Coordinate systems/Derivation of formulas/Original Copy from Wikipedia

Table from Wikipedia

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Table with the del operator in cylindrical, spherical and parabolic cylindrical coordinates
Operation Cartesian coordinates (x, y, z) Cylindrical coordinates (ρ, ϕ, z) Spherical coordinates (r, θ, ϕ) Parabolic cylindrical coordinates (σ, τ, z)
Definition
of
coordinates
       
       
Definition
of
unit
vectors
       
     
A vector field          
Gradient          
Divergence          
Curl          
Laplace operator          
Vector Laplacian    
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Material derivative[1]

 

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Differential displacement        
Differential normal area          
Differential volume          
Non-trivial calculation rules:
  1.  
  2.  
  3.  
  4.   (Lagrange's formula for del)
  5.  

Original Wikipedia Table

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hidden because it uses the Wikiversity-dysfunctional collapsable template
Table with the del operator in cylindrical, spherical and parabolic cylindrical coordinates
Operation Cartesian coordinates (x, y, z) Cylindrical coordinates (ρ, ϕ, z) Spherical coordinates (r, θ, ϕ) Parabolic cylindrical coordinates (σ, τ, z)
Definition
of
coordinates
       
       
Definition
of
unit
vectors
       
     
A vector field          
Gradient          
Divergence          
Curl          
Laplace operator          
Vector Laplacian     Template:Collapsible section Template:Collapsible section
Material derivative[1]

 

Template:Collapsible section Template:Collapsible section Template:Collapsible section
Differential displacement        
Differential normal area          
Differential volume          
Non-trivial calculation rules:
  1.  
  2.  
  3.  
  4.   (Lagrange's formula for del)
  5.  
  1. 1.0 1.1 Weisstein, Eric W. "Convective Operator". Mathworld. Retrieved 23 March 2011.