Re: Vector Analysis
- To: mathgroup at smc.vnet.net
- Subject: [mg15656] Re: Vector Analysis
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Sat, 30 Jan 1999 04:28:50 -0500 (EST)
- Organization: University of Western Australia
- References: <78pcue$d5h@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
adam.smith at hillsdale.edu wrote: > I am using Mathematica Ver. 3 and am teaching a course in > Electromagnetism which relies heavily on the del operator. The use of > the <<Calculus`VectorAnalysis` package has been quite useful as far as > Grad[],Div [],Curl[], etc. I'd be interested to hear more about your course. I too teach a course on Electromagnetism. My course notes are available at http://www.pd.uwa.edu.au/Physics/Courses/Second_Year/ElectroMagnetism.html > However, in trying to confirm some often cited identities (see any book > on Electromagnetism) such as: > > Grad[A.B] = Cross[A,Curl[B]] + Cross[B,Curl[A]] + (A.Del)B + (B.Del)A > where A and B are vectors with 3 components that are functions of > Cartesian components x, y and z. > > I have not been able to come up with an elegant method for representing > things with the form of the last 2 terms, i.e. (A.Del)B. There is no real easy way to represent operator algebra in Mathematica. Why not formally use A.Grad[B] (since Mathematica will differentiate each component of the vector B). > Can anyone tell me a way of defining a function that I can input any 2 > vectors and do this. What I have in mind is something like > AdotDelB[a,b]. There may be a better way. Have a look at ftp://ftp.physics.uwa.edu.au/pub/Mathematica/MathGroup/Gradient.nb which is slated to appear in the forthcoming issue of the Mathematica Journal. Cheers, Paul ____________________________________________________________________ Paul Abbott Phone: +61-8-9380-2734 Department of Physics Fax: +61-8-9380-1014 The University of Western Australia Nedlands WA 6907 mailto:paul at physics.uwa.edu.au AUSTRALIA http://www.physics.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________