I need yr help in Green theorem,

In summary, the conversation revolves around seeking help with solving two questions related to Green's theorem on Abstract Algebra. The speaker is in a critical time and is looking for any ideas or assistance in solving the problems. They mention that the problems involve a function g(x,y) and ask for clarification on how to write dg. Another individual points out that the problems are standard identities and can be found in advanced textbooks. The speaker is advised to try solving the problem first before asking for further help.
  • #1
Mechano
5
0
I need yr help in Green theorem, please please please

Dear Frends and Teachers,

This is Issam, I'm really need your help to solve anyone of the following 2 questions as shown in attached files, it's about Green theorem on Abstract Algebra

I'm really in critical time and I hope to get any idea to solve them or help me to solve anyone

I'm looking forward to get yr help ASAP
 

Attachments

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  • #2


You know Green's Theorem, correct? Start with the second problem.
If you have a function [itex]g(x,y)[/itex], how do you write [itex]dg[/itex]? I'm not going to give any more info right now. Try that, take a look and ask more questions if it isn't clear (also, this should be in calc, not intro phys).
 
  • #3


Both of your problems are pretty standard identities and uses for EM waves. You could probably find proofs of those in an advanced electrodynamics or optics book. Before we can really help you, we have to know where you're stuck, so try out the problem somewhat.
 

Related to I need yr help in Green theorem,

What is Green's theorem and how does it work?

Green's theorem is a fundamental theorem in multivariable calculus that relates a line integral around a simple closed curve to a double integral over the region enclosed by the curve. It states that the line integral of a two-dimensional vector field around a closed curve is equal to the double integral of the curl of the vector field over the region enclosed by the curve.

What are the applications of Green's theorem?

Green's theorem has many practical applications in physics, engineering, and other scientific fields. It is commonly used to calculate work done by a force field, as well as to solve problems involving fluid flow, electromagnetism, and heat transfer. It is also a key tool in the study of complex functions in mathematics.

What are the conditions for using Green's theorem?

In order to apply Green's theorem, the region enclosed by the curve must be simply connected, meaning that it does not contain any holes or intersect itself. Additionally, the vector field must be continuously differentiable within this region.

What is the difference between Green's theorem and Stokes' theorem?

Green's theorem is a special case of Stokes' theorem, which is a more general theorem in vector calculus. While Green's theorem relates line integrals to double integrals in two dimensions, Stokes' theorem extends this relationship to higher dimensions. Stokes' theorem is also used to calculate surface integrals, while Green's theorem is limited to line integrals.

How can I use Green's theorem to solve problems?

To use Green's theorem to solve a problem, first identify the region enclosed by the curve and ensure that it meets the necessary conditions. Then, calculate the curl of the vector field and set up the double integral according to the formula in Green's theorem. Finally, evaluate the integral to find the desired result.

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