
ekeri aswasthata

ganitat, ekvachan vikshobh samasya hii eka lahan mapdand asaleli samasya aahe jee mapdand moolya shunyavar seet karoon andaje kelee jaau shakat nahee. adhik tantotantpane, lakshanrahit vistaradvare dravanacha eksaman andaj lavala jaau shakat nahee
sootra _ 2 mhanoon. yethe sootra _ 3 haah samasyecha lahan mapdand aahe aanee sootra _ 4 haah vadhatya kramachya sootra _ 3 chya karyancha kram aahe, jase qee sootra _ 6. heey niyamit vikshobh samasyanchya viruddha aahe, jyasathi yaa swarupache eksaman andaj prapt kele jaau shakate. ektya aswasth jhalelya samasya samanyatah anek pramananvar karyarat asalelya gatishilatedware darshavilya jaatat. ekeri vikshobhanche anek varg khalee darshavile aahet.
ekvachan vikshobh' haah shabd hota
1940 chya dashakat curt oto friedrich aanee wolfgang aar. yanni tyachi nirmiti kelee. vosso.
vishleshanachya paddhati.
eka aswasth samasya jyache nirakaran sampoorn samasya kshetravar, mug teey jaaga asso kinwa vel, ekach asymptotic vistaradvare andaje kele jaau shakate, tyat niyamit vikshobh asato. byavachada anuprayoganmadhye, samasyechya vidhanat sarvatra fakt lahan mapdand sootra _ 3 shoonyane badaloon niyamitpane gondhalalelya samasyecha sweekarya andaj aadhalato. heey vistarachi keval pahili mudat ghenyashi sambandhit aahe, jyamule andaje milate jeey kadachit haloohaloo, sootra _ 3 qamee hott asatana khyan samadhanat ekatra yete. ektya gondhalalelya samasyeche nirakaran asha prakare andajit kele jaau shakat naheeh khaleel udaharananmadhye pahilyapramane, jevha samasyeche lahan mapdand tyachya sarvoch operatorla gunakar karato tevha samanyatah ekeri gondhal hoto. asha prakare nishkapatapane mapdand shoonya ghetalyane samasyeche swarupach badalate. vibhedak samikarananchya babatit, seema atty purn kelya jaau shakat naheet; bijganitiy samikarananmadhye, upayanchi sambhavya sankhya qamee hote.
ekeri vikshobh siddhant heey ganitshastradnya, bhautikshastradnya aanee itar sanshodhkansathi sanshodhanache eka samruddha aanee chaloo kshetra aahe. yaa kshetratil samasyanche nirakaran karnyasathi vaparlya jaanarya anek paddhati aahet. yapaiki adhik moolbhut goshtinmadhye julalelya asymptotic vistaranchi paddhat aanee sthanik samasyansathi doubleu. keey. bii. andaj aanee kalantarane, poinker-lindstead paddhat, ekadhik scalechi paddhat aanee niyatkalik sarasari yancha samavesh hoto.
ekeri vikshobh samasya sodavanyasathi sankhyatmak paddhati dekhil khoop lokpriy aahet.
odd aanee pde madheel ekeri vikshobhavaril pustakansathi, udaharanarth homes, "vikshobh paddhatincha parichay", "hinz," vikshobh paddhati "kinwa bender aanee aurzag," shastradnya aanee abhiyantyansathi pragat ganiteey paddhati "pahaa.
ekeri ashant samasyanchi udaharane.
khalee varnan keleli pratyek udaharan dakhavate qee, samasya ekeriaivaji niyamit aahe asey gruheet dharnare nishkapat vikshobh vishleshan kase ayashasvi hoil. adhik atyadhunik ekeri paddhatinni samasya kashee sodavali jaau shakate heey kahee jann dakhavtat.
samanya vibhedak samikarananmadhye gunank gayab hone.
uchch kramachya sandnyela purvgunit karnare eka lahan mapdand asaleli vibhedak samikarane samanyatah seema thurr pradarshit karatat, jenekarun samadhan done vegvegalya pramananmadhye vikasit hote. udaharanarth, seema mulyanchya samasyecha vichar qaraa.
tyache samadhan jevha sootra _ 10 heey khalee darshavilele ghan vakr asate. lakshat ghya qee dravan moodajaval vegane badalate. jarr aapan nishkapatapane sootra _ 11 nishchit kele, tarr aaplyala 'bahya' asey label kelele samadhan milel jyachya khalee seema thurr model kelele nahee, jyasathi 'x' shoonyachya jawal aahe. eksaman vaidh andaj kassa midvayacha heey darshavina adhik tapashilansathi, julalelya asymptotic vistaranchi paddhat pahaa.
velevar udaharane.
vidyut chalit yantramanav hatalani yantramadhye mand yantrik gatishilata aanee vegwan vidyut gatishilata asoo shakate, asha prakare done vel praman pradarshit hote. asha paristhitit, aapan pranaliche done uppranalit vibhajan karoo shakato, eka vegwan gatishilateshi sambandhit aanee dusari mand gatishilateshi sambandhit aanee nantar tyanchyapaiki pratyekasathi swatantrapane niyantrakanchi rachana karoo shakato. eka ekal vikshobh tantrachya madhyamatoon, aapan yaa done upapranali ekmekanpasun swatantra karoo shakato, jyamule niyantran samasya sopee hote.
khaleel samikarananchya sanchadvare varnan kelelya pranalichya vargacha vichar karah
sootra 15 saha. dusare samikaran soochit karate qee sootra 16 chee gatishilata sootra 17 peksha khoop vegwan aahe. tikhonovmule eka pramey asey sangate qee, pranalivaril yogya attins, teey samikarananchya samadhanacha suruvatila aanee atishay lavkar andaj lavel
kahee velechya antarane aanee teey, sootra _ 3 shoonyachya dishene qamee hott asatana, tyach madhyantarat pranali samadhanakade adhik jawalun jaeel.
antaralatil udaharane.
drav yantrikimadhye, thodyasha chikat dravache gunadharm arund seema tharachya baher aanee aat natakiyaritya bhinn asatat. asha prakare drav anek avkashiy praman darshavite.
pratikriya-prasar pranali jyamadhye eka abhikarmak dusyapekaiishaa khoop haloo pasarato, tyaa darmyan tikshna sankramanansah abhikarmak astitvat asalelya kshetranni aanee too astitvat nasalelya kshetranni chinhankit kelele avkashiy namune tayar karoo shakatat. paryavaranshastrat, shikari-shikar models jase qee
jethe sootra 24 haah shikar aahe aanee sootra 25 haah shikari aahe, tethe asey namune pradarshit kelyache darshavile gele aahe.
bijganitiy samikarane.
bahupadi sootra _ 26 chee serve mule shodhanyachya samasyecha vichar qaraa. maryada sootra _ 27 madhye, heey ghan sootra _ 29 varr moolansah vargakar sootra _ 28 madhye ksheen hote. niyamit vikshobh malika badalane
samikaranamadhye aanee sootra _ 3 chya samaan shaktinchi samikarane kelyas keval yaa done moolanmadhye sudharana hotatah
dusare mool shodhanyasathi, ekeri vikshobh vishleshan vaparale jaane aavashyak aahe. jevha aapan sootra _ 3 laa shunyakade jaau deto tevha samikaran dvighatmadhye adhogati hote, tyaa maryadet eka mool anantakade pall kadhate yaa vastusthitishi aapan vyavhar keela pahije. heey mool vikshipt vishleshanasathi adrushya honyapasoon rokhanyasathi, yaa sutananya moodavar laksh thevanyasathi aapan sootra _ 34 punha vikale pahije jenekarun punarprapt kelelya chalanchya babatit, teey sutanar nahee. aapan eka punarnirdharit chull sootra _ 35 paribhashit karato jithe ghatank sootra _ 36 asha prakare nivadle jaeel qee aapan fakt vegane punarvikri karoo jenekarun mool sootra _ 3 teey shoonyachya maryadet sootra _ 37 chya maryadit mulyavar asel, parantu teey shunyavar kosalanar nahee jithe itar done mule sampatil. sootra _ 37 chya sandarbhat aamchyakade aahe
aapan pahoo shakato qee formula _ 41 sathee formula _ 42 varr loar degree termsche varchasva aahe, tarr formula _ 43 varr teey formula _ 44 tarmaitkech prabhavi hote tarr teey donhi urvarit termwar varchasva gajavatat. dusya sandnyeshi samaan prabhav padoon, jyaa maryadechya sutramadhye sarvoch kramachi sandnya yapudhe nahishi honar nahee, tyaa bindula significant degeneration mhanatat; yamule urvarit mool drishyaman honyasathi yogya punarnirdharan hote. hii nivad fayadeshir tharate
vikshobh malika badalane
utpann
mug aaplyala sootra _ 49 madheel moolat rus aahe; sootra _ 50 vareel duheri mool hii done mule aahet jee aaplyala tyaa kosalanyachya varr anant punarniman maryadet shunyavar aadhalali aahet. malikechya pahilya kahee atinchi ganana kelyas nantar utpann milate