- #1
Nanas
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Please , can anyone recommend me to a reference containing Full proof of Green theorem.
Thank you.
Thank you.
Bacle said:Micromass: I don't mean to diss you, but I think Rudin's proof is way too
ungeometric, in case Nanas wants a somewhat-geometric argument, i.e.
Rudin axiomatizes diff. forms, and does not give much of what I would
consider enough background. But that comes down to a matter of taste.
Most books in advanced calculus should have a proof
Nanas said:Please , can anyone recommend me to a reference containing Full proof of Green theorem.
Thank you.
Green's theorem is a fundamental theorem in vector calculus that relates the line integral of a two-dimensional vector field over a closed curve to the double integral of the curl of the vector field over the region enclosed by the curve.
Green's theorem is important because it is used to solve a variety of problems in physics and engineering, such as calculating work done by a force and finding the area of a region bounded by a curve.
To prove Green's theorem, you need to use the fundamental theorem of calculus and apply it to both the line integral and the double integral in the theorem. This will allow you to show that they are equal and thus prove the theorem.
You can find a full proof of Green's theorem in many calculus textbooks or online resources. Some reputable sources include Khan Academy, MIT OpenCourseWare, and Paul's Online Math Notes.
Yes, Green's theorem can be extended to higher dimensions through the use of the generalization of curl, known as the exterior derivative. This leads to a more general theorem known as Stokes' theorem.