For example in a 2-dimensional case, we have the vector d{\bf l} = dx {\bf i} + dy {\bf j}. The angle or direction of this vector can be said to be tan\theta = dy/dx radians w.r.t x-axis. But both dx, dy are infinitesimally small quantities. Perhaps introducing limits, we can say \theta =...
Thank you for the answer. I however found it strange that the magnitudes of these dx, dy, dz are relatively different, when they themselves are all infinitesimally small quantities...
In 'Introduction to Electrodynamics' by Griffiths, in the section of explaining the Gradient operator, it is stated a theorem of partial derivatives is:
$$ dT = (\delta T / \delta x) \delta x + (\delta T / \delta y) \delta y + (\delta T / \delta z) \delta z $$
Further he goes onto say:
$$ dT =...