Applied Math Trick #1: Integration by Parts

I often tell my students that Integration by Parts is Applied Math Trick #1.  I once had someone retort with “last year, you said Taylor Series was trick #1”.

Well, Taylor series is just really integration by parts… Forever! I was surprised that students hadn’t seen this before.  It’s remarkably simple, and yields the remainder theorem quite nicely.

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Getting ready for sabbatical

I finished writing a draft showing the connection between AFM and the conserved quantities of Olver.  These notes also extend the idea to constant vorticity and outline a  process for extending to 3-d. I hope to post this soon.  I’m really excited about how this project is going.  Sal is making excellent contributions and I’m really looking forward to see where he pushes this!

For now, it’s all about getting the house rented. Which means I’ve been doing a lot of the following

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It’s been a while…

It’s been a while.  Over the last week, I’ve been working on documenting the conservation laws via a weak formulation of the water-wave problem using some of the work of Sal (undergraduate research student).  At this point, we can systematically derive the 8 7 conservation laws for the irrotational problem (the Hamiltonian is the 8th).  We also have the system in place for constant vorticity.

Hopefully, we’ll have a really rough draft posted soon.