Differential equations?

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Boris Lagutin
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Joined: Thu Aug 28, 2014 9:17 pm
Location: USA

Differential equations?

Postby Boris Lagutin » Mon Aug 31, 2015 5:29 am

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
Boris Lagutin
student

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joe
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Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

Re: Differential equations?

Postby joe » Thu Sep 03, 2015 11:44 am

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
Posts: 173
Joined: Thu Aug 28, 2014 9:17 pm
Location: USA

Re: Differential equations?

Postby Boris Lagutin » Thu Sep 03, 2015 1:23 pm

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 :)
Boris Lagutin
student


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