เค, ใน, แคลค, สเวกเตอร, งกฤษ, curl, เป, นต, วดำเน, นการเวกเตอร, อธ, บาย, การหม, นของสนามเวกเตอร, ในสามม, ของแต, ละจ, ดในสนามแทนด, วยเวกเตอร, งม, ณล, กษณะ, ความยาวและท, ศทาง, แสดงถ, งล, กษณะการหม, นท, ดน, นท, ศทางของค, อแกนของการหม, นตามท, กำหนดโดยกฎม, อขวา, แล. in aekhlkhulsewketxr ekhirl xngkvs curl epntwdaeninkarewketxr thixthibay karhmunkhxngsnamewketxr insammiti ekhirlkhxngaetlacudinsnamaethndwyewketxr sungmikhunlksna khwamyawaelathisthang thiaesdngthunglksnakarhmunthicudnnthisthangkhxngekhirlkhuxaeknkhxngkarhmuntamthikahndodykdmuxkhwa aelakhnadkhxngekhirlkhuxkhnadkhxngkarhmun echn thasnamewketxraethn khwamerwkarihlkhxngkhxngihlthikalngekhluxnthiaelwekhirlcaepnkhwamhnaaennkhxngkarihlewiyn khxngkhxngihl snamewketxrthiekhirlepnsuny eriykwairkarhmun irrotational ekhirlepnrupaebbkhxng xnuphnthsahrbsnamewketxr odyrupthwipkhxngthvsdibthphunthankhxngaekhlkhulsthiichkbekhirl khux thvsdibthkhxngsotks sungechuxmoyngpriphnthtamphiwkhxngekhirlkhxngsnamewketxrkb priphnthtamesnkhxngsnamewketxrrxbesnokhngkhxbekhtkhxngphunphiwnnsykrnkhxngekhirl ekhiynepn curl F hrux F sungichtwdaeninkaredlaelaphlkhunikhw bangkhrngxaceriykekhirlwa oretchn rotation hrux oretchnnxl rotational ekhiynepnsykrnwa rot Fekhirlaetktangcaktwdaeninkarekrediyntaelaidewxrecns enuxngcakkarprayuktsumitixun yakkwa odymikhwamepnipidbangwithi aetcamiephiynginsammitiethannthiekhirlkhxngsnamewketxrcaepnsnamewketxrehmuxnedim praktkarnnikhlaykb phlkhunikhw sungniyaminsammitiaelakhyayipichinmitixunidyakechnediywkn khwamsmphnthnisathxninsykrn sahrbekhirlchux ekhirl esnxepnkhrngaerkody ecms ekhlirk aemksewll in kh s 1871 1 aetaenwkhidnimikarichngantngaet kh s 1839 inthvsdisnamechingaesngkhxngecms aemkkhllkh 2 xngkhprakxbkhxng F thitaaehnng r inthispktiaelathissmphskbesnokhngpid C inranabaebn thilxmrxbphunthiechingewketxr A An niyam aekikhekhirlkhxngsnamewketxr F aethndwy curl F hrux F hrux rot F thicudhnung niyamcakphaphchaykhxngmnlngbnesntang thiphancudnn tha n epnewketxrhnunghnwyid phaphchaykhxngekhirlkhxng F ipbn n niyamodylimitkhxngpriphnthtamesnpidinranabthitngchakkb n hardwyphunthithithuklxmrxb emuxesnthangkarhapriphnthldkhnadlngsucudtwdaeninkarekhirlnafngkchnthihaxnuphnthidxyangtxenuxng f ℝ3 ℝ3 ipsufngkchntxenuxng g ℝ3 ℝ3 aelaodythwipaelwcaaeplngfngkchn Ck in ℝ3 epnfngkchn Ck 1 in ℝ3 aebbaephnsahrbkarwangaenwewketxrkhxngpriphnthtamesn odypriyay niyamkhxngekhirl ekhiynepnsmkaridepn 3 4 F p d e f lim A 0 1 A C F d r n displaystyle nabla times mathbf F p overset underset mathrm def lim A to 0 left frac 1 A oint C mathbf F cdot d mathbf r right mathbf hat n odythi C F dr khux xinthikrltamesn tamkhxbekhtkhxngphunthirxbcudaela A khuxkhnadkhxngphunthi tha n epnewketxrhnunghnwythitngchakkbranab aela v epnewketxrpktithiinranabthichixxkipdannxkphunthi duphaphkhwa aelw thisthangkhxng C caeluxkihewketxrsmphs w khxng C thaih n n w epnchudewketxrthiepniptamkdmuxkhwakarichngan aekikhinthangptibti niyamkhangtnimkhxyidichephraainekuxbthukkrni twdaeninkarekhirlsamarthnamaichinkrxbkhxngrabbphikdechingesnokhngbangrabb thimikarkhanwnhasutrthingaykwaexaiwaelwsykrn F mitnkaenidinkhwamkhlaykhlungkbphlkhunikhwsammiti aelamipraoychninkarchwycasutrhaekhirlinrabbphikdkharthiesiyn ody aethntwdaeninkaredl sykrnechnnithuxepnpktiin fisiks aela phichkhnitemuxkracaysutr F inrabbphikdkharthiesiynsammiti du edlinphikdthrngkrabxkaelathrngklm sahrbsutrinrabbphikdthrngklm aelathrngkrabxk phikd sahrb F thimixngkprakxbewketxrepn Fx Fy Fz caidepn i j k x y z F x F y F z displaystyle begin vmatrix mathbf i amp mathbf j amp mathbf k 5pt dfrac partial partial x amp dfrac partial partial y amp dfrac partial partial z 10pt F x amp F y amp F z end vmatrix odythi i j aela k epn ewketxrhnwy sahrb aekn x y aela z tamladb singnicakhyayxxkdngni 5 F z y F y z i F x z F z x j F y x F x y k displaystyle left frac partial F z partial y frac partial F y partial z right mathbf i left frac partial F x partial z frac partial F z partial x right mathbf j left frac partial F y partial x frac partial F x partial y right mathbf k aemwacaaesdnginrupaebbkhxngphikd phllphthnicaimepliynaeplngphayitkarhmunthiehmaasmkhxngaeknphikd aetcaphlikdanphayitkarsathxnxangxing aekikh Proceedings of the London Mathematical Society March 9th 1871 Collected works of James MacCullagh Mathematical methods for physics and engineering K F Riley M P Hobson S J Bence Cambridge University Press 2010 Vector Analysis 2nd Edition M R Spiegel S Lipschutz D Spellman Schaum s Outlines McGraw Hill USA 2009 ISBN 978 0 07 161545 7 Arfken p 43 bthkhwamekiywkbkhnitsastrniyngepnokhrng khunsamarthchwywikiphiediyidodyephimkhxmul duephimthi sthaniyxy khnitsastrekhathungcak https th wikipedia org w index php title ekhirl amp oldid 8329465, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,