Sistema Bibliotecario de la Universidad de Quintana Roo

I Introduction to Linear Algebra and Differential Geometry.-1 Vector Space and Linear Maps.-2 Tensor Algebra.-3 Skew-symmetric Tensors and Exterior Algebra.-4 Euclidean and Symplectic Vector Spaces.-5 Duality and Euclidean Tensors.-6 Differentiable Manifolds.-7 One-Parameter Groups of Diffeomorphisms.-8 Exterior Derivative and Integration.-9 Absolute Differential Calculus -- 10 An Overview of Dynamical Systems.-II Mechanics.-11 Kinematics of a Point Particle.-12 Kinematics of Rigid Bodies.-13 Principles of Dynamics.-14 Dynamics of a Material Point.-15 General Principles of Rigid Body Dynamics.-16 Dynamics of a Rigid Body.-17 Lagrangian Dynamics.-18 Hamiltonian Dynamics.-19 Hamilton-Jacobi Theory.-20 Completely Integrable Systems.-21 Elements of Statistical Mechanics of Equilibrium.-22 Impulsive Dynamics.-23 Introduction to Fluid Mechanics -- A First-Order PDE.-B Fouriers Series.-References.-Index.

This textbook takes a broadyet thorough approach to mechanics, aimed at bridging the gap between classicalanalytic andmoderndifferential geometric approaches to the subject. Developed by the authorfrom 35 years of teaching experience, the presentation is designed to give students an overview of the many different modelsused through the history of the fieldfrom Newton to Lagrangewhile also painting a clear picture of the most modern developments. Throughout, it makes heavy use of the powerful tools offered by Mathematicaë . The volume is organized into two parts. The first focuses on developing themathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, HamiltonJacobi theory, completely integrable systems, statistical mechanics of equilibrium, andimpulsive dynamics, among others. With a unique selection of topics and a largearray of exercises to reinforce concepts, Classical Mechanics with Mathematicais an excellentresource for graduate students in physics. It can also serve as a reference for researchers wishing to gain a deeper understanding of both classical and modern mechanics.

ZDB-2-SMA