Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics, Vol. 60)

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

• Ordinary Differential Equations (The MIT Press)
• Calculus of Variations (Dover Books on Mathematics)
• Gravitation
• Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)
• The Variational Principles of Mechanics (Dover Books on Physics)
• Mechanics: Volume 1 (Course of Theoretical Physics S)
• Partial Differential Equations: Second Edition (Graduate Studies in Mathematics)
• Quantum Theory for Mathematicians (Graduate Texts in Mathematics)
• Differential Forms in Algebraic Topology (Graduate Texts in Mathematics)
• General Relativity