Chii chakakosha, uye chii chiri mumuviri zvarinoreva

Pakuonekwa akanga pfungwa chinokosha nokuda kudiwa kuwana chinyakare kushanda kwayo rinobva, uye kuona kukosha kwebasa nzvimbo dzakaoma zvitarisiko, daro akafamba chinhambwe, pamwe parameters akataura makakombama nokuda nonlinear equations.

Ichokwadi uye Physics tinoziva kuti basa iri zvakagadzirwa simba pamusoro kure. Kana zvose sangano iri kugara kumhanya kana Daro vanokurirwa pokushandisa chete simba, ipapo zvose zviri pachena, imi nyore muwande. Chii chinokosha pamusoro dzose? Uyu Linear kushanda muchimiro and = Kx + c.

Asi simba nokuda nokushanda kunogona siyana uye mune dzimwe yakarongeka ukama. Mamiriro ezvinhu akafanana anovapo dzemaitirwe kure vakafamba, kana kumhanya hakusi kugara.

Saka, zvinonzwisisika kuti nei pane chinokosha. Zvaraireva sezvo chitsama zvibereko tsika mashandiro pamusoro kamwoyo increment renharo anorondedzera chose chikuru zvinoreva izwi sezvo nzvimbo yacho mufananidzo rakatenderedzwa pamusoro mutsara mashandiro, uye micheto - tsanangudzo miganhu.

Jean Gaston Darboux yemasvomhu French, yechipiri yezana XIX remakore zvinotsanangurwa zvakajeka kwazvo kuti chinokosha ichi. Akaita izvozvo pachena kuti yose hakuzovi kwakaoma kunzwisisa kunyange mwana wechikoro mudiki chesekondari panyaya iyi.

Ngatiti pane kushanda chero zvakaoma chimiro. Y-akabatana, pamusoro izvo rakachengetedzwa kukosha nharo, rakakamurwa zvikamu zviduku, Zvakanakisa, vari anoramba diki, asi nekuti pfungwa kusaverengeka rakanyatsojeka husingaoneki, zvakakwana kufungidzira zvidimbu zviduku chete, uwandu iyo kazhinji runotaurwa netsamba Greek Δ (Delta).

Mashandiro akanga "sliced" madiki zvinogumbura.

kukosha nerimwe renharo unoenderana pfungwa pamusoro ordinate akabatana panguva iyo aisa runoenzanirana tsika mashandiro. Asi sezvo miganhu iri akasarudzwa nzvimbo mbiri, tsika uye mashandiro achava maviri kana kupfuura uye zvishoma.

Verengai zvibereko guru tsika nokuda increment Δ akadana Darboux yakawanda, uye anonzi S. Naizvozvo maduku tsika kuti zvishoma nharaunda, kane Δ, pamwe chete kuumba zvishoma Darboux s. Nzvimbo pacharo chakafanana rectangular trapezoid, saka ari kushanda curvature wedzinza nokuda ane kamwoyo increment chinogona kuregeredzwa. Nyore nzira kuwana nzvimbo imwe geometric chimiro - munhu akapeta zvidimbu makuru nemaduku tsika mashandiro musi Δ-increment uye chakaparadzanisa vaviri, kuti rinorondedzerwa so svomhu maturo.

Ndizvo zvakaita chinokosha Darboux:

S = Σf (x) Δ - chiduku;

S = Σf (x + Δ) Δ - zvizhinji.

Saka, chii chinokosha? Area rakatenderedzwa mutsetse kushanda uye tsanangudzo miganhu vachava akaenzana:

∫f (x) yori = {(S + s) / 2} + C

Kureva svomhu utsinye zvikuru uye zviduku rakawandisa Darbu.s - kugara kukosha, resettable pamusoro Kusiyanisa.

Pachishandiswa geometric kuratidza pfungwa iyi, zvinova pachena zvinorehwa chinokosha chaiko. Square zvitarisiko, akaronga kushanda nokukurumidza, uye shoma nguva penguva pamusoro x-akabatana ichava Kureba nechokure vaifamba.

L = ∫f (x) yori ari penguva kubva T1 kusvikira t2,

apo

d (x) - iri kushanda akurumidze, kuti ndiye nzira naro nayo Kuchinja pamusoro nguva;

L - Kureba nzira;

T1 - pakatanga nguva nzira;

t2 - nguva kupera nzira.

Anawo musimboti vagara vandifungira uwandu basa, asi achava iiswe pamusoro abscissa daro uye ordinate - uwandu simba rinobva pane mumwe nomumwe pfungwa.