r 2 = cos ( 2 ϕ ) , 0 ϕ 2 π . …
4: 36.7 Zeros
There are also three sets of zero lines in the plane z = 0 related by 2 π / 3 rotation; these are zeros of (36.2.20), whose asymptotic form in polar coordinates ( x = r cos θ , y = r sin θ ) is given by …
5: 1.15 Summability Methods
A ( r , θ ) is a harmonic function in polar coordinates ((1.9.27)), and …
6: 3.5 Quadrature
The steepest descent path is given by ( t - 2 t ) = 0 , or in polar coordinates t = r e i θ we have r = sec 2 ( 1 2 θ ) . …