
motham varumaana parisodhana

saambathikashaasthrathil, motham varumaana parisodhana ennathu demand ilaastik aano ilaastik allayo ennu nirnnayikkunnathinulla oru maargamaan. vilayile vardhanavu motham varumaanathil vardhanavinu kaaranamaakukayaanengil, vilayile vardhanavu aavashyappedunna alavil valia swaadheenam cheluthaatthathinaal demand asthiramaanennu parayaam. vilayile vardhanavu motham varumaanathil kuravundaakkukayaanenkil, demand ilaastik aanennu parayaam, kaaranam vilayile vardhanavu aavashyappedunna alavil valia swaadheenam cheluthunnu.
aalukalkk avaa (aavasyangal) aavashyamundo atho (aaksasarikal) aavashyamundo ennathine aashrayich vyathyastha charakkukalk vyathyastha ilaasthikatha undayirikkaam.
udaaharanangal
ganithashaasthraparamaaya vishadeekaranam.
avaa thammilulla ganithaparamaya bandham demandinte vila ilaasthikathayude soothravaakyathil ninnaan varunnathu
formula 2 vilaye soochippikkunnu, formula 3 aavashyappedunna alavinu, formula 4 aavashyappedunna alavil maattathinu, formula 5 vilayile maattathinu. ivide mainus chihnam phalam oru noonn-negatteevu samkhyayaayi parivartthanam cheiyunnu, parambaraagathavum ennaal saarvathrikamallathathum pole.
vilayile ananthamaaya maattangalkk paridhikal enna ashayam upayogichu, athinaal alavil, formula maarunnu.
motham varumanam formula _ 7 aanu nalkunnathu.
aavashyappedunna alavu q ennathu p vilayude oru pravarthanamaayathinaal, formula _ 8 motham varumanam ingane ezhuthaam
p-maayi bandhapetta motham varumaanathinte derivative iprakaaramaanu
ennaal formula _ 11, athinaal formula _ 12.
formula _ 3 kondu gunikkukayum harikkukayum cheytha sesham, samavaakyam ingane ezhuthaam
fomla _ 15-nte demandinte ilaasthikathaykku pakaramaayi neduka ennathaanu avasana ghattam
motham varumaana parisodhanayude ganithaparamaya vishadeekaranam upayogichu demandinte ilaasthikatha kandethunnathinu, inipparayunna niyamam upayogikkendathu aavasyamaanu
demand ilaastik aanenkil, formula 17, formula 18: vilayum motham varumaanavum vipareeta dishakalilekku neengunnu.
demand asthiramaanengil, formula _ 19, formula _ 20: vilayum motham varumaanavum ore dishayilaanu maarunnath.
demand yoonit ilaastik aanenkil, formula _ 21, appol formula _ 22: vilayile vardhanavu motham varumaanathe baadikkilla.
graaphikkal vishadeekaranam.
motham varumanam, uthppanna vila madangu uthppannathinte alavu, demand graphile inipparayunna naalu pooyintukalil konukalulla oru deerghachathuram upayogichu oru prarambha ghattathil prathinidheekarikkam vila (pii 1), aavashyappedunna alavu (kyu 1), demand karvil eiii pooyint, uthbhavam (vila akshatthinteyum alavu akshatthinteyum vibhajanam). pooyint eiii nankooramitta deerghachathurathinte vistheernnam motham varumaanathinte alavukolaanu.
vila maarumbol deerghachathuram maarunnu. vilayile maattam moolamundaakunna varumaanathile maattathe vila prabhavam ennum athinte falamaayundaakunna alavu maattam moolamundaakunna vipareeta dishayilulla varumaanathile maattathe alavu prabhavam ennum vilikkunnu.
formula 23ll ninnu formula 24 lake vila maarumbol vilayude phalatthinte vyaapthiye deerghachathura formula 25 prathinidheekarikkunnu, alavu phalatthinte vyaapthi deerghachathura formula 26 nalkunnu. vilayude phalam yadhaartha alavu kuranja vilaykk vilkkunnathiloode labhikkuna varumaana nashtamaanu; alavu prabhavam vilkkunna puthuthayi indues cheytha yoonittukalil puthiya vilayil nediya adhika varumaanamaan.
athinaal, vila prabhavam nalkunna deerghachathurathinte vistheernnam alavu prabhavam nalkunna deerghachathurathinte vistheernnathekkaal kooduthalaanengil, demand asthiramaanu formula _ 19. vipareethamaanengil, demand ilaastik aannu formula _ 17.
valuppangal thulyamaanengil, aavasyam yoonit ilaastik (allengil unitory ilaastik) aanu.

