Can anyone check this identity please?

  • Thread starter Deathcrush
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In summary, the conversation was about a person asking for help in verifying an identity involving vectors and scalars. Another person clarified that the identity only makes sense if one of the factors is a scalar, and even then it is incorrect. They provided the correct version of the identity, which includes a scalar function and a vector function. The person asking for help then mentioned they found the missing term in their case, which is 0 because they are working with fluid dynamics. They thanked the other person for their help.
  • #1
Deathcrush
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Homework Statement



I just want to check if this identity is true, since I have not found it anywhere, can anyone help me?

v is a vector (and that nu is supposed to be a v too)
 

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  • #2
The "identity" only makes sense if one of the factors is a scalar, and it's wrong even then. I think you want this, where f is a scalar function and V is a vector function:

[tex]\nabla \cdot f\vec V = \nabla f \cdot \vec V + f (\nabla \cdot \vec V)[/tex]
 
  • #3
I finally found it, looks like I was missing another term in the right side v(Div(v)), altough this is 0 in my case because I am working with fluid dynamics. Now everything makes perfect sense, thanks anyway
 

1. What does it mean to "check an identity"?

Checking an identity means verifying whether the given equation or statement is true for all values of the variables involved. This is commonly done by manipulating the equation algebraically or using mathematical properties to simplify and compare the two sides of the equation.

2. Why is it important to check identities?

Checking identities is important because it ensures the accuracy and validity of mathematical equations and statements. It allows us to confirm that the equation holds true for all values of the variables, and it can also help us identify and correct any errors in our calculations.

3. What are some common methods for checking identities?

Some common methods for checking identities include substitution, algebraic manipulation, and using mathematical properties such as the distributive, associative, and commutative properties. Additionally, trigonometric identities often require the use of trigonometric identities and formulas.

4. Can there be more than one way to check an identity?

Yes, there can be multiple ways to check an identity. Depending on the complexity of the equation and the available tools and knowledge, different methods may be more efficient or accurate. It is always recommended to use multiple methods to verify an identity and increase confidence in its validity.

5. What should I do if I am unable to prove or disprove an identity?

If you are unable to prove or disprove an identity, it is important to double-check your work and make sure there are no errors in your calculations. You can also try approaching the problem from a different angle or using a different method. If you are still unable to verify the identity, it may be worth consulting with a colleague or seeking assistance from a math teacher or tutor.

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