Grad, curl , div operator got any meaning?

F is the curl of F, which represents the rotation or vorticity of the vector field. It is not necessarily orthogonal to F.∇ dot F is the divergence of F, which represents the flux of the vector field. It is a scalar value, not a vector like ∇x F.In summary, the ∇x and ∇ dot operators have different meanings and purposes in vector calculus. ∇x F represents the curl or rotation of a vector field, while ∇ dot F represents the divergence or flux of a vector field. It is important to understand the definitions and uses of these operators in order to properly apply them in vector calculus.
  • #1
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grad, curl , div operator got any meaning??

∇x F (t) same as the first derivative of F with respect to t , or will get the gradient of F which is normal to the F ?
∇ dot F (t) , will get the scalar value of what??
lets say F is force , then can anyone please give me the meaning of those operator on the vector mean?
∇x F (t) will get the gradient of F which is normal to the F .
I think of this because in the stoke's theorem the ∇x F (t) have to dot with n , where n should be the unit normal vector of the surface.
I am blur , please guide .
Thank you.
 
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  • #2
First check the definition of Del as given in wiki.

Note that it is defined as the differential with respect to spatial coordinates, not time.
 
  • #3
Your use of the word "normal" is not correct. F is a vector field, not a surface. Perhaps you meant orthogonal instead of "normal".

∇x F is not the "the gradient of F which is normal to the F".
 

Related to Grad, curl , div operator got any meaning?

1. What is the "grad, curl, div" operator?

The "grad, curl, div" operator is a mathematical tool used in vector calculus to describe the behavior of vector fields in three-dimensional space.

2. What does the "grad" operator represent?

The "grad" operator, also known as the gradient operator, represents the rate of change of a scalar function in a given direction. It is a vector that points in the direction of greatest increase of the function and its magnitude represents the slope of the function in that direction.

3. What does the "curl" operator represent?

The "curl" operator represents the circulation or rotation of a vector field around a point. It is a vector that points in the direction of the axis of rotation and its magnitude represents the strength of the rotation.

4. What does the "div" operator represent?

The "div" operator, also known as the divergence operator, represents the flow of a vector field out of a point. It is a scalar that represents the rate at which the vector field is spreading out or converging at a given point.

5. Why are "grad, curl, div" important in physics and engineering?

The "grad, curl, div" operators are important in physics and engineering because they provide a way to mathematically describe and analyze vector fields, which are present in many physical phenomena and engineering systems. They are used in various applications such as fluid dynamics, electromagnetism, and heat transfer.

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