Area and volume elements in polar coordinate systems

Area and volume elements in polar coordinate systems - δ r...

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Return Elements in polar coordinate systems Plane polars Here's a picture to show the area element in plane polars: As the radius r increases by a small amount δ r and the angle θ increases by a small amount δθ , the area element that is produced is r δ r δθ . When we turn a sum over such elements into an area integral, the element becomes rdrd θ . Cylindrical polars Here's a picture to show the volume element in cylindrical polars: As the radius r increases by a small amount δ r, and the angle θ increases by a small amount δθ , and the vertical coordinate z increases by a small amount dz the volume element that is produced is r
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Unformatted text preview: δ r δθ δ z. When we turn a sum over such elements into an volume integral, the element becomes rdrd θ dz. Spherical polars Here's a picture to show the volume element in spherical polars: As the radius r increases by a small amount δ r, and the angle θ increases by a small amount δθ , and the angle φ increases by a small amount δφ the volume element that is produced is r 2 sin θ δ r δθ δφ . When we turn a sum over such elements into an volume integral, the element becomes r 2 sin θ drd θ d φ . Return...
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  • Spring '11
  • Ricardo
  • Coordinate system, Spherical coordinate system, Polar coordinate system, Cylindrical coordinate system, radius r increases

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