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I'll be teaching vector calculus to mechatronics engineers, and I'd like to provide them with industrially relevant examples, especially of the use of vector fields. Can anyone suggest either an example application that they have personally used or a text that I can use to glean some examples from?

Michael Stachowsky
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    Any computational fluid dynamics or computational electrodynamics simulation uses vector fields. Or do you ask for direct application of the vector fields in practice not in the underlying methods? – MrYouMath Apr 26 '17 at 16:50
  • Basically, I'm looking for a time in which someone practicing in industry needed either to understand the concept (then get a computer to do the math), or actually had to do the math to arrive at an equation/computer program. Extra points if it's for a robotics/mechatronics application, but I'll take what I can get – Michael Stachowsky Apr 26 '17 at 17:10
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    The jacobian is very widely used in robotics. And the derivation of the equations of motion is also using the jacobian (depends on the method you use) for tree-like kinematic chains. – MrYouMath Apr 26 '17 at 17:14
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    Gradient is a important concept when doing optimisation. Also knowing how to do some gradient descent method in multiple dimensions is important to understand, as well as why you might not be able to find the global minima. But basically understanding implications of turning 1D formula in a vectorized context is pretty central. – joojaa Apr 27 '17 at 07:26
  • I agree, but I'm looking specifically for vector field applications (vector valued functions of vector arguments). Many of my applications have come from scalar fields, which are a simpler concept and much more obviously applicable – Michael Stachowsky Apr 27 '17 at 11:30
  • This reads as a poll. Polls don't work very well within the StackExchange Q&A format. –  May 06 '17 at 22:48

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