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Vector Calculus Identities Pdf Download

 
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MessagePosté le: Dim 4 Sep - 12:35 (2016)    Sujet du message: Vector Calculus Identities Pdf Download Répondre en citant




Vector Calculus Identities Pdf Download > urlin.us/3zw93























































Vector Calculus Identities Pdf Download

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Third,,,,derivatives[edit].,,,,The,,,dotted,,,vector,,,,in,,,this,,,case,,,B,,,,is,,,differentiated,,,,while,,,the,,,(undotted),,,A,,,is,,,held,,,constant.,,,∂,,S,,{displaystyle,,{scriptstyle,,partial,,S}},,A,,⋅,,d,,ℓ,,=,,−,,{displaystyle,,mathbf,,{A},,cdot,,{rm,,{d}}{boldsymbol,,{ell,,}}=-},,∂,,S,,{displaystyle,,{scriptstyle,,partial,,S}},,A,,⋅,,d,,ℓ,,.,,(1999).,,,,Below,,,the,,curly,,symbol,,,,means,,"boundary,,of".,,where,,,,JA,,,,denotes,,,,the,,,,Jacobian,,,,of,,,,A.,,,,(Errors,,and,,Omissions,,Exempted,,,plus,,Estimations),,Publisher,,Year,,2009,,Language,,English;,,Chinese,,Book,,contributor,,Kok-Wah,,Lee,,,,Xpree,,Jinhua,,Li,,Collection,,opensource,,Notes,,Originally,,available,,at,,public,,domain,,[URL:,,plus-circle,,Add,,Review,,comment,,Reviews,,There,,are,,no,,reviews,,yet.,,The,,,,following,,,,identities,,,,are,,,,important,,,,in,,,,vector,,,,calculus:.,,,,∇,,⋅,,(,,∇,,,,A,,),,=,,0,,{displaystyle,,nabla,,cdot,,(nabla,,times,,mathbf,,{A},,)=0},,∇,,,,(,,∇,,ψ,,),,=,,0,,{displaystyle,,nabla,,times,,(nabla,,psi,,)=mathbf,,{0},,},,∇,,⋅,,(,,∇,,ψ,,),,=,,∇,,2,,ψ,,{displaystyle,,nabla,,cdot,,(nabla,,psi,,)=nabla,,^{2}psi,,},,(scalar,,Laplacian),,∇,,(,,∇,,⋅,,A,,),,−,,∇,,,,(,,∇,,,,A,,),,=,,∇,,2,,A,,{displaystyle,,nabla,,left(nabla,,cdot,,mathbf,,{A},,right)-nabla,,times,,left(nabla,,times,,mathbf,,{A},,right)=nabla,,^{2}mathbf,,{A},,},,(vector,,Laplacian),,∇,,⋅,,(,,ϕ,,∇,,ψ,,),,=,,ϕ,,∇,,2,,ψ,,+,,∇,,ϕ,,⋅,,∇,,ψ,,{displaystyle,,nabla,,cdot,,(phi,,nabla,,psi,,)=phi,,nabla,,^{2}psi,,+nabla,,phi,,cdot,,nabla,,psi,,},,ψ,,∇,,2,,ϕ,,−,,ϕ,,∇,,2,,ψ,,=,,∇,,⋅,,(,,ψ,,∇,,ϕ,,−,,ϕ,,∇,,ψ,,),,{displaystyle,,psi,,nabla,,^{2}phi,,-phi,,nabla,,^{2}psi,,=nabla,,cdot,,left(psi,,nabla,,phi,,-phi,,nabla,,psi,,right)},,∇,,2,,(,,ϕ,,ψ,,),,=,,ϕ,,∇,,2,,ψ,,+,,2,,∇,,ϕ,,⋅,,∇,,ψ,,+,,ψ,,∇,,2,,ϕ,,{displaystyle,,nabla,,^{2}(phi,,psi,,)=phi,,nabla,,^{2}psi,,+2nabla,,phi,,cdot,,nabla,,psi,,+psi,,nabla,,^{2}phi,,},,∇,,2,,(,,ψ,,A,,),,=,,A,,∇,,2,,ψ,,+,,2,,(,,∇,,ψ,,⋅,,∇,,),,A,,+,,ψ,,∇,,2,,A,,{displaystyle,,nabla,,^{2}(psi,,mathbf,,{A},,)=mathbf,,{A},,nabla,,^{2}psi,,+2(nabla,,psi,,cdot,,nabla,,)mathbf,,{A},,+psi,,nabla,,^{2}mathbf,,{A},,},,∇,,2,,(,,A,,⋅,,B,,),,=,,A,,⋅,,∇,,2,,B,,−,,B,,⋅,,∇,,2,,A,,+,,2,,∇,,⋅,,(,,(,,B,,⋅,,∇,,),,A,,+,,B,,,,∇,,,,A,,),,{displaystyle,,nabla,,^{2}(mathbf,,{A},,cdot,,mathbf,,{B},,)=mathbf,,{A},,cdot,,nabla,,^{2}mathbf,,{B},,-mathbf,,{B},,cdot,,nabla,,^{2}mathbf,,{A},,+2nabla,,cdot,,((mathbf,,{B},,cdot,,nabla,,)mathbf,,{A},,+mathbf,,{B},,times,,nabla,,times,,mathbf,,{A},,)},,(Green's,,vector,,identity),,.,,

P.;,,Leighton,,,R.,,A,,,,+,,,,B,,,,=,,,,B,,,,+,,,,A,,,,{displaystyle,,,,mathbf,,,,,,,,4,,,,+mathbf,,,,,,,,3,,,,=mathbf,,,,,,,,2,,,,+mathbf,,,,,,,,1,,,,},,,,A,,,,⋅,,,,B,,,,=,,,,B,,,,⋅,,,,A,,,,{displaystyle,,,,mathbf,,,,,,,,6,,,,cdot,,,,mathbf,,,,,,,,5,,,,=mathbf,,,,,,,,4,,,,cdot,,,,mathbf,,,,,,,,3,,,,},,,,A,,,,,,,,B,,,,=,,,,−,,,,B,,,,,,,,A,,,,{displaystyle,,,,mathbf,,,,,,,,8,,,,times,,,,mathbf,,,,,,,,7,,,,=mathbf,,,,{-B},,,,times,,,,mathbf,,,,,,,,6,,,,},,,,(,,,,A,,,,+,,,,B,,,,),,,,⋅,,,,C,,,,=,,,,A,,,,⋅,,,,C,,,,+,,,,B,,,,⋅,,,,C,,,,{displaystyle,,,,left(mathbf,,,,,,,,2,,,,+mathbf,,,,,,,,1,,,,right)cdot,,,,mathbf,,,,,,,,0,,,,=mathbf,,,,,,,,9,,,,cdot,,,,mathbf,,,,,,,,8,,,,+mathbf,,,,,,,,7,,,,cdot,,,,mathbf,,,,,,,,6,,,,},,,,(,,,,A,,,,+,,,,B,,,,),,,,,,,,C,,,,=,,,,A,,,,,,,,C,,,,+,,,,B,,,,,,,,C,,,,{displaystyle,,,,left(mathbf,,,,,,,,8,,,,+mathbf,,,,,,,,7,,,,right)times,,,,mathbf,,,,,,,,6,,,,=mathbf,,,,,,,,5,,,,times,,,,mathbf,,,,,,,,4,,,,+mathbf,,,,,,,,3,,,,times,,,,mathbf,,,,,,,,2,,,,},,,,A,,,,⋅,,,,(,,,,B,,,,,,,,C,,,,),,,,=,,,,B,,,,⋅,,,,(,,,,C,,,,,,,,A,,,,),,,,=,,,,C,,,,⋅,,,,(,,,,A,,,,,,,,B,,,,),,,,{displaystyle,,,,mathbf,,,,,,,,4,,,,cdot,,,,left(mathbf,,,,,,,,3,,,,times,,,,mathbf,,,,,,,,2,,,,right)=mathbf,,,,,,,,1,,,,cdot,,,,left(mathbf,,,,,,,,0,,,,times,,,,mathbf,,,,,,,,9,,,,right)=mathbf,,,,,,,,8,,,,cdot,,,,left(mathbf,,,,,,,,7,,,,times,,,,mathbf,,,,,,,,6,,,,right)},,,,(scalar,,,,triple,,,,product),,,,A,,,,,,,,(,,,,B,,,,,,,,C,,,,),,,,=,,,,(,,,,A,,,,⋅,,,,C,,,,),,,,B,,,,−,,,,(,,,,A,,,,⋅,,,,B,,,,),,,,C,,,,{displaystyle,,,,mathbf,,,,,,,,6,,,,times,,,,left(mathbf,,,,,,,,5,,,,times,,,,mathbf,,,,,,,,4,,,,right)=left(mathbf,,,,,,,,3,,,,cdot,,,,mathbf,,,,,,,,2,,,,right)mathbf,,,,,,,,1,,,,-left(mathbf,,,,,,,,0,,,,cdot,,,,mathbf,,,,Saved,,,,in,,,,parser,,,,cache,,,,with,,,,key,,,,enwiki:pcache:idhash:3114930-0!*!0!!en!4!*!math=5,,,,and,,,,timestamp,,,,20160815023837,,,,and,,,,revision,,,,id,,,,732531237,,,,9,,,,right)mathbf,,,,Saved,,,,in,,,,parser,,,,cache,,,,with,,,,key,,,,enwiki:pcache:idhash:3114930-0!*!0!!en!4!*!math=5,,,,and,,,,timestamp,,,,20160815023837,,,,and,,,,revision,,,,id,,,,732531237,,,,8,,,,},,,,(vector,,,,triple,,,,product),,,,(,,,,A,,,,,,,,B,,,,),,,,,,,,C,,,,=,,,,(,,,,A,,,,⋅,,,,C,,,,),,,,B,,,,−,,,,(,,,,B,,,,⋅,,,,C,,,,),,,,A,,,,{displaystyle,,,,left(mathbf,,,,{A},,,,times,,,,mathbf,,,,{B},,,,right)times,,,,mathbf,,,,{C},,,,=left(mathbf,,,,{A},,,,cdot,,,,mathbf,,,,{C},,,,right)mathbf,,,,{B},,,,-left(mathbf,,,,{B},,,,cdot,,,,mathbf,,,,{C},,,,right)mathbf,,,,{A},,,,},,,,(vector,,,,triple,,,,product),,,,(,,,,A,,,,,,,,B,,,,),,,,⋅,,,,(,,,,C,,,,,,,,D,,,,),,,,=,,,,(,,,,A,,,,⋅,,,,C,,,,),,,,(,,,,B,,,,⋅,,,,D,,,,),,,,−,,,,(,,,,B,,,,⋅,,,,C,,,,),,,,(,,,,A,,,,⋅,,,,D,,,,),,,,{displaystyle,,,,left(mathbf,,,,{A},,,,times,,,,mathbf,,,,{B},,,,right)cdot,,,,left(mathbf,,,,{C},,,,times,,,,mathbf,,,,{D},,,,right)=left(mathbf,,,,{A},,,,cdot,,,,mathbf,,,,{C},,,,right)left(mathbf,,,,{B},,,,cdot,,,,mathbf,,,,{D},,,,right)-left(mathbf,,,,{B},,,,cdot,,,,mathbf,,,,{C},,,,right)left(mathbf,,,,{A},,,,cdot,,,,mathbf,,,,{D},,,,right)},,,,(,,,,A,,,,⋅,,,,(,,,,B,,,,,,,,C,,,,),,,,),,,,D,,,,=,,,,(,,,,A,,,,⋅,,,,D,,,,),,,,(,,,,B,,,,,,,,C,,,,),,,,+,,,,(,,,,B,,,,⋅,,,,D,,,,),,,,(,,,,C,,,,,,,,A,,,,),,,,+,,,,(,,,,C,,,,⋅,,,,D,,,,),,,,(,,,,A,,,,,,,,B,,,,),,,,{displaystyle,,,,left(mathbf,,,,{A},,,,cdot,,,,left(mathbf,,,,{B},,,,times,,,,mathbf,,,,{C},,,,right)right)mathbf,,,,{D},,,,=left(mathbf,,,,{A},,,,cdot,,,,mathbf,,,,{D},,,,right)left(mathbf,,,,{B},,,,times,,,,mathbf,,,,{C},,,,right)+left(mathbf,,,,{B},,,,cdot,,,,mathbf,,,,{D},,,,right)left(mathbf,,,,{C},,,,times,,,,mathbf,,,,{A},,,,right)+left(mathbf,,,,{C},,,,cdot,,,,mathbf,,,,{D},,,,right)left(mathbf,,,,{A},,,,times,,,,mathbf,,,,{B},,,,right)},,,,(,,,,A,,,,,,,,B,,,,),,,,,,,,(,,,,C,,,,,,,,D,,,,),,,,=,,,,(,,,,A,,,,⋅,,,,(,,,,B,,,,,,,,D,,,,),,,,),,,,C,,,,−,,,,(,,,,A,,,,⋅,,,,(,,,,B,,,,,,,,C,,,,),,,,),,,,D,,,,{displaystyle,,,,left(mathbf,,,,{A},,,,times,,,,mathbf,,,,{B},,,,right)times,,,,left(mathbf,,,,{C},,,,times,,,,mathbf,,,,{D},,,,right)=left(mathbf,,,,{A},,,,cdot,,,,left(mathbf,,,,{B},,,,times,,,,mathbf,,,,{D},,,,right)right)mathbf,,,,{C},,,,-left(mathbf,,,,{A},,,,cdot,,,,left(mathbf,,,,{B},,,,times,,,,mathbf,,,,{C},,,,right)right)mathbf,,,,{D},,,,},,,,.,,,,Divergence[edit].,,,ISBN978-0-521-71595-9.,,,,Gradient[edit].,,,Curvesurface,,,integrals[edit].,,,W.,,,∇,,,,2,,,,(,,,,∇,,,,ψ,,,,),,,,=,,,,∇,,,,(,,,,∇,,,,⋅,,,,(,,,,∇,,,,ψ,,,,),,,,),,,,=,,,,∇,,,,(,,,,∇,,,,2,,,,ψ,,,,),,,,{displaystyle,,,,nabla,,,,^{2}(nabla,,,,psi,,,,)=nabla,,,,(nabla,,,,cdot,,,,(nabla,,,,psi,,,,))=nabla,,,,(nabla,,,,^{2}psi,,,,)},,,,∇,,,,2,,,,(,,,,∇,,,,⋅,,,,A,,,,),,,,=,,,,∇,,,,⋅,,,,(,,,,∇,,,,(,,,,∇,,,,⋅,,,,A,,,,),,,,),,,,=,,,,∇,,,,⋅,,,,(,,,,∇,,,,2,,,,A,,,,),,,,{displaystyle,,,,nabla,,,,^{2}(nabla,,,,cdot,,,,mathbf,,,,{A},,,,)=nabla,,,,cdot,,,,(nabla,,,,(nabla,,,,cdot,,,,mathbf,,,,{A},,,,))=nabla,,,,cdot,,,,(nabla,,,,^{2}mathbf,,,,{A},,,,)},,,,∇,,,,2,,,,(,,,,∇,,,,,,,,A,,,,),,,,=,,,,−,,,,∇,,,,,,,,(,,,,∇,,,,,,,,(,,,,∇,,,,,,,,A,,,,),,,,),,,,=,,,,∇,,,,,,,,(,,,,∇,,,,2,,,,A,,,,),,,,{displaystyle,,,,nabla,,,,^{2}(nabla,,,,times,,,,mathbf,,,,{A},,,,)=-nabla,,,,times,,,,(nabla,,,,times,,,,(nabla,,,,times,,,,mathbf,,,,{A},,,,))=nabla,,,,times,,,,(nabla,,,,^{2}mathbf,,,,{A},,,,)},,,,.,,,,

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