आतानक विश्लेषण  हिन्दी देवनागरी में पढ़ें।

atanak vishleshan (tensar ainalisis) ka mukhy uddeshy aise niyamon ki rachana aur adhyayan hai, jo sadharanataya sahachar (kovairiaint) rahate hain, arthath‌ yadi ham niyamakon ki ek snhati se doosari men jaen to e niyam jyon ke tyon bane rahate hain. isilie avakal jyamiti ke lie yah vishay mahatvapoorn hai.

is vishay ke purane vicharakon men gaus, riman aur kristaaufel ke nam ullekhaniy hain. kintu is vishay ko vyavasthit roop richi aur levi chivita ne diya. inhonne is vishay ka nam badalakar nirapeksh chalan kalan (aibsolyoot difareshiyal kailkulas) kar diya. is vishay ka prayog anuprayakt ganit ki bahut si shakhaon men hota hai.

man lijie, ek trivistari avakash (spes) a3hai jisake pratyek bindu pa ke niyamak tin vastavik rashiyon y1y2 y3 par ashrit hain. man lijie, pa ke nikat hi pha ek doosara bindu hai jisake niyamak (y1+tay1y2+tay2y3+tay3) hain, to is avakal kulak (set aauv difarenshiyals)

tay'1 tay'2 tay'3

ko ek sadish (vektar) kahate hain; ya yon kahie ki binduyugm pa, pha ko ek sadish kahate hain.

man lijie, ham y'1, y2, y3,ko ek doosari niyamak paddhati y'1 y'2 y'3 men parivartit karate hain, jo aisi hai ki pahale niyamak doosare niyamakon ke satat phalan hain. isake atirikt avakal gunak

tay1 tay2 tay3 tay1 tay2

tay1 tay2 tay3 tay1 tay3

bhi satat hain (jahan t º ¶ )aur jaikobiyan

t (y1, y2, y3,)

t (y1', y2', y3',)

parimit hai, par shoony nahin to hamare parivartanasootr is prakar ke honge:

tay1' =tay1/tay3 * tay2

ab man lijie, ka1, ka2, ka3 tin rashiyan hain, to inaka roopantar is ke sootron se hoga:

tay1'=tay1/tay3 * tay2

to is rashi kulak ka1, ka2, ka3 ko padavi ek ke pratichal atanak (kntravairiaint tensar aauv raink van) kahenge aur rashiyan ka1, ka2, ka3, ukt atanak ke 3 snghatak kahalaengi. sadharanataya atanakon men uchch pratyay lagae jate hain

isake atirikt, yadi ka1, ka2, ka3, tin rashiyan hon, jinake pavirtanasootr is prakar ke hon:

tay2'=tay3/tay3 ,* tay2

to unake kulak ko sahachar atanak (kovairiaint tensar) kahate hain. in rashiyon ke lie nimnalikhit pratyayon ka prayog kiya jata hai.[1]

padavi 1 ke in tinon prakar ke atanakon ko sadish (vektar) bhi kahate hain is prakar, yadi s2 rashiyan kachachh hon, jinaka parivartanasootr ho to ve bhi ek sahachal ka srijan karati hain aur jo rashiyan kachachh hon, jinaka parivartanasootr

ho,to vah padavi 2 ke ek pratichal ka srijan karati hain. spasht hai ki ham in paribhashaon ka kisi bhi padavi tak vistar kar sakate hain. padavi. ke atanak ko adish bhi kahate hain. yah y ka ekaki phalan hota hai, jo niyamakon ke kisi bhi paritarvan ph'= ph ke lie nishchal (invairient) rahata hai.[2]


panne ki pragati avastha
adhar
prarambhik
madhyamik
poornata
shodh

tika tippani aur sndarbh

  1. hindi vishvakosh, khand 1 |prakashak: nagari pracharini sabha, varanasi |snkalan: bharat diskavari pustakalay |prishth snkhya: 362 |
  2. sn.grn.-el.pi.aizenahart : kntinyuas groops aauv trainsaphaaurmeshns (1933); o.veblen : invairientas aauv kvadraitik difarenshiyal farms (1927); e.di. maikel : maitriks aind tensar kailakyulas vid aiplikeshans tu mekainiks, ilaistisiti aind earonaautiks (1946).

snbndhit lekh

varnamala kramanusar lekh khoj

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