Green's theorem

[′grēnz ‚thir·əm]

(mathematics)

Under certain general conditions, an integral along a closed curve C involving the sum of functions P (x,y) and Q (x,y) is equal to a surface integral, over the region D enclosed by C, of the partial derivatives of P and Q; namely,

Green's Theorem

(humour)

(TMRC) For any story, in any group of people there will be at least one person who has not heard the story. A refinement of the theorem states that there will be *exactly* one person (if there were more than one, it wouldn't be as bad to re-tell the story). The name of this theorem is a play on a fundamental theorem in calculus.

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References in periodicals archive

Now, using Green's theorem with limiting process and Holder's inequality, we obtain

Composition Operators Mapping Logarithmic Bloch Functions into Hardy Space

The SPM2 formulation is reviewed using a coupled Lippmann-Schwinger equations derived from Green's theorem. The zeroth order, first order, and second order (coherent averaged) fields are solved recursively.

By applying Green's theorem [32] to region 0, we obtain the integral equation

Scattering and Transmission of Waves in Multiple Random Rough Surfaces: Energy Conservation Studies with the Second Order Small Perturbation Method

The odd title of Dan Teague's (2015) Everyone Has A Personal Green's Theorem, refers to the fact that for everyone studying mathematics, although the mathematics may begin as something that is easy to learn, sooner or later it becomes hard, and students have to work hard to understand it.

Everyone has a personal green's theorem. National Council of Mathematics Teachers (NCTM).

Responce: relevance, challenge, engagement and not running away from hard mathematics

These are special cases of Green's Theorem and the Divergence Theorem, but the ideas and methods introduced here are accessible to a wider audience.

We do not require readers to have knowledge of Green's Theorem or the Divergence Theorem.

Finding signed areas and volumes inspired by technology

We will see that this problem is solved by using the generalized Green's theorem and the construction of the adjoint operator.

Orthogonal least squares solutions for linear operators

George Green (1793-1841) is best known for Green's theorem, which is used in computer codes that solve partial differential equations.

Mathematical papers. (reprint, 1871)

To this end, we will discuss the derivation of generalized Green's theorem and surface integral equations for the vector potential formulation as well.

Vector Potential Electromagnetics with Generalized Gauge for Inhomogeneous Media: Formulation