आतानक विश्लेषण
atanak vishleshan (teansar ainalisis) ka mukhy uddeshy aise niyamoan ki rachana aur adhyayan hai, jo sadharanataya sahachar (kovairiaiant) rahate haian, arthath yadi ham niyamakoan ki ek sanhati se doosari mean jaean to e niyam jyoan ke tyoan bane rahate haian. isilie avakal jyamiti ke lie yah vishay mahatvapoorn hai.
is vishay ke purane vicharakoan mean gaus, riman aur krist aaufel ke nam ullekhaniy haian. kiantu is vishay ko vyavasthit roop richi aur levi chivita ne diya. inhoanne is vishay ka nam badalakar nirapeksh chalan kalan (aibsolyoot difareshiyal kailkulas) kar diya. is vishay ka prayog anuprayakt ganit ki bahut si shakhaoan mean hota hai.
man lijie, ek trivistari avakash (spes) a3hai jisake pratyek biandu pa ke niyamak tin vastavik rashiyoan y1y2 y3 par ashrit haian. man lijie, pa ke nikat hi pha ek doosara biandu hai jisake niyamak (y1+tay1y2+tay2y3+tay3) haian, to is avakal kulak (set aauv difareanshiyals)
tay'1 tay'2 tay'3
ko ek sadish (vektar) kahate haian; ya yoan kahie ki bianduyugm pa, pha ko ek sadish kahate haian.
man lijie, ham y'1, y2, y3,ko ek doosari niyamak paddhati y'1 y'2 y'3 mean parivartit karate haian, jo aisi hai ki pahale niyamak doosare niyamakoan ke satat phalan haian. isake atirikt avakal gunak
tay1 tay2 tay3 tay1 tay2
tay1 tay2 tay3 tay1 tay3
bhi satat haian (jahaan t º ¶ )aur jaikobiyan
t (y1, y2, y3,)
t (y1', y2', y3',)
parimit hai, par shoony nahian to hamare parivartanasootr is prakar ke hoange:
tay1' =tay1/tay3 * tay2
ab man lijie, ka1, ka2, ka3 tin rashiyaan haian, to inaka roopaantar is ke sootroan se hoga:
tay1'=tay1/tay3 * tay2
to is rashi kulak ka1, ka2, ka3 ko padavi ek ke pratichal atanak (kantravairiaiant teansar aauv raiank van) kaheange aur rashiyaan ka1, ka2, ka3, ukt atanak ke 3 sanghatak kahalaeangi. sadharanataya atanakoan mean uchch pratyay lagae jate haian
isake atirikt, yadi ka1, ka2, ka3, tin rashiyaan hoan, jinake pavirtanasootr is prakar ke hoan:
tay2'=tay3/tay3 ,* tay2
to unake kulak ko sahachar atanak (kovairiaiant teansar) kahate haian. in rashiyoan ke lie nimnalikhit pratyayoan ka prayog kiya jata hai.[1]
padavi 1 ke in tinoan prakar ke atanakoan ko sadish (vektar) bhi kahate haian is prakar, yadi s2 rashiyaan kachachh hoan, jinaka parivartanasootr ho to ve bhi ek sahachal ka srijan karati haian aur jo rashiyaan kachachh hoan, jinaka parivartanasootr
ho,to vah padavi 2 ke ek pratichal ka srijan karati haian. spasht hai ki ham in paribhashaoan ka kisi bhi padavi tak vistar kar sakate haian. padavi. ke atanak ko adish bhi kahate haian. yah y ka ekaki phalan hota hai, jo niyamakoan ke kisi bhi paritarvan ph'= ph ke lie nishchal (invairieant) rahata hai.[2]
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tika tippani aur sandarbh
- ↑ hindi vishvakosh, khand 1 |prakashak: nagari pracharini sabha, varanasi |sankalan: bharat diskavari pustakalay |prishth sankhya: 362 |
- ↑ san.gran.-el.pi.aizenahart : kantinyuas groops aauv traiansaph aaurmeshans (1933); o.veblen : invairieantas aauv kvadraitik difareanshiyal farms (1927); e.di. maikel : maitriks aiand teansar kailakyulas vid aiplikeshans tu mekainiks, ilaistisiti aiand earon aautiks (1946).
sanbandhit lekh
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varnamala kramanusar lekh khoj
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