Keyword Analysis & Research: exterior derivative


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Keyword CPC PCC Volume Score Length of keyword
exterior derivative0.420.338149119
exterior0.640.77310968
derivative10.360852610

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Keyword CPC PCC Volume Score
exterior derivative1.020.3899680

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  • Exterior derivative - Wikipedia

    wikipedia.org

    https://en.wikipedia.org/wiki/Exterior_derivative

    WEBDefinition. The exterior derivative of a differential form of degree k (also differential k -form, or just k -form for brevity here) is a differential form of degree k + 1 . If f is a smooth function (a 0 -form), then the exterior derivative of f is the differential of f .

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  • Exterior Derivative -- from Wolfram MathWorld

    wolfram.com

    https://mathworld.wolfram.com/ExteriorDerivative.html

    WEB2 days ago · The exterior derivative of a function f is the one-form df=sum_(i)(partialf)/(partialx_i)dx_i (1) written in a coordinate chart (x_1,...,x_n). Thinking of a function as a zero-form, the exterior derivative extends linearly to all differential k-forms using the formula d(alpha ^ beta)=dalpha ^ beta+(-1)^kalpha ^ dbeta, (2) when alpha is a …

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  • 4.1 The exterior derivative - University of Toronto Department …

    toronto.edu

    https://www.math.toronto.edu/mgualt/MAT1300/week11.pdf

    WEBThe exterior derivative is uniquely speci ed by the following requirements: rst, it satis es d(df) = 0 for all functions f. Second, it is a graded derivation of the algebra of exterior di erential forms of degree 1, i.e. d( ^ ) = d ^ + ( 1)j j ^d : This allows us to compute its action on any 1-form d(˘ idxi) = d˘

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  • What is the exterior derivative intuitively? - MathOverflow

    mathoverflow.net

    https://mathoverflow.net/questions/21024/what-is-the-exterior-derivative-intuitively

    WEB11 Answers. Sorted by: 87. Many years back I wrote something about an intuitive way to look at differential forms here. In particular, figure 4 illustrates Stokes' theorem in a way that generalises to higher dimensions.

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  • Differentiating k-forms: the exterior derivative - University of Alberta

    ualberta.ca

    https://sites.ualberta.ca/~vbouchar/MATH215/section_exterior_derivative.html

    WEBThe exterior derivative of a k -form ω = ∑ 1 ≤ i 1 < ⋯ < i k ≤ n f i 1 ⋯ i k d x i 1 ∧ ⋯ ∧ d x i k on U ⊂ R n is the ( k + 1) -form d ω on U given by: d ω = ∑ 1 ≤ i 1 < ⋯ < i k ≤ n d ( f i 1 ⋯ i k) ∧ d x i 1 ∧ ⋯ ∧ d x i k, where d ( f i 1 ⋯ i k) means the exterior derivative of the zero-form (function ...

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  • LECTURE 22: THE EXTERIOR DERIVATIVE - 中国科学技术 …

    ustc.edu.cn

    http://staff.ustc.edu.cn/~wangzuoq/Courses/21F-Manifolds/Notes/Lec22.pdf

    WEBLECTURE 22: THE EXTERIOR DERIVATIVE 3 (2) d!fis multi-linear at each point, i.e. d!fis C1(U)-linear on U. Note that fd!is obviously R-linear. So in view of (1), it is enough to prove for any...

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  • LECTURE 25: DIFFERENTIAL FORMS. - Mathematics

    jhu.edu

    https://math.jhu.edu/~brown/courses/s19/Lectures/Lecture25.pdf

    WEBis called the exterior derivative of !. Some notes: We call a C1-function f : DˆRn!R a (di erential) 0-form. Thus the exterior derivative of a function is simply its di erential, a 1-form. Thus theexterior derivative of any di erential m-form is always an (m+ 1)-form. For each set of indices, the term d(F i 1i 2 im) is the standard di erential ...

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  • 12.6: Directional Derivatives - Mathematics LibreTexts

    libretexts.org

    https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/12%3A_Functions_of_Several_Variables/12.06%3A_Directional_Derivatives

    WEBMar 22, 2024 · Partial derivatives give us an understanding of how a surface changes when we move in the x and y directions. We made the comparison to standing in a rolling meadow and heading due east: the amount of rise/fall in doing so is comparable to fx.

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  • Exterior Derivatives

    sinica.edu.tw

    https://idv.sinica.edu.tw/ftliang/diff_geom/*diff_geometry(II)/3.04/exterior_derivative_1.pdf

    WEBExterior Derivatives • In this section we define a natural differential operator on smooth forms, called the exterior derivative. It is a generalization of the diffeential of a function. Motivations: • Recall that not all 1-forms are differentials of functions: Given a smooth 1-form ω, a necessary condition for the existence of a smooth function f such that ω = df is …

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  • Exterior Differential Forms

    ucdavis.edu

    https://www.math.ucdavis.edu/~saito/data/tensor/Suhubi_book/Chapter-V-Exterior-Differential-Forms_2013_Exterior-Analysis.pdf

    WEBterior differential forms as exterior products of differentials of coordinates (exterior derivatives) and thus equipping them with an algebraic structure. In Sec. 5.2, the exterior differential forms on differentiable manifolds and exterior algebra formed by them are defined and it is shown that they constitute a module.

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