curl ♦ One matching page ♦ SearchAdvancedHelp (0.000 seconds) One matching page 1: 1.6 Vectors and Vector-Valued Functions … ►The curl of 𝐅 is ► 1.6.22 curl 𝐅 = ∇ × 𝐅 = | 𝐢 𝐣 𝐤 ∂ ∂ x ∂ ∂ y ∂ ∂ z F 1 F 2 F 3 | = ( ∂ F 3 ∂ y − ∂ F 2 ∂ z ) 𝐢 + ( ∂ F 1 ∂ z − ∂ F 3 ∂ x ) 𝐣 + ( ∂ F 2 ∂ x − ∂ F 1 ∂ y ) 𝐤 . ⓘ Defines: curl : of vector-valued function Symbols: det : determinant, ∂ f ∂ x : partial derivative of f with respect to x , ∂ x : partial differential of x , z : variable, 𝐢 : unit vector, 𝐣 : unit vector, 𝐤 : unit vector and F j : vector function components Permalink: http://dlmf.nist.gov/1.6.E22 Encodings: pMML, png, TeX See also: Annotations for §1.6(iii), §1.6(iii), §1.6 and Ch.1 … ► 1.6.27 ∇ ⋅ ( ∇ × 𝐅 ) = div curl 𝐅 = 0 , ⓘ Symbols: curl : of vector-valued function and div : divergence of vector-valued function Permalink: http://dlmf.nist.gov/1.6.E27 Encodings: pMML, png, TeX See also: Annotations for §1.6(iii), §1.6(iii), §1.6 and Ch.1 … ► 1.6.29 ∇ × ( ∇ f ) = curl grad f = 0 , ⓘ Symbols: curl : of vector-valued function and grad : gradient of differentiable scalar function Permalink: http://dlmf.nist.gov/1.6.E29 Encodings: pMML, png, TeX See also: Annotations for §1.6(iii), §1.6(iii), §1.6 and Ch.1 … ► 1.6.34 ∇ × ( ∇ × 𝐅 ) = curl curl 𝐅 = ∇ ( ∇ ⋅ 𝐅 ) − ∇ 2 𝐅 . ⓘ Symbols: curl : of vector-valued function Permalink: http://dlmf.nist.gov/1.6.E34 Encodings: pMML, png, TeX See also: Annotations for §1.6(iii), §1.6(iii), §1.6 and Ch.1 …