- #1
tim_lou
- 682
- 1
what does
[tex]\left (\vec{A}\cdot \vec\nabla \right ) \vec B[/tex] mean?
[tex]\left (\vec{A}\cdot \vec\nabla \right ) \vec B[/tex] mean?
HallsofIvy said:Specifically
[tex](\vec{A}\cdot \nabla)\vec{B}= \vec{A}\cdot (\nabla\vec{B})= A_x\frac{\partial B_x}{\partial x}+ A_y\frac{\partial B_y}{\partial y}+A_z\frac{\partial B_z}{\partial z}[/tex]
Semo727 said:How can vector multiplyed by scalar give scalar??
tim_lou said:wait, hold on, so the correct result is arildno's? the operation gives you a vector..?
I WON!arunma said:I see we've turned mathematics into a democracy today.
Yes, Arildno's explanation was the correct one.
what does [tex]\left (\vec{A}\cdot \vec\nabla \right ) \vec B[/tex]mean?
[tex](\vec{A}\cdot\nabla)\vec{B} = A_{x}\frac{\partial\vec{B}}{\partial{x}} + A_{y}\frac{\partial\vec{B}}{\partial{y}}+A_{z}\frac{\partial\vec{B}}{\partial{z}}[/tex]
Vector calculus notation is used to represent and manipulate mathematical concepts related to vectors and vector fields. It allows for concise and efficient communication of complex mathematical ideas.
Vector calculus notation includes symbols and operators specifically designed to represent vector quantities, such as vectors, dot and cross products, and divergence and gradient operators. This differs from regular calculus notation, which primarily deals with scalar quantities.
Some common vector calculus notations include:
- ∇ (del) operator, which represents the gradient of a scalar or vector field
- · (dot) product, which represents the magnitude of the projection of one vector onto another
- × (cross) product, which represents the magnitude of the vector perpendicular to two given vectors
- ∫ (integral) symbol, which represents the area or volume under a vector field
Vector calculus notation is used extensively in physics and engineering to describe and analyze physical phenomena and systems. It is especially useful in fields such as electromagnetism, fluid mechanics, and quantum mechanics.
Yes, vector calculus notation can be translated into other mathematical notations, such as matrix notation or index notation. This allows for different perspectives on the same mathematical concepts and can be helpful in solving complex problems.