Now, using Green's theorem
with limiting process and Holder's inequality, we obtain
The structure of these two models are very similar and they are a clear example where the theory of vector calculus is applied, since it is avoided to work with complex trigonometric and algebraic integrals, which is simplified by applying Green's theorem (1).
When applying Green's Theorem [.sup.3] [[.sup.3] For the theorem on Green's theorem, see texts ,  and ] we see that [[integral].sub.c] [x/[square root of [L.sup.2]-[x.sup.2]]] dx = 0 and we discover that the total distance traveled is
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  to region 0, we obtain the integral equation
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).
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.
We will see that this problem is solved by using the generalized Green's theorem
and the construction of the adjoint operator.
George Green (1793-1841) is best known for Green's theorem
, which is used in computer codes that solve partial differential equations.
To this end, we will discuss the derivation of generalized Green's theorem
and surface integral equations for the vector potential formulation as well.