
bhardast payari karya

havicide step function kinwa unit step function, jeey samanyatah kinwa (parantu kadhikadhi, kinwa) dware darshavile jaate, heey oliver hevicideveroon naav dilele eka step function aahe, jyache moolya nakaratmak yuktivadansathi shoonya aanee sakaratmak yuktivadansathi eka aahe. heey step functionschya samanya vargache eka udaharan aahe, jeey serve yachya anuvadanche resheey sanyojan mhanoon darshavile jaau shakatat.
heey karya moolatah vibhedak samikarananchya samadhanasathi karyatmak gananat vikasit kele gele hote, jithe teey eka sanketala darshavate jeey vishisht velee chaloo hote aanee anishchit kalasathi chaloo rahate. telegraphic sampreshanachya vishleshanamadhye eka sadhan mhanoon operational calculus vikasit karananya oliver havicidene karya asey darshavile.
havicide functionchi vyakhya ashee kelee jaau shakateh
diarac delta karya heey havicide karya vyutpann aahe 
sootra _ 5
tyamule havicide function heey diarac delta functionche avibhajya ghatak manale jaau shakate. heey kadhikadhi asey lihile jaate
sootra _ 6
jaree haah vistar kadachit lagoo honar nahee (kinwa arthahi nahee), parantu tyat samavisht asalelya samakalananna arth denyasathi ekhadi vyakti konatya aupchariktecha vapar karate yavar avalambun aahe. yaa sandarbhat, havicide function heey yadruchchik chalche sanchayi vitaran karya aahe jeey jawaljawal nishchitpane 0 aahe. (sthir yadruchchik chull pahaa.)
operational calculusmadhye, upayukt uttare kvachitach konatya mulyasathi vaparali jaatat yavar avalambun asatat, kaaran tee mukhytah vitaran mhanoon vaparali jaate. tathapi, nivadiche karyatmak vishleshan aanee khel siddhantamadhye kahee mahattvache parinam houu shakatat, jethe satatya adhik samanya prakarancha vichar keela jaato. kahee samanya paryay khalee pahile jaau shakatat.
jaiv rasayanshastra aanee tantrikashastrat havicide step functionsche andaje upayog aahet, jethe rasayanik sanketanchya pratisadat binary cellular switch andaje karnyasathi step functionsche logistic andaje (jase qee hiill aanee michelis-menton samikarane) vaparale jaau shakatat.
vishleshanatmak andaj.
step functionchya sahaj andajasathi, ekhadi vyakti logistic function vaparu shakate
sootra _ 7
jethe eka motha haah tikshna sankramanashi sambandhit asato. jarr aapan ghetale tarr samanata maryadet rahateh
sootra _ 8
step functionsathi itar anek gulgulit, vishleshanatmak andaj aahet. shakyata khalilpramane aaheth
sootra _ 9
yaa maryada binduroop aanee vitaranachya arthane aahet. tathapi, sarvasadharanpane, binduvruttiy abhisaran mhanje vitaranatmak abhisaran soochit karanyachi aavashyakta nahee aanee ulat vitaranatmak abhisaran mhanje binduvruttiy abhisaran soochit karanyachi aavashyakta nahee. (tathapi, jarr functionschya binduvar abhisari kramache serve sadasya kahee "chhan" karyane eksamanpane baddh asateel, tarr abhisaran vitarananchya arthane dekhil aahe.)
sarvasadharanpane, satat sambhavyatechya vitaranache konatehi sanchayi vitaran karya jeey shoonyachya aaspas shikharavar aahe aanee tyat farak niyantrit karnara mapdand aahe, too farak shoonyachya jawal pohochat asatana maryadet andaje mhanoon kaam karoo shakato. udaharanarth, vareel tinhi andaj heey samanya sambhavyata vitarananchi sanchayi vitaran karye aaheth anukrame logistic, kachee aanee samanya vitaran.
avibhajya pratinidhitva.
byavachada havicide step functionsche avibhajya pratinidhitva upayukt asateh
sootra _ 10
jethe dusare pratinidhitva pahilya pasoon anuman lavane sope aahe, heey lakshat gheta qee step function vastavik aahe aanee tyamule tyache swatache jatil sanyugma aahe.
shoonya yuktivad.
kaaran samanyatah samakalanamadhye vaparale jaate aanee ekach binduvaril karyachya mulyacha tyachya samakalanavar parinam hott nahee, tyamule konatya vishisht mulyachi nivad kelee jaate heey kvachitach mahattvache asate. kharokhar jevha vitaran kinwa (jaaga pahaa) ghatak mhanoon manale jaate tevha shunyavar mulyabaddal bolanyatahi arth nahee, kaaran asha vastoo jawaljawal sarvatra paribhashit kelya jaatat. jarr kahee vishleshanatmak andaj (vareel udaharananpramane) vaparla tarr bahutek vela shunyavar sambandhit maryada jee kahee hote tee vaparali jaate.
vishisht moolya nivadanyachi vividh karane aahet. 
swatantra swaroop.
tyaeivaji eka karya mhanoon paribhashit kelelya ekak tappyache paryayi swaroop (mhanje, swatantra chull ghetalele) aaheh
sootra _ 14
kinwa ardh-kamal parampara vaparah
sootra _ 15
purnank kuthe aahe? jarr purnank asel tarr, teey soochit karane aavashyak aahe, tarr karyat ekata prapt hote heey soochit karane aavashyak aahe. mhanoon 'step function' heey 'chya' kshetravar rampsarkhe vartan darshavate aanee ardh-kamal paddhaticha vapar karoon pramanitpane step function asoo shakat nahee. 
satatchya prakaranachya ulat, yachee vyakhya mahattvapoorn aahe.
swatantra-vel ekak aaveg haah swatantra-vel tappyatil pahila farak aahe.
sootra _ 16
heey karya kronekar tribhuj pradeshachi sanchayi berries aaheh
sootra _ 17
kuthe?
sootra _ 18
heey swatantra ekak aaveg karya aahe.
pratidravak aanee vyutpann.
ramp function heey havicide step functionche antidirative aaheh 
sootra _ 19
diarac delta function heey havicide step functionche vitaran vyutpann aaheh
sootra _ 20
forier rupantaran.
havicide step functionsche forier transform heey eka vitaran aahe. aaplyajaval asalelya forier transformchya vyakhyesathi sthirankanchi eka nivad vaparoon
sootra _ 21
yethe vitaran aahe jeey chachani karya sootra _ 22 chya kachee mukhya mulyaparyant gheuun jaate. avibhajyamadhye disanari maryada dekhil (tempered) vitarananchya arthane ghetali jaate.
ektarfi laplas rupantaran.
havicide step functionsche laplas transform heey eka meromorphic function aahe. ektarfi laplas transform vaparoon aamchyakade aaheh
sootra _ 23
jevha dwaipakshik parivartan vaparale jaate, tevha avibhajya done bhaganmadhye vibhagale jaau shakate aanee parinam samaan asel.
itar abhivyakti.
havicide step function hyperfunction mhanoon darshavile jaau shakate
sootra _ 24
jatil laghuganakache mukhya moolya kuthe aahe?
heey paripoorn moolya karyachya drushtine dekhil vyakt kele jaau shakate
sootra _ 25