The differential geometric formulation of analytical mechanics not only offers a new insight into Mechanics, but also provides a more rigorous formulation of its physical content from a mathematical viewpoint.Topics covered in this volume include differential forms, the differential geometry of tangent and cotangent bundles, almost tangent geometry, symplectic and pre-symplectic Lagrangian and Hamiltonian formalisms, tensors and connections on manifolds, and geometrical aspects of variational and constraint theories.The book may be considered as a self-contained text and only presupposes that readers are acquainted with linear and multilinear algebra as well as advanced calculus.

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.

With the direct, accessible, and pragmatic approach of Fowles and Cassiday's ANALYTICAL MECHANICS, Seventh Edition, thoroughly revised for clarity and concision, students will grasp challenging concepts in introductory mechanics. A complete exposition of the fundamentals of classical mechanics, this proven and enduring introductory text is a standard for the undergraduate Mechanics course. Numerical worked examples increased students' problem-solving skills, while textual discussions aid in student understanding of theoretical material through the use of specific cases.

Differential Forms in Mathematical Physics

A comprehensive graduate-level textbook on classical dynamics with many worked examples and over 200 homework exercises, first published in 1998.

Presents a comprehensive treatment of quantum mechanics from a mathematics perspective. Including traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin.

The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.