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It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ) .

Within this room, the heat obey a certain equation ( for e.g. $T = 25 + 5z$ ) .We know that heat flows from higher temperature regions to lower temperature regions. With this information in mind

How could I be able to determine the amplitude and the direction of travel of the thermal energy with the Del operator ( gradient ) ? .

I'm not looking for a definitive response, but an equation that could give me potentially the result for the amplitude and the direction. I also want to know if thermal energy follows a loop pattern within my room (and be able to explain it mathematically by using the del operator once again of course)?

You can find the lecture source here.

Thank you.

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    Instead of lowering my question, maybe you could point me out what am I missing...2012-07-09
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    Dear fneron , I think you are new to Math.SE. Welcome to Math.SE. The problem with your question is this : 1) You didn't state what you are looking for precisely. 2) You didn't follow punctuation and formatting tips while writing. 3) Please state where you are stuck. Thank you, BTW +1 for your question.2012-07-09
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    Thank you very much. Is that better?2012-07-09
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    Wait, I edit this one for you.2012-07-09
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    perfect thx! Overall question is clear?2012-07-09
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    I think the most appropriate forum to ask this things is http://physics.stackexchange.com/ , try posting it there, if you don't get a response here.2012-07-09
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    Please add Physics tag to your question in addition to differential-equations and vector-analysis tags.2012-07-09
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    thank you. Appreciated this formatting help! I'm a programmer, most of the time I just copy/paste my code into those forums with a brief explanation. But physics and math are different ;)2012-07-09
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    Sorry for removing all the stuff you said. The people in this community are only interested in the question, if you say the background in writing up the question they will simply down-vote. Another issue is that, don't use BOLD letters unless for headings. That will make your question look tidy. But I need to remove all the unnecessary part and kept the quintessence. You are free to roll-back if you don't like my edit. Thank you .2012-07-09
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    Yes physics and mathematics are different. But this forum is only for mathematics. So it offers an adhoc relaxation for the physics questions , if you can keep the "physics" tag. See the matter present below the tag.2012-07-09
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    No you are right. I trust you ;)2012-07-09

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