Ib tug ua tiav kev tshawb no ntawm kev khiav dej num thiab differential calculus

Muaj nws kim heev kev txawj ntse nyob rau hauv cov yam ntxwv uas peb teem armed nrog txaus lub cuab tam mus nqa tawm ib tug ua tiav kev tshawb no lej predetermined qauv nyob rau hauv daim ntawv ntawm ib tug qauv (muaj nuj nqi). Ntawm cov hoob kawm, ib tug yuav mus rau feem ntau yooj yim tab sis laborious txoj kev. Piv txwv li, muab uas sib cav xaiv luv, xam muaj nuj nqi nqi rau nws thiab tsim ib tug teeb. Nyob rau hauv lub xub ntiag ntawm lub haib niaj hnub lub computer systems, qhov teeb meem no yog solved nyob rau hauv ib tug teeb meem ntawm vib nas this. Tab sis rau tshem tawm tag nrho cov arsenal ntawm nws cov kev tshawb ntawm cov nuj nqi ntawm kev kawm txog zauv nyob rau hauv tsis muaj hurry, vim hais tias los ntawm cov kev muaj peev xwm yuav siv tau rau kev ntsuam xyuas cov correctness ntawm lub lag luam ntawm computer systems nyob rau hauv kev daws tej teeb meem. Nyob rau hauv txhua yam plotting, peb yuav tsis lav cov neeg teev saum toj no ntau yam nyob rau hauv cov kev xaiv sib cav.

Thiab tsuas yog tom qab ib tug ua tiav kev tshawb nrhiav ntawm cov nuj nqi, koj yuav tau nco ntsoov, hais tias yuav siv sij hawm mus rau hauv tus account tag nrho cov nuances ntawm "tus cwj pwm" nws tus kheej yog tsis nyob rau cov zauv luv, thiab nyob rau hauv tag nrho cov ntau yam ntawm cov lus.

Nyob rau hauv thiaj li yuav daws tau ntau yam kev pab raws qib nyob rau hauv lub teb ntawm physics, lej thiab technology muaj ib tug yuav tsum tau lees paub ib tug txoj kev tshawb no ntawm tej dependence ntawm lub zog kev koom tes nyob rau hauv no phenomenon. Xeem, muab analytically los ntawm ib tug los yog ib tug txheej ntawm ob peb cov qauv, tso cai rau txoj kev tshawb no ntawm txoj kev xyuam xim analytics.

Yuav kom ib tug tag nrho cov kev tshawb nrhiav txog lub zog - mus nrhiav thiab txheeb xyuas tej qhov chaw uas nws yuav tsub (txo), qhov chaw uas nws nce mus txog tus siab tshaj plaws (yam tsawg kawg nkaus), raws li zoo li lwm yam nta ntawm nws lub sij hawm.

Muaj tej yam schemes, uas tsim ib tug ua tiav kev tshawb ntawm cov nuj nqi. Piv txwv ntawm cov npe ntawm cov zauv tshawb fawb nqa tawm yog txo mus nrhiav zoo zoo tib yam lub sij hawm. Approximate tsom xam ntawm lub hom phiaj yuav cov nram qab no kev tshawb fawb:

- nrhiav tus sau ntawm cov nuj nqi, peb soj ntsuam tus cwj pwm nyob rau hauv nws ciam teb rau lwm;

- raug nrhiav so ntsiab lus rau kev faib los ntawm txoj kev unilateral txwv;

- mus nqa tawm tej yam asymptotes;

- peb nrhiav tau cov extremum taw tes thiab monotonicity Team sib;

- tsim ib tug tej yam inflection, Team sib ntawm concavity thiab convexity;

- nqa tawm cov kev siv lub sij hawm nyob rau hauv lub hauv paus ntawm qhov kev tshwm sim ntawm txoj kev tshawb.

Thaum xav tsuas yog ib cov ntsiab lus ntawm lub hom phiaj yog tsim nyog sau cia hais tias lub differential calculus tau zoo heev lub cuab tam rau txoj kev tshawb no ntawm kev khiav dej num. Muaj yooj yim heev mus uas muaj nyob ntawm tus cwj pwm ntawm cov nuj nqi thiab nws derivative nta. Yuav kom daws tau qhov teeb meem no nws yog txaus los mus xam tus thawj thiab thib ob derivative.

Xav txog tus txheej txheem rau kev nrhiav cov Team sib txo, kom muaj nuj nqi, lawv tseem tau txais lub npe ntawm monotony Team sib.

Nws yog txaus los mus txiav txim lub kos npe rau ntawm tus thawj derivative ntawm ib tug tej lub sij hawm. Yog hais tias nws yog tas li nyob rau hauv lub luv yog ntau tshaj pes tsawg, ces peb yuav tau xyuam xim txiav txim rau cov monotonic nce muaj nuj nqi nyob rau hauv no ntau, thiab vice versa. Tsis zoo qhov tseem ceeb ntawm cov thawj derivative yog yus raws li ib tug monotonically zuj zus lawm muaj nuj nqi.

Nrog kev pab los ntawm lub xam ntawm derivatives xws site graphics, hu ua bulges thiab concave zog. Nws yog muaj pov thawj hais tias yog nyob rau hauv lub chav kawm ntawm suav tau derivative muaj nuj nqi tas mus li thiab tsis zoo, nws qhia hais tias tus convexity, laaj ntawm lub thib ob derivative thiab nws zoo nqi ntawd hais tias cov concavity ntawm lub teeb.

Nrhiav lub sij hawm, thaum muaj ib tug kev hloov ntawm kos npe rau nyob rau hauv lub thib ob derivative, los yog tej qhov chaw uas nws tsis muaj nyob, qhia tau hais tias qhov kev txiav txim ntawm tus taw tes ntawm inflection. Hais tias nws yog ib tug ciam ntawm ua mib ntawm convexity thiab concavity.

Tag nrho cov kev tshawb ntawm cov nuj nqi tsis xaus nrog lub saum toj no cov ntsiab lus, tab sis txoj kev siv cov differential calculus heev simplifies tus txheej txheem no. Nyob rau hauv cov ntaub ntawv no, cov kev tshwm sim ntawm tus tsom xam muaj ib tug tshaj plaws degree ntawm kev cog qoob loo, uas tso cai rau kom lawv muaj ib lub teeb, yog nkaus raws li lub zog ntawm cov kev xeem zog.