A course in mathematics for students of physics
by Paul G. Bamberg, Shlomo Sternberg, Paul Bamberg · first published 1988
100% recommend
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 integr
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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.
on “10 Awesome Theorems & Result” ↗"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…
on “Structure and Interpretation of Classical Mechanics” ↗…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…
on “Too Much Calculus – Gilbert Strang (2001) [pdf]” ↗…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…
on “Beautiful Apps, Ugly Code” ↗