Name: A course in mathematics for students of physics
ISBN: 9780521406499

A course in mathematics for students of physics

This text breaks new ground in presenting and applying sophisticated mathematics in an elementary setting. Aimed at physics students, it covers the theory and physical applications of linear algebra and of the calculus of several variables, particularly the exterior calculus. The exterior differential calculus is now being recognized by mathematicians and physicists as the best method of formulating the geometrical laws of physics, and the frontiers of physics have already begun to reopen fundamental questions about the geometry of space and time. Covering the basics of differential and integral calculus, the authors then apply the theory to interesting problems in optics, electronics (networks), electrostatics, wave dynamics, and finally to classical thermodynamics. The authors adopt the "spiral method" of teaching (rather than rectilinear), covering the same topic several times at increasing levels of sophistication and range of application.

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xlm1717Mar 2015

I think taking less calculus and more linear algebra is a mistake.

There is a really good book in two volumes that I feel shows how methods of linear algebra can be extended using calculus to solve a wide range of problems: A Course in Mathematics for Students of Physics:

http://www.goodreads.com/book/show/2685577-a-course-in-mathe...

Volume 2 is more important. It starts demonstrating how methods of Linear Algebra can be used to solve circuit problem, then generalizes this to higher dimensions and from discrete to continuous spaces using the exterior derivative. Seeing this demonstrated gave me a much clearer, more intuitive understanding for both calculus and linear algebra.

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aufreak3Dec 2013

"A course in mathematics for students of physics" (volumes 1 and 2) by Paul Bamberg and Schlomo Sternberg. [1] [2]

I loved both the books! I replaced my course textbooks with these and am eternally thankful I did that. Volume 2, in particular, is really cool where you get introduced to the exterior calculus formulation of circuit theory, leading to Maxwell's equations.

[1] http://www.amazon.com/Course-Mathematics-Students-Physics/dp... [2] http://www.amazon.com/Course-Mathematics-Students-Physics-Vo...

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aufreak3Feb 2011

So glad to see "Stokes' theorem"! Back in college, I devoured the books "A Course in Mathematics for Students of Physics" by Paul Bamberg and Schlomo Sternberg that covered exterior calculus. It was awesome to see kirchoff's laws in circuits, flux and loop integral laws in electromagnetism all take the same form.

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aufreak3Feb 2012

I find code that does more with less to be beautiful and valuable. Note that I'm not including code that does the same with less. As with all things beautiful, this is tough to illustrate, so I'll use an analogy here from Physics.

Page "xv" of the book "A course in mathematics for students of physics" (volume 2) by Paul Bamberg and Shlomo Sternberg contains a table (do a "look inside" on Amazon) that shows four forms of Maxwell's equations as they evolved over the course of history. Each change expresses what the previous one did, but contributes something more that wasn't possible or was very difficult to express with the earlier form.

The first form explicitly uses cartesian coordinates. The second form is the vector notation, which helps conceptualize and work with the equations in any coordinate system appropriate to the problem (circular, cylindrical, etc.). The third is the relativistic "four-vector" formulation, which, though it says the same thing as the vector form, allows extension to curved spacetime. The fourth exterior calculus formulation (which just reads "dF = 0, and 𝛿F = J"!) covers all of the preceding ones, and also takes exactly the same form when applied to circuits (the kirchoff laws, etc.) which is not something you can say for the preceding forms, while allowing generalization to higher dimensions. The mathematical machinery invented for that simple looking expression is incredibly beautiful (and that book does a great job of its exposition, imo).

This kind of beauty in software is very desirable in my opinion and we do have examples like MapReduce to show for it. Yes the machinery to do a distributed MapReduce is complex, but the concept is simple and flexible and has a bit of the "exterior calculus" fragrance to it. Another is continuations in Scheme - which not only can replace any "mundane" control transfer (break, continue, throw, catch, and ilk) but can do much more than just those and lets you roll your own too.

I believe that is the kind of beauty we should be striving for in software, not just the "pretty code" kind.

(minor edits)

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