TY  - BOOK
AU  - Torres del Castillo,Gerardo F.
ED  - SpringerLink (Online service)
TI  - Differentiable Manifolds: A Theoretical Physics Approach 
SN  - 9780817682712
U1  - 514.34 23
PY  - 2012///
CY  - Boston
PB  - Birkhäuser Boston
KW  - MATHEMATICS
KW  - TOPOLOGICAL GROUPS
KW  - CELL AGGREGATION
KW  - MATHEMATICAL PHYSICS
KW  - MECHANICS
KW  - MANIFOLDS AND CELL COMPLEXES (INCL. DIFF.TOPOLOGY)
KW  - MATHEMATICAL METHODS IN PHYSICS
KW  - TOPOLOGICAL GROUPS, LIE GROUPS
N1  - Preface.-1 Manifolds.-  2 Lie Derivatives -- 3 Differential Forms -- 4 Integral Manifolds -- 5 Connections  -- 6. Riemannian Manifolds -- 7 Lie Groups -- 8 Hamiltonian Classical Mechanics -- References.-Index
N2  - This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics. The work's first three chapters introduce the basic concepts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequently employed in the study of differential equations (Chapter 4), connections (Chapter 5), Riemannian manifolds (Chapter 6), Lie groups (Chapter 7), and Hamiltonian mechanics (Chapter 8). Throughout, the book contains examples, worked out in detail, as well as exercises intended to show how the formalism is applied to actual computations and to emphasize the connections among various areas of mathematics. Differentiable Manifolds is addressed to advanced undergraduate or beginning graduate students in mathematics or physics. Prerequisites include multivariable calculus, linear algebra, differential equations, and (for the last chapter) a basic knowledge of analytical mechanics
UR  - http://dx.doi.org/10.1007/978-0-8176-8271-2
ER  -