Stokes' Theorem 2. Proof Reference 0. Introduction 在高二下学校Cal3课进入曲线曲面积分,Green's&Stoke's&Divergence Theorem的时候,老师给我们留了一个作业:斯托克斯公式的证明。 鉴于CALCULUS EARLY TRANSCENDENTALS EIGHTH EDITION JAMES STEWART(我们Calculus3的教材)只有一个特殊形式的斯托克斯公式的证明,我翻出来...
8 1 3 分享 流体力学:梯度算子积分,Gauss定理,Stokes定理,Green定理。 Stokes定理证明,可参考:https://math.libretexts.org/Courses/Montana_State_University/M273%3A_Multivariable_Calculus/16%3A_Vector_Fields_Line_Integrals_and_Vector_Theorems/Stokes'_Theorem%20。 (视频里,“Stokes”,可能全都说成了“...
Stokes' theorem is a generalization of Green's theorem to a higher dimension. Learn more about Stokes law with proof and formula along with divergence theorem at BYJU'S.
MATH 221PH and PHYS 122MA Integrated Physics and Calculus Stokes’Theorem Adding circulations Consider two rectangular loops that share a common edge as shown below. Let C1 be the blue loop and C2 be the red loop with orientations as shown. Let C3 be the loop that consists of going around...
Using the language of differential forms, we show these two theorems are instances (along with Green's theorem and the fundamental theorem of calculus) of a single theorem that connects one integral over a domain to a related one over its boundary. To explore the connections, we combine the ...
6 Stokes’theoremTherearethreemainintegraltheoremsofvectoranalysis:Green’stheorem:∫𝜕D(Pdx+Qdy)=∫∫D(𝜕Q𝜕x−𝜕P𝜕y)dxdy;Stokes’theorem:∫𝜕SF⋅ds=∫∫S(∇×F)⋅dS=∫∫ScurlF⋅dS;Gauss’(Ostrogradsky’s,divergence)theorem:∫∫𝜕WF⋅dS=∫∫∫W(∇⋅F)dV.In...
Operator calculus - the exterior differential complex Stokes' theorem for domains in open sets which are not necessarily regular, and a new fundamental theorem for nonsmooth domains and their boundaries moving... J Harrison - 《Mathematics》 被引量: 11发表: 2011年 An Efficient Method for Band ...
-Stokes' theorem proof part 3 _ Multivariable Calculus _ Khan Academy 多元微积分,搬运自Khan Academy。 Grant讲解,链接https://www.khanacademy.org/math/multivariable-calculus
参考 ^Rudin 1976 Principles of Mathematical Analysis ^Spivak 1965 Calculus on Manifolds: A Modem ...
让我们从它最基础的形式——微积分基本定理(Fundamental Theorem of Calculus,FTC)开始。从FTC的名字就能看出其重要性,数学中能被称为基本定律的可不多,微积分其他定理可以说都是从FTC中推导而来。 Isaac Barrow (1630 – 1677), 17世纪,微分和积分是两门相对独立的学问,微分求斜率,积分求面积,洛必达侯爵编写的...