Cálculo Vectorial

 

 

Bpudtos Lâcluck Yoltkr`bc

 

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@dst`tutk Dbl`kdbc mo Eàx`lk  @dst`tutk ]oldkcüa`lk ]oldkcüa`lk mo Cb ^bz, HL\

 

 

@dst`tutk Dbl`kdbc mo Eàx`lk

@dst`tutk ]oldkcüa`lk mo Cb ^bz, HL\.  HL\. 

Cb bs`adbturb lkdtr`huyo b mosbrrkccbr ud podsbe`odtk cüa`lk-ebtoeât`lk bc pori`c moc `daod`ork y bpkrtb cbs jorrbe`odtbs hâs`lbs pbrb `dtrkmul`rso bc ostum`k moc lâcluck voltkr`bc y su bpc`lbl`üd, bså lkek cbs hbsos pbrb oc ekmocbmk ebtoeât`lk. Bmoeâs prkpkrl`kdb jorrbe`odtbs quo pore`tod ekmocbr iodüeodks mo lkdtoxtk. Cb `epkrtbdl`b moc ostum`k moc Lâcluck Yoltkr`bc rbm`lb pr`dl`pbceodto od quo od m`vorsbs bpc`lbl`kdos mo cb `daod`oråb, cb lkdlurrodl`b mo vbr`bhcos ospbl`bcos y toepkrbcos, jblo dolosbr`k oc bdâc`s`s mo iodüeodks dbturbcos luyks ekmocks ut`c`zbd iudl`kdos voltkr`bcos k oslbcbros mo vbr`bs vbr`bhcos. Cb bs`adbturb ostâ m`soòbmb mo ebdorb quo oc ostum`bdto puomb roprosodtbr lkdloptks, quo bpbrolod od oc lbepk mo cb `daod`oråb pkr eom`k mo voltkros7 roskcvor prkhcoebs od cks quo `dtorv`odod vbr`bl`kdos lkdt`dubs7 roskcvor prkhcoebs aokeàtr`lks od ikreb voltkr`bc7 arbi`lbr iudl`kdos mo vbr`bs vbr`bhcos7 mor`vbmbs pbrl`bcos7 prkvodabd lbclucbr moc arbm`odto mo ud lbepk roprosodtbr oslbcbr, bså lbepks lkek suvoltkr`bcos m`voraodl`bquoy rktbl`kdbc7 roskcvor `dtoarbcos mkhcos y tr`pcos7 bpc`lbr cbs `dtoarbcos od oc lâcluck mo ârobs y vkcöeodos. Lkd ostb bs`adbturb so osporb mosbrrkccbr cb lbpbl`mbm mo bdâc`s`s y sådtos`s od blt`v`mbmos mo ekmocbl`üd ebtoeât`lb7 bmqu`r`r ostrbtoa`bs pbrb roskcvor prkhcoebs7 ocbhkrbr mosbrrkccks bdbcåt`lks pbrb cb bmqu`s`l`üd mo ud lkdloptk7 podsbr lkdloptubceodto, mosbrrkccbr blt`tumos pbrb cb `dtoarbl`üd b arupks `dtorm`sl`pc`dbr`ks7 bpc`lbr cks lkdkl`e`odtks bmqu`r`mks b cb prâlt`lb y bprkvoljbr cks rolursks quo cb toldkckaåb kirolo, lkek oc usk mo ]@L‐s.  Ostb bs`adbturb tbcos s`rvo lkek pbrb ktrbs bs`adbturbs mo cbs m`iorodtos ospol`bc`mbmos lkek6hbso ostât`lb, m`dâe`lb y eolbd`seks, lkd cb roprosodtbl`üd aokeàtr`lb y âcaohrb mo voltkros7 ocoltrkebadot`sek y tokråb ocoltrkebadàt`lb lkd oc lâcluck moc arbm`odto, m`voraodl`b y rktbl`kdbc mo ud lbepk voltkr`bc7 od torekm`dâe`lb lkd oc lâcluck mo mor`vbmbs pbrl`bcos od cbs m`iorodtos ikrebs mo cb soaudmb coy7 od iodüeodks mo trbdspkrto, trbdsiorodl`b mo ebsb y trbdsiorodl`b mo lbckr, lkd oc lâcluck mo mor`vbmbs pbrl`bcos y cbs olubl`kdos quo ekmocbd ostks iodüeodks. \o puomod m`soòbr prkyoltks `dtoarbmkros lkd lubcqu`orb mo occbs.

@da. Lbrcks ^bm`ccb Xbeks  

^bao 2

 

@dst`tutk Dbl`kdbc mo Eàx`lk

@dst`tutk ]oldkcüa`lk mo Cb ^bz, HL\.  HL\. 

Cb bs`adbturb mo Lâcluck Yoltkr`bc so krabd`zb od l`dlk toebs. Od oc pr`eor toeb mo cb bs`adbturb so `d`l`b lkd cb lkeprods`üd, ebdofk bcaohrb`lk y roprosodtbl`üd aokeàtr`lb mo cks voltkros, ut`c`zbdmk oc prkmultk cb khtodl`üd robc`zbmk pkr udbodtro iuorzbktrbs y oc prkmultk oslbcbr voltkr`bcpbrb pbrb oc lâcluck moc moctrbhbfk ekeodtk mo cb e`seb, bpc`lbl`kdos. \o ostum`b oc tr`pco prkmultk oslbcbr lkek pbrto mo cbs prkp`ombmos mo cks prkmultks mo voltkros pbrb lbclucbr oc vkcueod mo ud pbrbcocopåpomk roltbdaucbr y oc ekeodtk mo udb iuorzb lkd rospoltk b ud ofo, odtro ktrbs bpc`lbl`kdos. ]ore`dbdmk oc toeb lkd cb khtodl`üd mo olubl`kdos mo roltbs y pcbdks od oc ospbl`k. Od oc soaudmk toeb so ostum`bd m`iorodtos t`pks mo lurvbs od oc pcbdk pbrb su bpc`lbl`üd od oc ostum`k y roprosodtbl`üd moc ekv`e`odtk mo ud luorpk, su pks`l`üd, vockl`mbm y blocorbl`üd. \o trbhbfb od lkkrmodbmbs roltbdaucbros y lkkrmodbmbs pkcbros, mo od bluormk b cbcb ibl`c`mbm aokeotråbod mo cbs trbyoltkr`bs prkpuostbs y bprkvoljbdmk lbmb lbsk, oc ebdofk bcaohrb`lk mo cbs olubl`kdos ut`c`zbmbs. \o kht`odo cbs tbdaodtos jkr`zkdtbc y vort`lbc b udb lurvb y cb ckda`tum mo brlk, bså lkek oc ârob mo udb supori`l`o. Od oc torlor toeb so `d`l`b lkd oc ostum`k mo m`iorodtos t`pks mo lurvbs od oc ospbl`k od ikreb pbrbeàtr`lb. Bdbc`zb oc cåe`to mo cbs iudl`kdos y su lkdt`du`mbm. \o kht`odo cb mor`vbmb mo udb iudl`üd voltkr`bc y sus prkp`ombmos, y cbs `dtoarbcos lkrrospkdm`odtos. Moc e`sek ekmk so bdbc`zbd cks voltkros tbdaodto, dkrebc y h`dkrebc quo lbrbltor`zbd udb lurvb od oc ospbl`k, bså lkek cb ckda`tum mo brlk y su lurvbturb. \o ostum`bd cbs bpc`lbl`kdos mo iudl`kdos voltkr`bcos pbrb roprosodtbr ekmocks iås`lks lkek6 oslbcorbs mo lbrblkc, jàc`los lüd`lbs, otl. Od oc lubrtk toeb so arbi`lbd iudl`kdos mo mks vbr`bhcos y so ut`c`zbd cks ebpbs mo lkdtkrdk y cbs lurvbs mo d`voc pbrb lkeprodmor cb moi`d`l`üd mo iudl`üd mo mks vbr`bhcos. Bdbc`zb oc cåe`to mo cbs iudl`kdos mo vbr`bs vbr`bhcos y su lkdt`du`mbm. \o kht`odod cbs mor`vbmbs pbrl`bcos mo udb iudl`üd y so ostum`bd sus prkp`ombmos. \o lbclucbd cbs mor`vbmbs pbrl`bcos mo cbs iudl`kdos mo mks vbr`bhcos y so euostrb cb `dtorprotbl`üd aokeàtr`lb mo cbs e`sebs. \o ostum`b oc lkdloptk mo m`iorodl`bc y cb c b c`dobc`zbl`üd mo udb iudl`üd. @da. Lbrcks ^bm`ccb Xbeks  

^bao 8

 

@dst`tutk Dbl`kdbc mo Eàx`lk

@dst`tutk ]oldkcüa`lk mo Cb ^bz, HL\.  HL\. 

\o lkepcoeodtb oc toeb mo mor`vbl`üd lkd cb roacb mo cb lbmodb, cb mor`vbl`üd `epcål`tb y mor`vbmbs pbrl`bcos mo krmod supor`kr. \o `dtrkmulo cb moi`d`l`üd mo arbm`odto pbrb oc lâcluck mo mor`vbmbs m`roll`kdbcos. \o tore`db oc toeb lbclucbdmk cks vbckros oxtroeks mo iudl`kdos mo vbr`bs vbr`bhcos. Od oc öct`ek toeb so ostum`bd cbs `dtoarbcos mkhcos y tr`pcos od m`iorodtos s`stoebs mo lkkrmodbmbs lkek udb jorrbe`odtb pbrb oc lâcluck mo ârobs y vkcöeodos pr`dl`pbceodto, mkdmo oc usk mo roa`kdos t`pk @ y t`pk @@ pore`to ut`c`zbr cb `dtoarbc eöct`pco pbrb osto i`d. Cb `dtoarbc eöct`pco so lkds`morb lkek toeb iudmbeodtbc. \o `dtrkmulod cb moi`d`l`üd mo lbepk voltkr`bc, rosbctbdmk cb `epkrtbdl`b aokeàtr`lb y iås`lb, tkebdmk ofoepcks prâlt`lks lkek oc icufk mo lbckr, icufk mo odoraåb, oc lbepk arbv`tbtkr`k k oc bskl`bmk b lbrabs ocàltr`lbs, odtro ktrks7 bdâc`s`s quo sorv`râ pbrb mbr s`ad`i`lbmk b cb roprosodtbl`üd aokeàtr`lb moc arbm`odto, cb m`voraodl`b y oc rktbl`kdbc mo ud lbepk voltkr`bc. \o i`dbc`zb oc toeb lkd cb `dtoarbc mo cådob y cks tokroebs lcâs`lks mo `dtoarbcos6 mo Arood, mo \tkgos y mo cb m`voraodl`b mo Abuss. Oc ostum`bdto moho mosbrrkccbr cb jbh`c`mbm pbrb ekmocbr s`tubl`kdos lkt`m`bdbs od su odtkrdk. Os `epkrtbdto quo oc ostum`bdto vbckro cbs blt`v`mbmos quo robc`zb, quo mosbrrkcco jâh`tks mo ostum`k y mo trbhbfk pbrb quo bmqu`orb lbrbltoråst`lbs tbcos lkek6 cb lur`ks`mbm, cb pudtubc`mbm, oc odtus`bsek, oc `dtoràs, cb todbl`mbm, cb icox`h`c`mbm ico x`h`c`mbm y cb butkdkeåb. Oc Lâcluck Yoltkr`bc lkdtr`huyo pr`dl`pbceodto pbrb oc mosbrrkcck mo cbs s`au`odtos lkepotodl`bs aodàr`lbs6 mo lbpbl`mbm mo bhstrbll`üd, bdâc`s`s y sådtos`s, lbpbl`mbm pbrb `modt`i`lbr, pcbdtobr y roskcvor prkhcoebs, jbh`c`mbm pbrb trbhbfbr od ikreb butüdkeb, jbh`c`mbmos od oc usk mo cbs ]@L‐s, lbpbl`mbm lråt`lb y butklråt`lb y cb lbpbl`mbm mo trbhbfk od oqu`pk. Oc mklodto mo Lâcluck Yoltkr`bc moho ekstrbr y khfot`vbr su lkdkl`e`odtk y oxpor`odl`b od oc ârob pbrb lkdstru`r oslodbr`ks mo bprodm`zbfo s`ad`i`lbt`vk od cks ostum`bdtos quo `d`l`bd su ikrebl`üd prkios`kdbc. Oc mklodto odibt`zb oc mosbrrkcck mo cbs blt`v`mbmos mo bprodm`zbfo mo ostb bs`adbturb b i`d mo quo occbs roiuorlod cks bspoltks ikrebt`vks6 `dlodt`vbr cb lur`ks`mbm, oc odtus`bsek, cb pudtubc`mbm, cb lkdstbdl`b, oc `dtoràs pkr eofkrbr, oc rospotk y cb tkcorbdl`b jbl`b sus lkepbòorks y mklodtos, b sus `mobs y odikquos y lkds`morbr tbeh`àd cb rospkdsbh`c`mbm skl`bc y oc rospotk bc eom`k beh`odto.

@da. Lbrcks ^bm`ccb Xbeks  

^bao <

 

@dst`tutk Dbl`kdbc mo Eàx`lk

@dst`tutk ]oldkcüa`lk mo Cb ^bz, HL\.  HL\. 

2.2 Moi`d`l`üd mo ud voltkr od oc pcbdk y od oc ospbl`k y su `dtorprotbl`üd aokeàtr`lb. 2.8 Âcaohrb voltkr`bc y su aokeotråb. 2.< ^rkmultk oslbcbr y voltkr`bc. 2.= Olubl`üd mo cb roltb. 2.? Olubl`üd moc pcbdk. 2.9 Bpc`lbl`kdos.

8.2 Olubl`kdos pbrbeàtr`lbs mo bcaudbs lurvbs pcbdbs y su s u roprosodtbl`üd arâi`lb. 8.8 8.< Mor`vbmb ]bdaodtosmob udb lurvb lurvb.od ikreb pbrbeàtr`lb. 8.= Ârob y ckda`tum mo brlk. 8.? Lurvbs pcbdbs y arbi`lbl`üd od lkkrmodbmbs l kkrmodbmbs pkcbros. 8.9 Lâcluck od lkkrmodbmbs pkcbros.