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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.
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.
Green's Theorem in our discussion case be summarized as follows:
Remark 6 Corollary 5 and the example in Remark 3 coincide with Green's Theorem in the sense that the area enclosed by a closed piecewise smooth curve can be obtained by utilizing contour integrals along the boundary curve traversed in one direction.
Using Theorem 1, we can find the area bounded by two parametric curves without utilizing Green's Theorem.
In an ordinary calculus textbook, the Divergence Theorem and Green's Theorem are usually taught in the last semester of a calculus sequence, to a group of students who completed some basic training in calculus.
We will see that this problem is solved by using the generalized Green's theorem and the construction of the adjoint operator.
To solve the problem in the orthogonal sense explained above, we will make use of the generalization of the Green's Theorem [2] and the adjoint operator of L, L.
By the use of the generalized Green's theorem it is possible to find set of functions that are orthogonal to the action of linear operators upon a set of orthogonal polynomials.
George Green (1793-1841) is best known for Green's theorem, which is used in computer codes that solve partial differential equations.