Teorema de Divergencia

7/17/2019 Teorema de Divergencia

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8EE4DED90B648A58C3C6DFBF85D83F208056360194EE0482082370E8353F19E9577A7DCDB5947A95A466DE38441FBB717616D21815676230444D1348876124B92A226F98007A05E78F3C0DA858C965777E935B48BB5A36B597047FDF3C564FFC24BE15FB27D87FE13CF10FF67F4FB279D36CDBFDCCF97BB6F6C66BC86C2548351B69656D91A4A8CCDE42CD800824F96E42BFFBAC707A1E2BD220F893A4C1AE4F793DADF6A51CF2DA452B5E492B1368BE699E350D3B3056DE9FBA79248D8AB16006D5500DCD43C67E0C87C217FA4E957A9186B39628214B79402CC840192BDC9EA68AF1451B8E338FAD1401FFD9}}}}}{\shp{\*\shpinst\shpleft1586\shptop15133\shpright10320\shpbottom15133\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2028\shpz2\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}

{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 8734}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(8733,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}

{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}\paperw11893\paperh16826\margl666\margr133\margt666\margb346\cols3\colno1\colw3320\colsr-0\colno2\colw6226\colsr-0\colno3\colw1546\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0\fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-386\slmult0 \fs30\cf0\f0\charscalex100 {ndice}\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-266\slmult0 \fs20\cf0\f0\charscalex100 {1. Introduccin}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0\fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slm

ult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-360\slmult0 \fs36\cf0\f0\charscalex100 {Teoremas de Stokes y Gauss}\par\pard\li1026\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li1026\ri0\sl-413\slmult0 \fs24\cf0\f0\ch


5/202

arscalex100 {I}\fs20\cf0\f0\charscalex100 {SABEL}{ }\fs24\cf0\f0\charscalex100 {M}\fs20\cf0\f0\charscalex100 {ARRERO}\par\pard\li120\ri0\sl-346\slmult0 \fs24\cf0\f0\charscalex100 {Departamento de Anlisis Matemtico}\par\pard\li693\ri0\sl-346\slmult0 \fs24\cf0\f0\charscalex100 {Universidad de La Laguna}\par\pard\li1040\ri0\sl-360\slmult0 \fs24\cf0\f0\charscalex100 {[email protected]}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\

pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-226\slmult0 \fs20\cf

1\f0\charscalex100 {{\field{\*\fldinst{HYPERLINK "#3"}}{\fldrslt {1}}}}\par\pard\sect\sectd\sbknone\pard\li1213\ri0\sl-306\slmult0 \*\tx9546\fs20\cf0\f0\charscalex100 {1.1. El rotacional y la divergencia de un campo vectorial . . . . . . .. . . . . . . . . . . . . . . .}\tab \fs20\cf1\f0\charscalex100 {{\field{\*\fldinst{HYPERLINK "#3"}}{\fldrslt {1}}}}\par\pard\li1213\ri0\sl-293\slmult0 \*\tx9546\fs18\cf0\f0\charscalex100 {1.2. Propiedades . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .}\tab \fs18\cf1\f0\charscalex100 {{\field{\*\fldinst{HYPERLINK "#4"}}{\fldrslt {2}}}}\par\pard\sect\sectd\sbknone\cols2\colno1\colw9546\colsr-0\colno2\colw1546\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-280\slmult0 \fs20\cf0\f0\charscalex100 {2. Teorema de Stokes}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-280\slmult0 \fs20\cf1\f0\charscalex100 {{\field{\*\fldinst{HYPERLINK "#4"}}{\fldrslt {2}}}}\par\pard\sect\sectd\sbknone\pard\li1213\ri0\sl-306\slmult0 \*\

tx9546\fs20\cf0\f0\charscalex100 {2.1. Teorema de Stokes . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . .}\tab \fs20\cf1\f0\charscalex100 {{\field{\*\fldinst{HYPERLINK "#5"}}{\fldrslt {3}}}}\par\pard\li1213\ri0\sl-293\slmult0 \*\tx9546\fs18\cf0\f0\charscalex100 {2.2. Interpretacin fsica delrotacional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .}\tab\fs18\cf1\f0\charscalex100 {{\field{\*\fldinst{HYPERLINK "#7"}}{\fldrslt {5}}}}\par\pard\sect\sectd\sbknone\cols2\colno1\colw9546\colsr-0\colno2\colw1546\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-280\slmult0 \fs20\cf0\f0\charscalex100 {3. Teorema de la divergencia o de Gauss}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-280\slmult0 \fs20\cf1\f0\charscalex100 {{\field{\*\fldinst{HYPERLINK "#9"}}{\fldrslt {7}}}}\par\pard\sect\sectd\sbknone\pard\li1213\ri0\sl-306\slmult0 \*\tx9546\fs20\cf0\f0\charscalex100 {3.1.Teorema de Gauss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .}\tab \fs20\cf1\f0\charscalex100 {{\field{\*\fldinst{HYPERLINK"#9"}}{\fldrslt {7}}}}\par\pard\li1213\ri0\sl-293\slmult0 \*\tx4853\*\tx9453\fs20\cf0\f0\charscalex100 {3.2. Interpretacin fsica de la divergencia}\tab \fs20\cf0\f0\charscalex100 {. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .}\tab \fs20\cf1\f0\charscalex100 {{\field{\*\fldinst{HYPERLINK "#12"}}{\fldrslt {10}}}}\par\pard\sect\sectd\sbknone\cols2\colno1\colw7906\colsr-0\colno2\colw3186\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\

par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\s


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l-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-226\slmult0 \fs20\cf0\f0\chars

calex100 {C}\fs16\cf0\f0\charscalex100 {LCULO}{ }\fs20\cf0\f0\charscalex100 {I}\fs16\cf0\f0\charscalex100 {NTEGRAL}{ }\fs20\cf0\f0\charscalex100 {V}\fs16\cf0\f0\charscalex100 {ECTORIAL}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0\fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0

\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-226\slmult0 \fs20\cf0\f0\charscalex100 {OCW-ULL 2011/12}\par\pard\sect\sectd\sbknone\pard\sect\sectd\sbkpage\pard\sect\sectd\sbkpage{\shp{\*\shpinst\shpleft1586\shptop1653\shpright10320\shpbottom1653\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2031\shpz0\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}

{\sp{\sn geoRight}{\sv 8734}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(8733,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5426\shptop6586\shpright5640\shpbottom6586\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2032\shpz1\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 214}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(213,0);}}

{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}


7/202

{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}

{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5666\shptop6480\shpright5720\shpbottom6480\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2033\shpz2\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 54}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(53,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}

{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5960\shptop6586\shpright6160\shpbottom6586\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2034\shpz3\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}

{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 200}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(213,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft6186\shptop6480\shpright6280\shpbottom6480\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2035\shpz4\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 94}}

{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(93,0);}}


8/202

{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}

{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft6520\shptop6586\shpright6720\shpbottom6586\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2036\shpz5\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 200}}{\sp{\sn geoBottom}{\sv 0}}

{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(200,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}

{\shp{\*\shpinst\shpleft6733\shptop6466\shpright6826\shpbottom6466\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2037\shpz6\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 93}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(93,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5413\shptop7960\shpright5680\shpbottom7960\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2038\shpz7\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}

{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 267}}


9/202

{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(253,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}

{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5706\shptop7840\shpright5760\shpbottom7840\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2039\shpz8\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}


{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5986\shptop7960\shpright6253\shpbottom7960\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2040\shpz9\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 267}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(253,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft6280\shptop7840\shpright6373\shpbottom7840\shpfhdr0\shpw

r3\shpwrk0\shpfblwtxt1\shplid2041\shpz10\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}


10/202

{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 93}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(93,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}

{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft6600\shptop7960\shpright6866\shpbottom7960\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2042\shpz11\shpbxpage\shpbypage

{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 266}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(253,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}

{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft6880\shptop7840\shpright6973\shpbottom7840\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2043\shpz12\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 93}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(93,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}

{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft2106\shptop9013\shpright2240\shpbottom9013\shpfhdr0\shpw


11/202

r3\shpwrk0\shpfblwtxt1\shplid2044\shpz13\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 134}}{\sp{\sn geoBottom}{\sv 0}}

{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}

{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft3720\shptop9013\shpright3773\shpbottom9013\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2045\shpz14\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 53}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(53,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}

{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft4693\shptop9013\shpright4786\shpbottom9013\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2046\shpz15\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 93}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(93,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}

{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}


12/202

{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5666\shptop9000\shpright5760\shpbottom9000\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2047\shpz16\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}

{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 94}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(93,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}

{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft9960\shptop9013\shpright10093\shpbottom9013\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2048\shpz17\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 133}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}

{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft3853\shptop10146\shpright3986\shpbottom10146\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2049\shpz18\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 133}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}

{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}


13/202

{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft4400\shptop10253\shpright4653\shpbottom10253\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2050\shpz19\shpbxpage\shpbypage

{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 253}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(240,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}

{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft4906\shptop10253\shpright5173\shpbottom10253\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2051\shpz20\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}

{\sp{\sn geoRight}{\sv 267}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(266,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5373\shptop10146\shpright5426\shpbottom10146\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2052\shpz21\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 53}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(53,0);}}

{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}


14/202

{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}

{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5800\shptop10253\shpright6053\shpbottom10253\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2053\shpz22\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 253}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(240,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}

{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft6306\shptop10253\shpright6546\shpbottom10253\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2054\shpz23\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}




15/202







16/202




{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5400\shptop11213\shpright5453\shpbottom11213\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2060\shpz29\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 53}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(53,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5840\shptop11213\shpright5933\shpbottom11213\shpfhdr0\sh

pwr3\shpwrk0\shpfblwtxt1\shplid2061\shpz30\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}


17/202



{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 93}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(93,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}

{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5320\shptop11720\shpright5533\shpbottom11720\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2063\shpz32\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 213}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(213,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}

{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5786\shptop11720\shpright6000\shpbottom11720\shpfhdr0\sh


18/202

pwr3\shpwrk0\shpfblwtxt1\shplid2064\shpz33\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 214}}{\sp{\sn geoBottom}{\sv 0}}

{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(213,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}

{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft6240\shptop11720\shpright6440\shpbottom11720\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2065\shpz34\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 200}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(200,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}

{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft7226\shptop11613\shpright7373\shpbottom11613\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2066\shpz35\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 147}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}

{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}


19/202

{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft3386\shptop12586\shpright3520\shpbottom12586\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2067\shpz36\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}

{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 134}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}

{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft7080\shptop12586\shpright7226\shpbottom12586\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2068\shpz37\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 146}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}

{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft7466\shptop12586\shpright7573\shpbottom12586\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2069\shpz38\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 107}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(93,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}

{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}


20/202

{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft6013\shptop14613\shpright6146\shpbottom14613\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2070\shpz39\shpbxpage\shpbypage

{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 133}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}

{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft1586\shptop15133\shpright10320\shpbottom15133\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2071\shpz40\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}

{\sp{\sn geoRight}{\sv 8734}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(8733,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}\pgwsxn11893\pghsxn16826\marglsxn666\margrsxn133\margtsxn666\margbsxn346\cols2\colno1\colw9293\colsr-0\colno2\colw1800\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-320\slmult0 \fs20\cf0\f0\charscalex100 {T}\fs16\cf0\f0\charscalex100 {EOREMAS DE}{ }\fs20\cf0\f0\charscalex100 {S}{ }\fs16\cf0\f0\charscalex100 {TOKES Y}{ }\fs20\cf0\f0\charscalex100 {G}\fs16\cf0\f0\charscalex100 {AUSS}\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-360\slmult0 \*\tx1426\fs30\cf0\f0\charscalex100 {1.}\tab \fs30\cf0\f0\charscalex100 {Introduccin}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\s

l-320\slmult0 \fs20\cf0\f0\charscalex100 {{\field{\*\fldinst{HYPERLINK "#13"}}{\fldrslt {1/}}}}\fs20\cf1\f0\charscalex100 {{\field{\*\fldinst{HYPERLINK "#13"}}{\fldrslt {11}}}}\par\pard\sect\sectd\sbknone\pgwsxn11893\pghsxn16826\marglsxn666


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\margrsxn133\pard\li1213\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li1213\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li1213\ri0\sl-240\slmult0 \fs20\cf0\f0\charscalex100{Nos ocupamos ahora de dos generalizaciones del segundo teorema fundamental delclculo a integrales de}\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-186\slmult0 \fs18\cf0\f0\charscalex100 {super\uc1\u64257Xcie: el}{ }\fs18\cf0\f0\charscalex100 {teorema de Stokes}{ }\fs18\cf0\f0\charscalex100 {y el}{ }\fs18\cf0\f0\charscalex100 {teorema de Gauss}\fs18\cf0\f0\charscalex100 {. sto

s, junto con el teorema de Green, constituyen los}\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-186\slmult0 \fs20\cf0\f0\charscalex100 {tres teoremas fundamentales del clculo integral vectorial.}\par\pard\li1213\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li1213\ri0\sl-226\slmult0 \fs18\cf0\f0\charscalex100 {Los teoremas de Stokes y Gauss proporcionarn la interpretacin fsica de los conceptos de rotacional y}\par\pard\li920\ri0\sl-386\slmult0 \fs20\cf0\f0\charscalex100 {divergencia, con cuya de\uc1\u64257Xnicin y propiedades comenzamos esta seccin.}\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-346\slmult0 \*\tx1520\fs24\cf0\f0\charscalex100 {1.1.}\tab \fs24\cf0\f0\charscalex100 {El rotacional y la divergencia de un campo vectorial}\par\pard\li1213\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li1213\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li

1213\ri0\sl-173\slmult0 \fs20\cf0\f0\charscalex100 {Sea}{ }\fs20\cf0\f0\charscalex100 {\uc1\u8711X}{ }\fs20\cf0\f0\charscalex100 {el operador}\par\pard\sect\sectd\sbknone\pgwsxn11893\pghsxn16826\marglsxn666\margrsxn133\cols7\colno1\colw4813\colsr-0\colno2\colw186\colsr-0\colno3\colw333\colsr-0\colno4\colw213\colsr-0\colno5\colw333\colsr-0\colno6\colw186\colsr-0\colno7\colw5026\pard\li4346\ri0\sl-400\slmult0 \fs20\cf0\f0\charscalex100 {\uc1\u8711X}{ }\fs20\cf0\f0\charscalex100{=}\par\column\pard\li0\ri0\sl-213\slmult0 \fs20\cf0\f0\charscalex100 {\uc1\u8706X}\par\column\pard\li0\ri0\sl-386\slmult0 \fs20\cf0\f0\charscalex100 {i}{ }\fs20\cf0\f0\charscalex100 {+}\par\column\pard\li0\ri0\sl-213\slmult0 \fs20\cf0\f0\charscalex100 {\uc1\u8706X}\par\column\pard\li0\ri0\sl-386\slmult0 \fs20\cf0\f0\charscalex100 {j}{ }\fs20\cf0\f0\charscalex100 {+}\par\column\pard\li0\ri0\sl-213\slmult0 \fs20\cf0\f0\charscalex100 {\uc1\u8706X}\par\column\pard\li0\ri0\sl-386\slmult0 \fs20\cf0\f0\charscalex100 {k}\fs20\cf0\f0\charscalex100 {.}\par\pard\

sect\sectd\sbknone\pgwsxn11893\pghsxn16826\marglsxn666\margrsxn133\cols3\colno1\colw5293\colsr-0\colno2\colw560\colsr-0\colno3\colw5240\pard\li4760\ri0\sl-173\slmult0 \fs18\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs18\cf0\f0\charscalex100 {x}\par\column\pard\li0\ri0\sl-173\slmult0 \fs18\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs18\cf0\f0\charscalex100 {y}\par\column\pard\li0\ri0\sl-173\slmult0 \fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {z}\par\pard\sect\sectd\sbknone\pgwsxn11893\pghsxn16826\marglsxn666\margrsxn133\pard\li1213\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li1213\ri0\sl-293\slmult0 \fs20\cf0\f0\charscalex100 {Recurdese que el}{ }\fs20\cf0\f0\charscalex100 {gradiente}{ }\fs20\cf0\f0\charscalex100 {de un campo escalar}{ }\fs20\cf0\f0\charscalex100 {\uc1\u981X}{ }\fs20\cf0\f0\charscalex100 {\uc1\u8712X}{ }\fs20\cf0\f0\charscalex100 {C}{\super\fs16\up2\cf0\f0\charscalex100 {1}}\fs20\cf0\f0\charscalex100 {viene dado por}\par\pard\sect\sectd\sbknone\pgwsxn11893\pghsxn16826\marglsxn666\margrsxn133\cols7\colno1\colw4746\colsr-0\colno2\colw293\colsr-0\colno3\colw280\colsr-0\colno4\colw320\colsr-0\colno5\colw293\colsr-0\colno6\colw280\colsr-0\colno7\colw4880\pard\li4213\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li4213\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li4213\ri0\sl-306\slmult0 \fs20\cf0\f0\charscalex100 {\uc1\u8711X}\fs20\cf0\f0\charscalex100 {\uc1\u981X}{ }\fs20\cf0\f0\charscalex100 {=}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-120\slmult0 \fs20\cf0\f0\charscalex100 {\uc1\u8706X \uc1\u981X}\par\pard\li26\ri0\sl-320\slmult0 \fs18\cf0\f0\charscalex100 {\uc1\u8706X}{}\fs18\cf0\f0\charscalex100 {x}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-293\slmult0 \fs20\cf0\f0\charscalex100 {i}{ }\fs20\cf0\f0\charscalex100 {+}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\

li0\ri0\sl-120\slmult0 \fs20\cf0\f0\charscalex100 {\uc1\u8706X \uc1\u981X}\par\pard\li26\ri0\sl-320\slmult0 \fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {y}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\


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li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-293\slmult0 \fs20\cf0\f0\charscalex100 {j}{ }\fs20\cf0\f0\charscalex100 {+}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-120\slmult0 \fs20\cf0\f0\charscalex100 {\uc1\u8706X \uc1\u981X}\par\pard\li26\ri0\sl-320\slmult0 \fs18\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs18\cf0\f0\charscalex100 {z}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-293\slmult0 \fs20\cf0\f0\charscalex100

{k}\fs20\cf0\f0\charscalex100 {,}\par\pard\sect\sectd\sbknone\pgwsxn11893\pghsxn16826\marglsxn666\margrsxn133\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-373\slmult0 \fs20\cf0\f0\charscalex100 {expresin que puede interpretarse como una multiplicacin formal del operador}{ }\fs20\cf0\f0\charscalex100 {\uc1\u8711X}{ }\fs20\cf0\f0\charscalex100 {por el campo escalar}{ }\fs20\cf0\f0\charscalex100 {\uc1\u981X}\fs20\cf0\f0\charscalex100 {.}\par\pard\li1213\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li1213\ri0\sl-226\slmult0 \fs20\cf0\f0\charscalex100 {Si}{ }\fs20\cf0\f0\charscalex100 {F}\fs20\cf0\f0\charscalex100 {(}\fs20\cf0\f0\charscalex100 {x}\fs20\cf0\f0\charscalex100 {,}{ }\fs20\cf0\f0\charscalex100 {y}\fs20\cf0\f0\charscalex100 {,}\fs20\cf0\f0\charscalex100 {z}\fs20\cf0\f0\charscalex100 {) =}{ }\fs20\cf0\f0\charscalex100 {P}\fs20\cf0\f0\charscalex100 {(}\fs20\cf0\f0\charscalex100 {x}\fs20\cf0\f0\charscalex100 {,}{ }\fs20\cf0\f0\charsca

lex100 {y}\fs20\cf0\f0\charscalex100 {,}{ }\fs20\cf0\f0\charscalex100 {z}\fs20\cf0\f0\charscalex100 {)}\fs20\cf0\f0\charscalex100 {i}{ }\fs20\cf0\f0\charscalex100 {+}\fs20\cf0\f0\charscalex100 {Q}\fs20\cf0\f0\charscalex100 {(}\fs20\cf0\f0\charscalex100 {x}\fs20\cf0\f0\charscalex100 {,}{ }\fs20\cf0\f0\charscalex100 {y}{}\fs20\cf0\f0\charscalex100 {z}\fs20\cf0\f0\charscalex100 {)}{ }\fs20\cf0\f0\charscalex100 {j}{ }\fs20\cf0\f0\charscalex100 {+}{ }\fs20\cf0\f0\charscalex100 {R}\fs20\cf0\f0\charscalex100 {(}\fs20\cf0\f0\charscalex100 {x}\fs20\cf0\f0\charscalex100 {,}{ }\fs20\cf0\f0\charscalex100 {y}\fs20\cf0\f0\charscalex100 {,}{ }\fs20\cf0\f0\charscalex100 {z}\fs20\cf0\f0\charscalex100 {)}\fs20\cf0\f0\charscalex100 {k}{ }\fs20\cf0\f0\charscalex100 {es un campo vectorial de clase}{ }\fs20\cf0\f0\charscalex100 {C}{\super \fs16\up2\cf0\f0\charscalex100 {1}}\fs20\cf0\f0\charscalex100 {, el}{ }\fs20\cf0\f0\charscalex100 {rotacional}{ }\fs20\cf0\f0\charscalex100 {de}{ }\fs20\cf0\f0\charscalex100 {F}{ }\fs20\cf0\f0\charscalex100 {es

}\par\pard\li920\ri0\sl-386\slmult0 \fs20\cf0\f0\charscalex100 {otro campo vectorial de\uc1\u64257Xnido mediante la ecuacin}\par\pard\sect\sectd\sbknone\pgwsxn11893\pghsxn16826\marglsxn666\margrsxn133\cols7\colno1\colw3573\colsr-0\colno2\colw1133\colsr-0\colno3\colw253\colsr-0\colno4\colw1146\colsr-0\colno5\colw266\colsr-0\colno6\colw1133\colsr-0\colno7\colw3586\pard\li2920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li2920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li2920\ri0\sl-306\slmult0 \fs20\cf0\f0\charscalex100 {rot}{ }\fs20\cf0\f0\charscalex100 {F}{ }\fs20\cf0\f0\charscalex100 {=}\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-306\slmult0 \fs20\cf0\f0\charscalex100 {que formalmente escribimos}\par\column\pard\li0\ri0\sl-213\slmult0\fs18\cf0\par\pard\li0\ri0\sl-493\slmult0 \fs20\cf0\f0\charscalex100 {(}\fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {R}{ }\fs20\cf0\f0\charscalex100 {\uc1\u8722X}{ }\fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {Q}\par\pard\li186\ri0\sl-173\slmult0 \*\tx706\fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {y}\tab \fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {z}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-306\slmult0 \fs20\cf0\f0\charscalex100 {i}{ }\fs20\cf0\f0\charscalex100 {+}\par\pard\li26\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li26\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li26\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li26\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li26\ri0\sl-226\slmult0 \fs20\cf0\f0\charscalex100 {i}\par\pard\li0\ri0\sl-266\slmult0 \fs20\cf0\f0\charscalex100 {\uc1\u8706X}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-493\slmult0 \fs20\cf0\f0\charscalex100 {(}{ }\fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {P}{ }\fs20\cf0\f0\charscalex100 {\uc1\u8722X}{ }\fs20\cf0\f

0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {R}\par\pard\li200\ri0\sl-173\slmult0 \*\tx693\fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {z}\tab \fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\c


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harscalex100 {x}\par\pard\li253\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li253\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li253\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li253\ri0\sl-293\slmult0 \*\tx666\fs20\cf0\f0\charscalex100 {j}\tab \fs20\cf0\f0\charscalex100 {k}\par\pard\li200\ri0\sl-266\slmult0 \*\tx653\fs20\cf0\f0\charscalex100 {\uc1\u8706X}\tab \fs20\cf0\f0\charscalex100 {\uc1\u8706X}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-306\slmult0 \fs20\cf0\f0\charscalex100 {j}{ }\fs20\cf0\f0\charsc

alex100 {+}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-493\slmult0 \fs20\cf0\f0\charscalex100 {(}{ }\fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {Q}{ }\fs20\cf0\f0\charscalex100 {\uc1\u8722X}{ }\fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {P}\par\pard\li200\ri0\sl-173\slmult0 \*\tx720\fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {x}\tab \fs20\cf0\f0\charscalex100 {\uc1\u8706X}{}\fs20\cf0\f0\charscalex100 {y}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-306\slmult0 \fs20\cf0\f0\charscalex100 {k}\fs20\cf0\f0\charscalex100 {,}\par\pard\sect\sectd\sbknone\pgwsxn11893\pghsxn16826\marglsxn666\margrsxn133\cols5\colno1\colw4653\colsr-0\colno2\colw466\colsr-0\colno3\colw453\colsr-0\colno4\colw440\colsr-0\colno5\colw5080\pard\li3813\ri0\sl-186\slmult0 \fs20\cf0\f0\charscalex100 {rot}{ }\fs20\

cf0\f0\charscalex100 {F}{ }\fs20\cf0\f0\charscalex100 {=}\par\column\pard\li0\ri0\sl-280\slmult0 \fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {x}\par\column\pard\li0\ri0\sl-280\slmult0 \fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {y}\par\column\pard\li0\ri0\sl-280\slmult0 \fs20\cf0\f0\charscalex100 {\uc1\u8706X}{ }\fs20\cf0\f0\charscalex100 {z}\par\column\pard\li0\ri0\sl-186\slmult0 \fs20\cf0\f0\charscalex100 {=}{ }\fs20\cf0\f0\charscalex100 {\uc1\u8711X}{ }\fs20\cf0\f0\charscalex100 {}\fs20\cf0\f0\charscalex100 {F}{ }\fs20\cf0\f0\charscalex100 {.}\par\pard\sect\sectd\sbknone\pgwsxn11893\pghsxn16826\marglsxn666\margrsxn133\pard\li4706\ri0\sl-306\slmult0 \*\tx5146\*\tx5613\fs20\cf0\f0\charscalex100 {P}\tab \fs20\cf0\f0\charscalex100 {Q}\tab \fs20\cf0\f0\charscalex100 {R}\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-306\slmult0 \fs20\cf0\f0\charscalex100 {Si un campo vectorial}{}\fs20\cf0\f0\charscalex100 {F}{ }\fs20\cf0\f0\charscalex100 {representa el \uc1

\u64258Xujo de un \uc1\u64258Xuido entonces rot}{ }\fs20\cf0\f0\charscalex100 {F}{ }\fs20\cf0\f0\charscalex100 {=}{ }\fs20\cf0\f0\charscalex100 {0 signi\uc1\u64257Xca fsicamente que el \uc1\u64258Xuido}\par\pard\li920\ri0\sl-400\slmult0 \fs20\cf0\f0\charscalex100 {no tiene rotaciones, o es}{ }\fs20\cf0\f0\charscalex100{irrotacional}\fs20\cf0\f0\charscalex100 {: esto es, no genera remolinos. La justi\uc1\u64257Xcacin de esta idea se ver ms}\par\pard\li920\ri0\sl-386\slmult0 \fs18\cf0\f0\charscalex100 {adelante, como consecuencia del teorema de Stokes; sin embargo, podemos decir informalmente que si el}\par\pard\li920\ri0\sl-213\slmult0\fs18\cf0\par\pard\li920\ri0\sl-186\slmult0 \fs18\cf0\f0\charscalex100 {campo esirrotacional entonces una pequea rueda con aspas colocada en el \uc1\u64258Xuidose mover con ste, pero no}\par\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-186\slmult0 \fs20\cf0\f0\charscalex100 {girar alrededor de su propioeje.}\par\pard\li1213\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li1213\ri0\sl-240\slmult0 \fs18\cf0\f0\charscalex100 {Similarmente, considerando el producto escalar}{ }\fs18\cf0\f0\charscalex100 {\uc1\u8711X}\fs18\cf0\f0\charscalex100 {}{ }\fs18\cf0\f0\charscalex100 {F}{ }\fs18\cf0\f0\charscalex100 {de un modo puramente formal obtenemos la expre-}\par\pard\sect\sectd\sbknone\pgwsxn11893\pghsxn16826\marglsxn666\margrsxn133\cols2\colno1\colw7906\colsr-0\colno2\colw3186\pard\li920\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li920\ri0\sl-373\slmult0 \fs20\cf0\f0\charscalex100 {C}\fs16\cf0\f0\charscalex100 {LCULO}{ }\fs20\cf0\f0\charscalex100 {I}\fs16\cf0\f0\charscalex100 {NTEGRAL}{ }\fs20\cf0\f0\charscalex100 {V}\fs16\cf0\f0\charscalex100 {ECTORIAL}\par\column\pard\li0\ri0\sl-213\slmult0 \fs18\cf0\par\pard\li0\ri0\sl-373\slmult0 \fs20\cf0\f0\charscalex100 {OCW-ULL 2011/12}\par\pard\sect\sectd\sbknone\pgwsxn11893\pghsxn16826\marglsxn666\margrsxn133\pard\sect\sectd\sbkpage

{\shp{\*\shpinst\shpleft1586\shptop1653\shpright10320\shpbottom1653\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2072\shpz0\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}


24/202

{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 8734}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(8733,0);}}

{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft6133\shptop2186\shpright6266\shpbottom2186\shpfhdr0\shpw

r3\shpwrk0\shpfblwtxt1\shplid2073\shpz1\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 133}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}

{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft6666\shptop2186\shpright6813\shpbottom2186\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2074\shpz2\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 147}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}

{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}


25/202

{\shp{\*\shpinst\shpleft4906\shptop2920\shpright5040\shpbottom2920\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2075\shpz3\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 134}}

{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}

{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5306\shptop3026\shpright5560\shpbottom3026\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2076\shpz4\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 254}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(240,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}

{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5813\shptop3026\shpright6080\shpbottom3026\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2077\shpz5\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 267}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(266,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}

{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}


26/202

{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft6346\shptop3026\shpright6586\shpbottom3026\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2078\shpz6\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}

{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 240}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(240,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}

{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft7106\shptop2920\shpright7240\shpbottom2920\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2079\shpz7\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 134}}{\sp{\sn geoBottom}{\sv 0}}

{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft3920\shptop4040\shpright4066\shpbottom4040\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2080\shpz8\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 146}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}

{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}


27/202

{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft8506\shptop4040\shpright8653\shpbottom4040\shpfhdr0\shpw

r3\shpwrk0\shpfblwtxt1\shplid2081\shpz9\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 147}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}

{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft6826\shptop5720\shpright6960\shpbottom5720\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2082\shpz10\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}

{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 134}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft7066\shptop5720\shpright7213\shpbottom5720\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2083\shpz11\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 147}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}

{\sp{\sn pVerticies}{\sv 8;2;(0,0);(146,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}


28/202

{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}

{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft1906\shptop6306\shpright1960\shpbottom6373\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2084\shpz12\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 54}}{\sp{\sn geoBottom}{\sv 67}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;5;(0,0);(0,66);(66,66);(66,0);(0,0);}}

{\sp{\sn pSegmentInfo}{\sv 2;12;16384;45824;1;45824;1;45824;1;45824;1;45824;24577;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 1}}{\sp{\sn fillColor}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft3026\shptop6760\shpright3160\shpbottom6760\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2085\shpz13\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}




29/202







30/202




{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft4320\shptop7213\shpright4466\shpbottom7213\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2091\shpz19\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 146}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft5066\shptop7213\shpright5213\shpbottom7213\shpfhdr0\shpw

r3\shpwrk0\shpfblwtxt1\shplid2092\shpz20\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}


31/202



{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 54}}{\sp{\sn geoBottom}{\sv 67}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;5;(0,0);(0,66);(66,66);(66,0);(0,0);}}{\sp{\sn pSegmentInfo}{\sv 2;12;16384;45824;1;45824;1;45824;1;45824;1;45824;24577;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 1}}{\sp{\sn fillColor}{\sv 0}}

{\sp{\sn fLine}{\sv 0}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft3040\shptop8280\shpright3173\shpbottom8280\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2094\shpz22\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 133}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}

{\sp{\sn fLayoutInCell}{\sv 1}}}}{\shp{\*\shpinst\shpleft3960\shptop8280\shpright4093\shpbottom8280\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2095\shpz23\shpbxpage\shpbypage


32/202

{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 133}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}

{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5;16384;45824;1;45824;32768}}{\sp{\sn fFillOK}{\sv 1}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn lineWidth}{\sv 5055}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineDashing}{\sv 0}}{\sp{\sn fLine}{\sv 1}}{\sp{\sn lineColor}{\sv 0}}{\sp{\sn lineType}{\sv 0}}{\sp{\sn fArrowheadsOK}{\sv 0}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}}

{\shp{\*\shpinst\shpleft4693\shptop8280\shpright4826\shpbottom8280\shpfhdr0\shpwr3\shpwrk0\shpfblwtxt1\shplid2096\shpz24\shpbxpage\shpbypage{\sp{\sn shapeType}{\sv 0}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn rotation}{\sv 0}}{\sp{\sn geoRight}{\sv 133}}{\sp{\sn geoBottom}{\sv 0}}{\sp{\sn shapePath}{\sv 4}}{\sp{\sn pVerticies}{\sv 8;2;(0,0);(133,0);}}{\sp{\sn pSegmentInfo}{\sv 2;5

Teorema de Divergencia

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Transcript of Teorema de Divergencia