Calculus question (no computation involved)

[RESmonkey]

I am flipping through some Physics material (not related to school, just yet) and I see Calc III material involved (Laplacians, gradients, Stokes/Greens theorem, etc.). I have taken Calc III already, but need to refresh my skills inorder to tackle some of the Physics material.

What is a good source to refresh all that? I have notes that allowed me to do well in Calc III, but I need to know how this is connected to Physics (especially E&M).


The book I'm looking at is Griffith's intro to E&M (recommended by born2bwire).


Thanks

 

[TuxDave]

I suppose the easy answer of finding your old calculus book is out of the picture? Usually it's one of those "look it over and in a couple minutes you remember the general idea of it and just need to get around to actually doing the work" type things...

 

[Born2bwire]

Do they still have Math 243? It's multivariable calculus with vector analysis. That textbook should be applicable.

Math 280 may have had some stuff on vector calc too. I had that with old man Lotz who I think has moved on to being an Emeritus.

 

[eLiu]

You sound like you're in college? Your library should have this:

Hildebrand, Francis. Advanced Calculus for Applications. 2nd ed. Englewood Cliffs: Prentice Hall, March 31, 1976. ISBN: 0130111899.

Since you've already had calc3, this book will be a great way to refresh what you've learned and then get a deeper understanding of the material. It's written at a more advanced level than most books I've seen used in basic calc3 courses without having the full-on insanity of an actual analysis course.

Also, wikipedia has pretty good articles on most of these fundamental math concepts. I'll summarize: gradient: a vector of derivatives in each coordinate direction; laplacian: a "smoothing" operator, it tends to smear things out (consider that a common way of interpreting laplacian(u) = 0 is as a steady-state heat flow problem) when the coefficients are real; it leads to exponential growth/decay with imaginary coefs; stokes thm: a way of changing a volume integral to a surface integral or area to arclength (generally: integral over d dimensions to d-1 dimensions) for certain classes of integrands. With it you can do things like change from integral of the curl of a vector field over a surface to a line integral over said surface's boundary. Or change the volume integral of the divergence of a vec-field to a surface integral of the flux through the boundary... which is really nothing more than "what's inside [the volume] = inflow minus outflow [thru boundaries]". Edit: those are common physical applications anyway; Stokes Thm is a lot more general than that.