![]() Thirring's Classical Mathematical Physics is an authoritative and concise text that not only presents classical mechanics, but also field theory in rigorous fashion. ![]() ![]() Arnold's Mathematical Methods of Classical Mechanics is a classic and concise text that is a must-have reference for those with an interest in the mathematical physics of classical mechanics. Differential Geometry Home Textbook Authors: Victor V.Fasano and Marmi's Analytical Mechanics, which contains some good chapters on statistical mechanics, chaos and ergodic theory in addition to classical mechanics built from the ground-up.It contains several historical and philosophical nuggets that would also give the working mathematician a rough idea about how physicists think about and approach a problem. Peter Petersan, Riemannian geometry is very good. 20 Best Differential Geometry Books of All Time Visual Differential Geometry and Forms Differential Geometry Mathematics for Physicists Differential. Spivak's Physics for Mathematicians: Mechanics I which covers classical mechanics from the ground-up using the language of differential geometry. The Carmos Riemannian geometry is an old book, may be you can use a new book for modern differential geometry.It talks about the differential geometry of curves and surfaces in real 3-space. Perhaps one of the nicest differential geometric accounts on classical mechanics, written by a mathematician and for mathematicians is, This is a beautiful book, certainly one of my favourites.
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