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Unformatted text preview: * ( Î± âˆ§ Î² ) = ( Î± 1 Î² 2Î± 2 Î² 1 ) dz( Î± 1 Î² 3Î± 3 Î² 1 ) dy + ( Î± 2 Î² 3Î± 3 Î² 2 ) dx , * [ Î± âˆ§ ( * Î² )] = Î± 1 Î² 1 + Î± 2 Î² 2 + Î± 3 Î² 3 , or * ( Î± âˆ§ Î² ) = Î± Ã— Î² , * [ Î± âˆ§ ( * Î² )] = Î± Â· Î² . 3.5.2 Vector Analysis in R 3 â€¢ ZeroForms. For a 0form f we have ( d f ) i = âˆ‚ i f , so that d f = grad f . â€¢ OneForms. For a 1form Î± = Î± 1 dx + Î± 2 dy + Î± 3 dz we have ( d Î± ) i j = âˆ‚ i Î± jâˆ‚ j Î± i that is, d Î± = ( âˆ‚ 1 Î± 2âˆ‚ 2 Î± 1 ) dx âˆ§ dy + ( âˆ‚ 2 Î± 3âˆ‚ 3 Î± 2 ) dy âˆ§ dz + ( âˆ‚ 3 Î± 1âˆ‚ 1 Î± 3 ) dz âˆ§ dx . di ï¬€ geom.tex; April 12, 2006; 17:59; p. 88...
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This note was uploaded on 11/26/2011 for the course MAT 4821 taught by Professor Wong during the Spring '10 term at FSU.
 Spring '10
 Wong
 Algebra, Geometry

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