partial derivatives

The directional derivative of the function $f$ given below at the point $(1,0)$ in the direction of $\frac{1}{2}(\hat{i} + \sqrt{3} \hat{j})$ is ________ (rounded off to 1 decimal...

For the differential equation given below, which one of the following options is correct? $$ \frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}=0,0 \leq x \leq 1,0...

For a two-dimensional, incompressible flow having velocity components u and v in the x and y directions, respectively, the expression $\frac{\partial(u^2)}{\partial x} + \frac{\par...

Solutions of Laplace's equation having continuous second-order partial derivatives are called

Curl of vector $$\,V\left( {x,y,x} \right) = 2{x^2}i + 3{z^2}j + {y^3}k\,\,$$ at $$x=y=z=1$$ is

The divergence of the vector field $$\,3xz\widehat i + 2xy\widehat j - y{z^2}\widehat k$$ at a point $$(1,1,1)$$ is equal to

The distance between the origin and the point nearest to it on the surface $$\,\,{z^2} = 1 + xy\,\,$$ is

The divergence of the vector field $$\left( {x - y} \right)\widehat i + \left( {y - x} \right)\widehat j + \left( {x + y + z} \right)\widehat k$$ is

The function $$f\left( {x,y} \right) = {x^2}y - 3xy + 2y + x$$ has