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  2. Volume element - Wikipedia

    en.wikipedia.org/wiki/Volume_element

    In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates. Thus a volume element is an expression of the form = (,,) where the are the coordinates, so that the volume of any set can be computed by ⁡ = (,,).

  3. Potential flow around a circular cylinder - Wikipedia

    en.wikipedia.org/wiki/Potential_flow_around_a...

    The solution for φ is obtained most easily in polar coordinates r and θ, related to conventional Cartesian coordinates by x = r cos θ and y = r sin θ. In polar coordinates, Laplace's equation is (see Del in cylindrical and spherical coordinates):

  4. Vector fields in cylindrical and spherical coordinates

    en.wikipedia.org/wiki/Vector_fields_in...

    Vectors are defined in cylindrical coordinates by (ρ, φ, z), where ρ is the length of the vector projected onto the xy-plane, φ is the angle between the projection of the vector onto the xy-plane (i.e. ρ) and the positive x-axis (0 ≤ φ < 2π), z is the regular z-coordinate. (ρ, φ, z) is given in Cartesian coordinates by:

  5. Spherical coordinate system - Wikipedia

    en.wikipedia.org/wiki/Spherical_coordinate_system

    Once the radius is fixed, the three coordinates (r, θ, φ), known as a 3-tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. The plane passing through the origin and perpendicular to the polar axis (where the polar angle is a right angle ) is called the reference plane (sometimes fundamental plane ).

  6. Cylindrical coordinate system - Wikipedia

    en.wikipedia.org/wiki/Cylindrical_coordinate_system

    The radius and the azimuth are together called the polar coordinates, as they correspond to a two-dimensional polar coordinate system in the plane through the point, parallel to the reference plane. The third coordinate may be called the height or altitude (if the reference plane is considered horizontal), longitudinal position, [1] or axial ...

  7. Solid of revolution - Wikipedia

    en.wikipedia.org/wiki/Solid_of_revolution

    Two common methods for finding the volume of a solid of revolution are the disc method and the shell method of integration.To apply these methods, it is easiest to draw the graph in question; identify the area that is to be revolved about the axis of revolution; determine the volume of either a disc-shaped slice of the solid, with thickness δx, or a cylindrical shell of width δx; and then ...

  8. Volume of an n-ball - Wikipedia

    en.wikipedia.org/wiki/Volume_of_an_n-ball

    The volume of the n-ball () can be computed by integrating the volume element in spherical coordinates. The spherical coordinate system has a radial coordinate r and angular coordinates φ 1, …, φ n − 1, where the domain of each φ except φ n − 1 is [0, π), and the domain of φ n − 1 is [0, 2 π). The spherical volume element is:

  9. Volume integral - Wikipedia

    en.wikipedia.org/wiki/Volume_integral

    It can also mean a triple integral within a region of a function (,,), and is usually written as: (,,).. A volume integral in cylindrical coordinates is (,,), and a volume integral in spherical coordinates (using the ISO convention for angles with as the azimuth and measured from the polar axis (see more on conventions)) has the form (,,) ⁡.