Masiyanidwe kakyulasi ntchito ya wina ndi zosintha angapo

Masiyanidwe kakyulasi ndi nthambi ya kusanthula masamu, amene amasanthula otumphukira, differentials ndi ntchito mu kuphunzira ntchito.

Nkhani ya

Masiyanidwe kakyulasi anatuluka ngati chilango wodzilamulira mu theka lachiwiri la m'ma 17, chifukwa cha ntchito ya Newton ndi Leibniz, amene anakonza chakudya kwakukulu mu mawerengedwe a differentials ndipo anaona kugwirizana kusakanikirana ndi zosiyanasiyana. Popeza chilango anayamba pamodzi ndi mawerengedwe a integrals, potero kupanga maziko a kusanthula masamu. Maonekedwe a calculi izi anatsegula latsopano ano nthawi mu dziko masamu ndipo anamupangitsa zikamera wa khalidwe latsopano mu sayansi. Komanso anawonjezera kuti n'zotheka kutsatira masamu mu sayansi zachilengedwe ndi zomangamanga.

mfundo zofunika

Masiyanidwe kakyulasi zachokera mfundo zikuluzikulu masamu. Iwo: weniweni chiwerengero, kupitiriza ndi malire a ntchito. Patapita kanthawi, iwo atenga tione ano, chifukwa cha yofunika ndi masiyanidwe kakyulasi.

The ndondomeko ya kulenga

Mapangidwe ndi masiyanidwe kakyulasi mu mawonekedwe a yofunsira, kenako njira za sayansi zinalipo kale zikamera chiphunzitso nzeru zaumunthu, amene analengedwa ndi Nikolay Kuzansky. ntchito Yake ankaona kuti chochitika zamoyo zinachita ku sayansi wakale wa chiweruzo. Ngakhale kuti nzeru zapamwamba yekha sanali masamu, anathandiza kuti chitukuko cha sayansi masamu ndi wosatsutsika. Cusa, mmodzi wa kunja loyamba la kulingalira masamu ndi sayansi zolondola kwambiri, masamu kuika nthawi mu funso.

Mu masamu wakale chilengedwe muyezo anali unit, pamene nzeru zapamwamba akufuna kukhala latsopano muyeso osawerengeka kubwerera chiwerengero chenicheni. Mogwirizana ndi chifaniziro ichi Imatithandiza olondola mu sayansi masamu. sayansi, mu maganizo ake, lagawidwa zomveka ndiponso anzeru. Lachiwiri ndi zolondola, molingana ndi wasayansi, chifukwa poyamba chimangooneka zotsatira pafupifupi.

lingaliro

Ganizo zikuluzikulu ndi mfundo masiyanidwe kakyulasi kugwirizana ndi ntchito ya a m'dera ka mfundo zina. Pakuti ichi ndikofunikira kuti akonze zida masamu liziyenda maphunziro amene makhalidwe a m'dera ka mfundo anaika pafupi khalidwe la ntchito liniya kapena polenomiyo. Kuchokera pa tanthauzo limeneli la otumphukira ndi masiyanidwe.

Zikamera wa mfundo ndilochokera pa chifukwa cha chiwerengero chachikulu cha mavuto a sayansi ndi masamu, zimene zinachititsa kuti mtima wa malire mfundo za mtundu womwewo.

Imodzi mwa ntchito zomwe zili zikuluzikulu anapereka chitsanzo, kuyambira ndi makalasi wamkulu sukulu, ndi kudziwa liwiro la zoyenda za mfundo mu mzere molunjika ndi pomanga tangent mzere kuti limaoneka lokongola lino. The masiyanidwe mwalumikiza, chifukwa n'zotheka kuyandikira kugwira ntchito a m'dera ka mfundo ya ntchito ndi liniya.

Poyerekeza ndi mfundo ndilochokera ku ntchito ya variable enieni, tanthauzo la differentials chabe akudutsa pa ntchito ya chikhalidwe ambiri, makamaka chifanizo cha danga Euclidean ndi mzake.

otumphukira

Tiyeni ukusunthira mfundo malangizo a Y-olamulira, chifukwa nthawi timatenga ×, amene anayeza kuyambira chiyambi cha kamphindi. Fotokozani gulu zinthu zimenezi ndi ntchito Y = f (x), amene amagwirizana ndi mfundo nthawi × ntchito displaceable mfundo. Izi foni ntchito mu zimango kutenga malamulo a apaulendo. Khalidwe lalikulu la zoyenda, makamaka m'goli, ndi a mathamangidwe yomweyo. Pamene tizindikirenso kuyenda kwa Y-olamulira monga mwa chilamulo cha zimango, longoponyapo nthawi mfundo izo amapeza ntchito × f (x). Mu nthawi mfundo × + Δh, kumene Δh umaimira increment wa nthawi, izo kordinaty f (× + Δh). Choncho anapanga chilinganizo Δy = f (× + Δh) - F (x), amene akutchedwa increment ntchito. Ndi mfundo njira anayendayenda nthawi kuchokera × kuti × + Δh.

Mogwirizana ndi kwa mawu mathamangidwe nthawi otumphukira chikuyendetsedwera. The ndilochokera ku ntchito iliyonse pa mfundo atathana otchedwa malire (poganiza kuti alipo). Iwo akhoza kunena kuti zilembo zina:

f '(x), Y, Y df / dx, Dy / dx, Df (x).

The ndondomeko ya kuwerengetsa ndi otumphukira kuitana zosiyanasiyana.

Masiyanidwe kakyulasi ntchito ya zosintha angapo

Njira umagwiritsidwa pamene kuwerengetsa ntchito phunziro, zosintha zambiri. Pamene pali zosintha ziwiri × ndi Y, ndi tsankho otumphukira ndi kulemekeza × pa mfundo A amatchedwa ndilochokera ku nchito imeneyi mu × ndi Y lokhazikika.

Akhoza anasonyeza ndi zizindikiro zotsatirazi:

f '(x) (×, Y), u' (x), ∂u / ∂x ndi ∂f (×, Y) '/ ∂x.

luso Amafuna

Kuti bwinobwino kuphunzira ndi kukhala okhoza kuthetsa diffury chofunika luso kusakanikirana ndi zosiyanasiyana. Kukhala kosavuta kumvetsa masiyanidwe maikwezhoni, ayenera kuzindikiridwa mutu otumphukira ndi kalekale yofunika. Komanso sakuwupweteka kuphunzira kuyang'ana ndilochokera ku ntchito ya wonse. Ichi ndi chifukwa chakuti mu ndondomeko ya maphunziro zambiri ntchito integrals ndipo zosiyanasiyana.

Mitundu ya maikwezhoni masiyanidwe

Pafupifupi onse kulamulira ntchito kugwirizana ndi woyamba kuti maikwezhoni masiyanidwe, pali mitundu 3 maikwezhoni: kwenikweni ndi zosintha mbali, liniya inhomogeneous.

Palinso mitundu yosowa kwambiri maikwezhoni ndi differentials okwana aone kuti pali Bernoulli, ndi anthu ena.

chikhazikitso zothetsera

Kuyamba, tiyenera kukumbukira algebraic aone kuti pali njira sukulu. Iwo ali ndi zosintha ndi manambala. Pofuna kuthetsa aone kuti pali ochiritsira ayenera kupeza zambiri manambala kuti akhutitse chikhalidwe yake. Childs, maikwezhoni awa ndi muzu wina, ndi kutsimikiza Pasakhale mmalo phindu ili mu malo osadziwika.

The masiyanidwe aone kuti pali ndi ofanana ndi uyu. Ambiri, ndi aone kuti pali dongosolo loyamba limapangidwa:

• Independent variable.
• A ndilochokera ku ntchito woyamba.
• Ntchito kapena yozungulira variable.

Nthawi zina, pasakhale wina wosadziwika, × kapena Y, koma si zofunika kwambiri monga m'pofunika kukhala otumphukira choyamba, palibe opangidwa kuchokera apamwamba kuti yankho ndi masiyanidwe kakyulasi zinali zoona.

Kuthetsa masiyanidwe aone kuti pali - zikutanthauza kuti mupeze mndandanda wa ntchito onse amene ali oyenera kupatsidwa mawu. adzabweretse kotereku ntchito limatchedwa ambiri kulamulira njira.

yofunika kakyulasi

Yofunika kakyulasi ndi chimodzi mwa zigawo kusanthula masamu, amene amafufuza mfundo yofunika, katundu ndi njira mawerengedwe ake.

Kawirikawiri mawerengedwe a yofunika kumachitika pamene kuwerengetsa dera mawonekedwe curvilinear. Ichi chimatanthauza dera malire, kwa amene anakonzeratu Malo alembedwa polygon mawonekedwe ndi kuwonjezeka pang'onopang'ono dzanja lake, ndi mbali deta akhale zochepa kuposa kale mwachindunji kufunika umasinthasintha yaing'ono.

The lingaliro lalikulu mu mawerengedwe a m'dera la mawonekedwe uliwonse zojambula ndi kuwerengetsa dera rectangle, ndiye pali umboni wakuti malo ake ali ofanana ndi mankhwala a m'litali ndi m'lifupi. Pankhani Masamu, ndiye zomangamanga onse pogwiritsa ntchito wolamulira ndi kampasi, ndiyeno chiŵerengero cha kutalika kwa m'lifupi ndi phindu zomveka. Pamene kuwerengetsa dera kansalu bwino zingadziŵike kuti akaika kansalu lotsatira, rectangle ndi aumbike. M'dera la parallelogram ndi masamu mu njira zofanana koma pang'ono zovuta, mkati rectangle ndi kansalu. M'dera la polygon imatengedwa ndi Triangles m'gulu izo.

Kudziwa chifundo cha umasinthasintha, njira imeneyi si woyenera pa pamapindikira. Ngati tinyema mu mabwalo payekha, iwo adzakhala malo unfilled. Pankhaniyi, yesani kugwiritsa ntchito malaya awiri, ndi rectangles pamwamba ndi pansi, chifukwa cha anthu zikuphatikizapo Zithunzi za ntchito ndi simaphatikiza. Ofunika pano ndi njira kuswa rectangles izi. Komanso, ngati ife kutenga yopuma zambiri yafupika, dera pamwamba ndi pansi ayenera converge pa mtengo ena.

Izo ziyenera kubwerera ku njira ya kulekanitsa ku rectangles. Pali njira ziwiri otchuka.

Riemann anali formalized tanthauzo la integral, analengedwa ndi Leibniz ndi Newton, monga dera subgraph. Pankhaniyi, tinaona chithunzi ongokhala nambala inayake ya rectangles ofukula akamagwira kugawa imeneyi. Pamene kuswa kuchepa pali malire omwe yafupika dera chithunzi chotere, malire uwu umatchedwa Riemann yofunika ya ntchito pa imeneyi mwachindunji.

A njira yachiwiri ndi yomanga Lebesgue integral, wopangidwa chakuti mu malo olekanitsa anasankha dera pa mbali ya integrand ndi kulemba pamenepo Uwerenge yofunika ya makhalidwe analandira m'madera amenewa, pa intervals anagawa osiyanasiyana ake amatsogoza, ndiyeno mwachidule ndi miyeso lolingana zithunzi osiyanitsidwa wa integrals izi.

othandiza masiku ano

Mmodzi mwa ubwino waukulu phunziro la masiyanidwe ndi yofunika kakyulasi Fikhtengol'ts analemba - "wa masiyanidwe ndi yofunika kakyulasi." buku lake ndi chida kwambiri kuti kuphunzira kusanthula masamu, amene anatsutsana ndi Mabaibulo ambiri ndipo Mabaibulo m'zinenero zina. Analengedwa kuti ophunzira kwa nthawi yaitali ntchito zosiyanasiyana sukulu ngati wina wa ubwino waukulu wa kuphunzira. Iwo amapereka mauthenga ongolankhula ndi luso othandiza. Inafalitsidwa koyamba mu 1948.

Aligorivimu ntchito kafukufuku

Kufufuza njira masiyanidwe kakyulasi ntchito, muyenera kutsatira kale anapatsidwa aligorivimu:

1. Pezani ulamuliro wa kugwira ntchito.
2. Pezani mizu ya anthu aone kuti pali anapatsidwa.
3. Kuwerengetsa monyanyira. Kuti tichite zimenezi, tiyenera kuwerengera otumphukira ndi poti ndi wofanana ndi ziro.
4. Ife mmalo phindu zopezera Eq.

Zosiyanasiyana maikwezhoni masiyanidwe

Control wa Choyamba (mwinamwake, masiyanidwe kakyulasi wa variable wina) ndi mitundu:

• Ndi mbali zosintha aone kuti pali: f (Y) Dy = ga (x) dx.
• Losavuta aone kuti pali kapena masiyanidwe kakyulasi ntchito ya variable umodzi, wochitirana njira: Y '= f (x).
• The liniya loyamba kuti nonuniform control: Y '+ P (x) Y = Q (x).
• Bernoulli masiyanidwe aone kuti pali: Y '+ P (x) Y = Q (x) Y.
• Aone kuti pali okwana differentials ndi: P (×, Y) dx + Q (×, Y) Dy = 0.

The masiyanidwe maikwezhoni dongosolo chachiwiri ndi mitundu:

• Homogeneous liniya chachiwiri kuti masiyanidwe aone kuti pali ndi ^{koefishienti zonse: Y N + py '+ qy} = 0 tsa, Q uli R.
• Inhomogeneous liniya kuti chachiwiri masiyanidwe aone kuti pali ndi koefishienti zonse ^{mtengo: Y N + py '+ qy} = f (x).
• Homogeneous liniya masiyanidwe ^{aone kuti pali: Y N + tsa (x)} Y '+ Q (x) Y = 0, ndi inhomogeneous chachiwiri kuti ^{aone kuti pali: Y N + tsa (x)} Y' + Q (x) Y = f (x).

maikwezhoni masiyanidwe a malamulo apamwamba ndi mitundu:

• The masiyanidwe aone kuti pali, kulola kuchepetsa ^{dongosolo: F (×, Y (k} ), Y (k + ^{1), .., Y (n)} = 0.
• A aone kuti pali liniya dongosolo apamwamba ^{_{homogeneous: Y (n) + f (}} n- ₁₎ Y ^(n-1) + ... + f ₁ Y '+ f ₀ Y = 0, ndi ^{_{inhomogeneous: Y (n) + f (}} N _-1) Y ^(n-1) + ... + f ₁ Y '+ f ₀ Y = f (x).

Masiteji kuthetseratu vuto ndi masiyanidwe aone kuti pali

Mothandizidwa ndi mphamvu ya kutali ndi kuthetsedwa osati masamu kapena matenda, komanso mavuto osiyanasiyana a sayansi, zachuma, Chaanthu ndi ena. Ngakhale zosiyanasiyana za lonse nkhani ayenera kutsatira limodzi mfundo zinayendera kwa kuthetsa mavuto awa:

1. Mafanizo ulamuliro. Imodzi mwa magawo ovuta kwambiri, chimene chimafuna molondola pazipita, chifukwa kulakwitsa chilichonse kungachititse kuti zotsatira zolakwika. M'pofunika kuganizira mfundo zonse zokhudza ndondomeko ndi kudziwa zinthu koyamba. Tiyeneranso timakhulupirira ndi mfundo zokhutiritsa.
2. Pakuti kuthetsa maikwezhoni. Zimenezi ndi kosavuta mpaka kuyamba pamafunika yekha okhwima kukhazikitsa masamu.
3. Analysis ndi kufufuza zotsatira. Linachokera njira ayenera imawunikidwa kwa unsembe lothandiza ndi ongolankhula zotsatira za.

Chitsanzo cha ntchito masiyanidwe maikwezhoni mankhwala

Kugwiritsa ntchito mphamvu ya kutali m'munda wa mankhwala opezeka mu yomanga AIDS chitsanzo masamu. Tisaiwale kuti maikwezhoni izi zimapezekanso mu zamoyo ndi zimapangidwira, amene ali pafupi ndi mankhwala, chifukwa amagwira ntchito yofunika kwambiri kuphunzira anthu osiyana kwachilengedwenso ndi mankhwala zako mu thupi la munthu.

Mu chitsanzo ichi mliri kufala kwa matenda angachiritsidwe ndi mudzi wakutali. anthu anawagawa mitundu itatu:

• Matenda, chiwerengero cha × (T), imene inali anthu, matenda onyamula, omwe ndi opatsirana (makulitsidwe nthawi ndi yochepa).
• Mtundu wachiwiri zikuphatikizapo atengeke anthu Y (T), matenda ndi kukhudzana ndi kachilombo.
• Mtundu wachitatu akuphatikizapo onse refractory z (T), amene ali m'thupi kapena anataya chifukwa matenda.

Chiwerengero cha anthu nthawi zonse, kusunga kubadwa, imfa achilengedwe ndiponso kusamuka si. Pa pakati adzakhala malingaliro awiri.

Peresenti matenda panthawi ina nthawi ndi wofanana × (T) Y (T) (zochokera kopanda pa chiphunzitso chakuti chiwerengero cha milandu mogwirizana ndi chiwerengero cha mphambano pakati pa odwala ndi mamembala uthe, imene chiyerekezo woyamba ndi njila kwa × (T) Y (T)), mu Choncho chiwerengero cha milandu zikuchulukirachulukira, ndipo chiwerengero cha amachepetsa atengeke pa mlingo umene masamu ndi chilinganizo nkhwangwa (T) Y (T) (a> 0).

Chiwerengero cha nyama sanali anafunsidwa kuti anafa kapena kugula chitetezo chokwanira, kuchuluka pa mlingo umene uli molingana ndi chiwerengero cha milandu, bx (T) (b> 0).

Chifukwa cha zimenezi, mukhoza kukhazikitsa dongosolo la maikwezhoni ndi zizindikiro zonse zitatu pa maziko a mfundo zake.

CHITSANZO ntchito zachuma

Masiyanidwe kakyulasi kawirikawiri amagwiritsidwa ntchito kusanthula zachuma. Ntchito yaikulu mu kusanthula zachuma imatengedwa kuti kuphunzira mfundo za chuma, amene amapezeka mu mawonekedwe a kugwira ntchito. Izo ntchito pothetsa mavuto monga kusintha ukuwonjezeka msonkho ukangotha, chindapusa kulowa, kusintha revenues pamene kusintha mtengo wa mankhwala, kodi chiwerengero akhoza m'malo ndi antchito anapuma ndi zida zatsopano. Kuti athetse mavuto zimenezi, chofunika kumanga ntchito kulankhulana kwa zosintha lilinkudza, amene pambuyo kuphunzira ndi kakyulasi masiyanidwe.

nthawi zambiri kuti tipeze kwambiri mulingo woyenera ntchito mu dera zachuma: zokolola pazipita, ndalama Kumwambamwamba, ndalama zosachepera ndi zina zotero. Aliyense chigawo ngati ndi ntchito za mfundo imodzi kapena kuposa. Mwachitsanzo, kupanga tinganene kuti ngati ntchito ya ntchito ndi likulu. Pa nkhani imeneyi, kupeza phindu abwino zikhoza kuchepetsedwa kupeza pazipita kapena osachepera ntchito ya zosintha umodzi kapena kuposerapo.

mavuto kulenga kalasi ya mavuto extremal m'munda zachuma, umene muyenera masiyanidwe kakyulasi. Pamene chizindikiro chuma chofunika kuchepetsa kapena kudzapeza ngati ntchito ya magawo ena, increment chiŵerengero pazipita mfundo ntchito kuti mfundo adzatengera ziro ngati increment mfundo amamuchititsa ziro. Apo ayi, pamene zimenezi amamuchititsa wina phindu zabwino kapena zoipa, mwachindunji mfundo siyabwino, chifukwa ndi kuwonjezeka kapena mwayamba kufooka mkangano zikhoza kusintha mtengo yozungulira motsogozedwa ankafuna. Mu masiyanidwe kakyulasi terminology, izi zikutanthauza kuti zinthu wofunikila ntchito pazipita ndi phindu ziro wa otumphukira ake.

chuma si zachilendo vuto chopeza extremum wa ntchito ya zosintha angapo, chifukwa zizindikiro zachuma amapangidwa ndi zifukwa zambiri. nkhani zimenezi ali bwinobwino mchiphunzitso cha ntchito za zosintha angapo, njira ya kuwerengetsa ndi masiyanidwe. mavuto kugwiritsa ntchito osati maximized ndipo sanamvere ntchito, komanso zofooka. mafunso awa ikukhudzana bwanji ndi mapulogalamu masamu, ndipo anathana mothandizidwa ndi njira mwapadera anayamba amagwiritsidwa zochokera nthambi izi wa sayansi.

Mwa njira masiyanidwe kakyulasi ntchito chuma, mbali zofunika ndi mayeso mtheradi. Mu dera zachuma, mawuwa amanena ya njira ya kafukufuku wa ntchito variable ndi zotsatira inu kusintha voliyumu ya chilengedwe, mowa, potengera kusanthula mfundo zawo malire. Kuchepetsa umboni ankaona otumphukira kapena ofanana nawo tsankho ndi zosintha angapo.

Masiyanidwe kakyulasi wa zosintha angapo - ndi nkhani yofunika kwambiri kusanthula masamu. Kuti kuphunzira zambiri, mukhoza kugwiritsa ntchito zosiyanasiyana pophunzitsa mabungwe maphunziro apamwamba. Mmodzi wa Fikhtengol'ts wotchuka analenga - "wa masiyanidwe ndi yofunika kakyulasi." Mochuluka bwanji dzina la za njira ya masiyanidwe maikwezhoni chapadera kwambiri kuti luso ntchito ndi integrals. Pamene pali masiyanidwe kakyulasi ntchito ya variable wina, chigamulo mosavuta. Ngakhale, tisaiwale, ndizoonekeratu chimodzimodzi malamulo zofunika. Zochita kufufuza ntchito ya masiyanidwe kakyulasi, mongotsatila aligorivimu kale, lopatsidwa mwa sekondale ndipo pang'ono chabe zovuta ndi kumayambiriro zosintha latsopano.