[MOSAIC-news] Math methods textbook: Request for help

Gary Felder gfelder at smith.edu
Thu Aug 12 13:32:31 CDT 2010

I am co-authoring a "Math Methods" textbook, of the sort that is commonly taught at an undergraduate level in Physics departments, and sometimes as an undergraduate or graduate course in engineering departments. Topics covered would include multivariate and vector Calculus (which is sometimes but not always a prerequisite for this course), differential equations (both ordinary and partial), Taylor series, Fourier series, complex analysis, linear algebra, probability and statistics, Calculus of variations, differential geometry, group theory, and others. 

I'm emailing to ask for some help and suggestions. There are three kinds of help we need. 

The first is, I hope, easy.  We need examples--lots and lots and lots and lots of concrete examples, from a wide variety of disciplines, of how all these topics are used.  You might be able to point us in the right direction ("I heard that they're using differential geometry to predict earthquakes, here's a guy who knows more about it"), or give us some equations ("here's an equation that is being used to model the spread of HIV"), or...well, anything.  The key point here is that we are not asking you to research anything: just tell us whatever pops into your head. (The one thing I'd ask you not to do is just point me to a book that might have some examples in it. It's simply too time-consuming to plow through lists of books in fields I'm marginally familiar with on the hope of finding an occasional useful example. I know because I've been trying.)

The second is more time-consuming, but we need reviewers.  If there are any chapters that you might be able to find the time to read and give us feedback on, of course that would be invaluable. 

Third, and also pretty easy, I hope: can you think of anyone else we should be sending this request to?  Someone who is really knowledgeable in some of these areas, and might be willing to give us a bit of time?  Perhaps someone who teaches a Math Methods course and would love to give feedback on a new text? 

Please let me know if you think you could help out in any of these ways. Right now we are working on the Taylor Series and Partial Differential Equations chapters so our most immediate need is for interesting applications of those two areas. If you could tell me any particular PDEs that you know of in any application beyond the most common ones (the wave equation, heat equation, Laplace's equation, Poisson's equation, and Schrodinger's equation) or any equation that gets approximated with one or more terms of a Taylor series to solve a problem, we'd love to see them. And if you think you might be able to help us out as we work on other topics we'd of course love to know that as well.

Thanks so much for anything you can offer! 

-Gary Felder 

Gary Felder
Smith College Physics Department
gfelder at smith.edu
"Not only is the universe stranger than we imagine, it is stranger than we can imagine." - Sir Arthur Eddington, based on a quotation from J.B.S. Haldane

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