Video: Koj puas tuaj yeem nqa qhov gradient ntawm vector?
2024 Tus sau: Miles Stephen | [email protected]. Kawg hloov kho: 2023-12-15 23:36
Cov gradient of a function, f(x, y), in twodimensions is definition as: gradf(x, y) = Vf(x, y) = ∂f ∂xi + ∂f ∂y j. Nws yog tau los ntawm kev siv lub vector tus neeg teb xov tooj V rau qhov kev ua haujlwm scalar f(x, y). Xws li ib vector teb hu ua a gradient (los yog conservative) vector teb.
Ntxiv rau qhov no, dab tsi yog qhov gradient ntawm vector?
Home › lej › Vector Calculus › Vector Calculus: Nkag siab qhov Gradient . Cov gradient yog ib lo lus zoo nkauj forderivative, los yog tus nqi ntawm kev hloov ntawm ib tug muaj nuj nqi. Nws yog ib vector (ib txoj kev txav mus los) ntawd. Cov ntsiab lus nyob rau hauv cov kev taw qhia ntawm qhov loj tshaj plaws ntawm ib tug muaj nuj nqi (intuition ntawm yog vim li cas)
Tsis tas li ntawd, puas yog gradient ib txwm rau saum npoo? Yog li ntawd, lub gradient yog perpendicular mus rau tangent vector ntawm lub nto ntawm p, rau txhua qhov nkhaus p ton tus nto uas hla p. Yog li cov gradient yuav tsum nyob rau hauv cov kev taw qhia ntawm lub ib txwm mus rau nto . Yog li ntawd, lub gradient yog ib txwm rau qhov nkhaus.
Qhov thib ob, koj pom qhov gradient ntawm ib txoj haujlwm li cas?
Rau nrhiav tus gradient , coj lub derivative ntawm lub muaj nuj nqi nrog rau x, ces hloov thex-coordinate ntawm lub ntsiab lus ntawm kev txaus siab rau x qhov tseem ceeb hauv thederivative.
Puas yog gradient ntawm vector yog scalar?
Cov gradient yog a vector kev ua haujlwm uas ua haujlwm ntawm a scalar muaj nuj nqi los tsim ib vector nws qhov loj yog qhov siab tshaj plaws ntawm kev hloov pauv ntawm kev ua haujlwm ntawm qhov taw tes ntawm qhov gradient thiab uas yog taw qhia nyob rau hauv cov kev taw qhia ntawm qhov siab tshaj plaws ntawm kev hloov.
Pom zoo:
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