Rules for curl test applicability

In summary, the conversation is discussing the applicability of the "curl test", specifically whether a two-variable differential is an "exact differential" and the criteria for that. The conversation also mentions the implications of this test for integrals around closed paths and from one point to another. Clarification is requested on which aspect of the test is being referred to.
  • #1
mathwizeguy
13
0
trying to remember rules for curl test applicability.

is it just simple closed curve?

is F=-ysin(x)i+cos(x)j able to use the curl test?
 
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  • #2
It would help if you would cite the "curl test" you are talking about. I think you are referring to the fact that a two variable differential, f(x,y)dx+ g(x,y)dy, is an "exact differential", that is, that there exist F(x,y) such that dF= f(x,y)dx+ g(x,y)dy, if and only if
[tex]\frac{\partial f}{\partial y}= \frac{\partial g}{\partial x}[/tex]
which the same as saying
[tex]curl \vec{f}= \nabla\times\vec{f}= \vec{0}[/tex] where
[tex]\vec{f}= f(x,y)\vec{i}+ g(x,y)\vec{j}[/tex].
It follows from that that the integral of f(x,y)dx+ g(x,y)dy around any closed path is 0 and that the integral from one point to another in the xy-plane is independent of the path. Which of those are you referring to?
 
  • #3
i was referring to the df/dy-dg/dx.
 
  • #4
Actually, that doesn't answer my question- were you referring to the fact that if df/dy- dg/dx= 0 implies that the integral around a closed path is 0 or to the fact that it implies the integral, from one point to another, is independent of the path.

The first obviously requires a closed path- it says so! The second does not.
 

1. What is the purpose of the Rules for Curl Test Applicability?

The purpose of the Rules for Curl Test Applicability is to provide guidelines for determining when the curl test should be used to assess the quality of a material or product.

2. How do I know if the curl test is appropriate for my material or product?

The curl test is most commonly used for flexible materials, such as paper or plastic, that can be bent or rolled. However, it may also be applicable to other materials depending on their properties and intended use.

3. What factors should be considered when determining if the curl test is applicable?

There are several factors to consider, including the thickness and flexibility of the material, the expected curvature of the product, and the intended use and handling of the product. These factors will help determine if the curl test is a relevant and accurate measure of quality.

4. What methods are used to perform the curl test?

The most common method is the 90-degree angle bend test, where the material is bent at a 90-degree angle and the amount of curl is measured. Other methods may include the cantilever bend test or the roller curl test, depending on the material and product being tested.

5. Are there any other considerations to keep in mind when using the curl test?

Yes, it is important to ensure that the test is performed consistently and accurately, with proper equipment and procedures. It is also important to consider any external factors that may affect the results, such as humidity or temperature, and to follow any relevant industry standards or guidelines.

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