Differential equations?

[Boris Lagutin]

Despite I have not completed a multi-variable calculus course yet but I am interested in some points. Could someone clarify how Gradient and Integral curve (in differential equations) are related to each other if related? As I understand Gradients in gradient fields are perpendicular to line integral curves because Gradient is always perpendicular to surface curves. However, Integral curves follow strictly along vectors in vectors' fields, i.e. vectors in differential equations fields are tangent to the integral curves.

Thank you

[joe]

The vector grad(V) is perpendicular to equipotential surfaces V = constant.
For me, 'line integral curve' means the curve along which one calculates a line integral. Its shape is arbitrary - you can choose it to be whatever you like.
So I don't see a problem.

[Boris Lagutin]

Thank you, Joe. I have not deeply enough gotten into fields' conceptions yet. I just iterate and rethink material learnt lately.

Have a nice day