Updates the mathematical treatment for the study of more advanced topics in quantum mechanics, statistical mechanics, and nonlinear & orbital mechanics. 

Hamiltonian dynamics and the concept of phase space are introduced early on. This allows integration of the concepts of chaos and other nonlinear effects into the main flow of the text. 

Stresses the role of symmetries and the underlying geometric structure of space-time. 

Designed for a one-semester course or an updated reference for scientists.