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Coordinate_Transformation_Formula_Sheet

Coordinate_Transformation_Formula_Sheet - Coordinate...

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1 Coordinate Transformation Formula Sheet Table with the Del operator in rectangular, cylindrical, and spherical coordinates Operation Cartesian coordinates (x,y,z) Cylindrical coordinates ( ρ , φ ,z) Spherical coordinates (r, θ , φ ) Definition of coordinates ˆ ˆ ˆ cos sin ˆ ˆ ˆ sin cos ˆ ˆ φ φ φ φ φ = + = − + = ρ x y x y z z Definition of unit vectors ˆ ˆ ˆ ˆ sin cos sin sin cos ˆ ˆ ˆ ˆ cos cos cos sin sin ˆ ˆ ˆ sin cos θ φ θ φ θ θ φ θ φ θ φ φ φ = + + = + = − + r x y z θ x y z x y ˆ ˆ ˆ sin cos ˆ ˆ ˆ cos sin ˆ ˆ θ θ θ θ φ φ = + = = r ρ z θ ρ z
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2 A vector field Gradient Divergence Curl Laplace operator Vector Laplacian Differential displacement Differential normal area
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3 Differential volume Non-trivial calculation rules: 1. 2. 3. 4. 5.
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