This will be a one hour crash course on some of the basic ideas of classical mechanics: configuration space, Lagrangians, the principle of stationary action, and Noether's theorem. A reference is the online book http://math.ucr.edu/home/baez/classical/texfiles/2005/book/classical.pdf . In the discussion after the talk, we will work out some JEE physics-style mechanics problems.
The importance of classical mechanics is hard to exaggerate. It forms the basis of all of modern physics, and has inspired many deep ideas in mathematics, from manifolds and topology, to Lie groups and representation theory, to symplectic and Kahler geometry. Classical mechanics is also of obvious importance for understanding most physical phenomena, including most biological phenomena. This talk will not develop any of these connections.
Prerequisites: High school-level mathematics and physics, including integration by parts, should suffice.