
verthirikkaavunna bhagika deferential samavaakyam

variabilukale verthirikkunna oru reethi vazhi thaazhnna alavilulla (kurachu swatantra variableukal) prathyeka samavaakyangalude oru koottamaayi vibhajikkaan kazhiyunna onnaanu verthirikkaavunna bhagika deferential samavaakyam. ithu saadhaaranayaayi chila prathyeka roopamo samamithiyo ulla prashnathe aasrayichirikkunnu. eee reethiyil, prashnathe oru dimensional samavakyangalaayi vibhajikkaan kazhiyumenkil, lalithamaaya oru koottam pdes allengil saadhaarana deferential samavaakyangal (odes) polum pariharichukondu paarshyal deferential samavaakyam (pde) pariharikkan kazhiyum. 
oro cordinatinteyum functionukalude oru uthppannam nalkunna roopathinte pariharam anumaanichukondu oru pariharam labhikkuna veriyabilukalude lalithamaaya verthirikkalaan veriyabilukalude verthirikkalinte ettavum saadhaaranamaaya roopam. oro cordinatinteyum functionukalude gunanafalathaal gunikkunna kordinettukalude oru prathyeka nischitha functionaayi pariharam ezhuthunnathiloode saadhikkunna formula _ 1-seppareshan oof variableukal ennu vilikkunna veriyabilukalude verthirikkalin oru prathyeka roopamundu. formula _ 2-leeii laplace samavaakyam oru bhagika deferential samavaakyathinte udaaharanamaanu, ithu formula _ 1-seppareshan oof veriyabilukaliloode pariharangal amgeekarikkunnu; trimana saahacharyathil ithu 6-gola kordinettukal upayogikkunnu.
udaaharanam.
udaaharanathinu, samaya-swatantra shroadinger samavaakyam pariganikkuka.
function formula _ 5-nuu (alavillaatha yoonittukalil, laalithyathinaayi). (thulyamaayi, asamamaya helmolts samavaakyam pariganikkuka.) thrimaanangalile function formula _ 6 roopathilaanengil
appol prashnathe formula _ 8, formula _ 9, formula _ 10 ennivaykkaayi moonnu ekamaana oodukalaayi verthirikkamennum anthima pariharam formula _ 11 ennu ezhuthaamennum maarunnu. (kooduthal pothuve, shroadinger samavaakyathinte verthirikkaavunna kesukal 1948 ll isenhart kanakkakki.)