 Home

Codex Wiki

List of universities

University of Oxford

Course of the University of Oxford

Undergraduate course of the University of Oxford

Mathematics course of the University of Oxford

Past exam of the mathematics course of the University of Oxford

2015

Prelims

Mathematics V resit

Question 2

{c}

In <Cartesian coordinates>, write the constant <vector> as $\mathbf c=(c_1,c_2,c_3)$. The <product rule> and constancy of its components give
$$
\nabla\cdot(\phi\mathbf c)
=\partial_x(c_1\phi)+\partial_y(c_2\phi)+\partial_z(c_3\phi)
=c_1\phi_x+c_2\phi_y+c_3\phi_z.
$$
The last expression is the <dot product> with the <gradient>, so
$$
\boxed{\nabla\cdot(\phi\mathbf c)=\mathbf c\cdot\nabla\phi.}
$$

Solution

Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics V resit / Question 2 / a / ii / Solution

Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics V resit / Question 2 / a / ii / Solution

 Ancestors (13)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics V resit / Question 2 / a / ii / Solution

 Ancestors (13)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)