Greens theorem and parametrization

In summary, the conversation discusses the use of parametrization in a vector line integral over a plane. It is mentioned that sometimes parametrization is necessary while other times it is not, but ultimately it is up to the individual. The purpose of parametrization is to simplify the functions being used. It is also noted that parametrization is typically used in the line integral for greens theorem, but not for the double integral for a region bounded by a line. Parametrization is more useful for non-flat surfaces and the more general Stokes theorem for three or more dimensions.
  • #1
Syrena
6
0
Hello. I just wonder if anybody know if there are any rules, when to use parametrization to greens theorem in a vector line integral over a plane. Becouse, it seems sometimes, you have to parametrizice, and other places you dont. I get confused.
 
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  • #2
It's completely up to you. Of course sometimes you might be asked to re-parametrize or not depending on the problem, but in general it doesn't make a difference. The whole point of parameterizing is to re-write functions in a different way, with the goal of making your parametrization simpler than the problem you began with. So even though one way might be easier than the other, it's totally up to you when to parametrize.
 
  • #3
Usually you always parameterize the line integral in greens, and don't parameterize the double integral for the region bounded by the line, parameterization for those only comes in handy for not non flat surfaces ie. for the more general Stokes theorem for R3 and up.
 

FAQ: Greens theorem and parametrization

1. What is Greens theorem?

Green's theorem is a mathematical tool used in multivariable calculus to relate the line integral around a simple closed curve to the double integral over the region enclosed by the curve. It is also known as the divergence theorem in two dimensions.

2. How is Green's theorem applied?

Green's theorem is used to calculate the area of a region enclosed by a curve, as well as to evaluate line integrals in a two-dimensional plane. It is also used in vector calculus to solve problems related to fluid dynamics and electromagnetism.

3. What is parametrization?

Parametrization is the process of representing a curve or surface in terms of one or more independent parameters. In other words, it is a way to express the coordinates of a point on a curve or surface in terms of a set of variables.

4. How is parametrization used in Green's theorem?

In Green's theorem, parametrization is used to transform a double integral over a region into a line integral along a curve. This makes it easier to calculate the area enclosed by a curve and to evaluate line integrals in two dimensions.

5. What are some real-world applications of Green's theorem and parametrization?

Green's theorem and parametrization are used in a variety of fields, including physics, engineering, and economics. In physics, they are used to study fluid flow and electromagnetic fields. In engineering, they are used to analyze structural and mechanical systems. In economics, they are used to model supply and demand curves.

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