Question

What does the upside of a triangle mean?It's a slogan concerning the Langrange Multiplier.L'm new here.I'm from China

Answer 1

Hi, welcome to OpenStudy.

It is called the del or nabla symbol, and is known as the gradient operator. For scalar functions \(f(x,y,z)\) the gradient derives a vector field \(\vec F(F_x,F_y,F_z)\) \[\nabla f(x,y,z)=\frac{\partial f}{\partial x}\hat i+\frac{\partial f}{\partial y}\hat j+\frac{\partial f}{\partial z}\hat k\]for vector fields we can use the del symbol to find either curl or divergence\[\text{curl}\vec F=\nabla\times \vec F=\left|\begin{matrix}\hat i&\hat j&\hat k\\\frac{\partial}{\partial x}&\frac{\partial}{\partial y}&\frac{\partial}{\partial z}\\\vec F_x&\vec F_y&\vec F_z\end{matrix}\right|\]\[\text{div}\vec F=\nabla\cdot\vec F=\frac{\partial \vec F_x}{\partial x}\hat i+\frac{\partial\vec F_y}{\partial y}\hat j+\frac{\partial\vec F_z}{\partial z}\hat k\]for further info I suggest reading this:

http://tutorial.math.lamar.edu/Classes/CalcIII/GradientVectorTangentPlane.aspx

http://tutorial.math.lamar.edu/Classes/CalcIII/CurlDivergence.aspx

Answer 2

thanks and good luck