E-raamat: Tensors and Manifolds: With Applications to Physics

This is a paperback reprint of the 2004 cloth edition of Wasserman's essential textbook, with no additions or changes. Ideally suited for the advanced undergraduate or beginning graduate course, the text is derived from Wasserman's courses at Michigan State University and fills the gap for math directly applicable to current applications in physics, yet not too advanced for the non-specialist. Vector spaces, multilinear mappings, dual spaces, tensor product spaces, tensors, symmetric and skew-symmetric tensors, and exterior or Grassmann algebra are described in the initial chapters, with definitions and examples provided. Subsequent chapters offer the math underlying the physics in manifolds, mechanics, and various theories of spacetime, as well as lie groups, fiber bundles, and gauge theory, all presented in an engaging prose style. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)

This book sets forth the basic principles of tensors and manifolds and describes how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics.

This second edition of Tensors and Manifolds is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics, giving an introduction to the expanse of modern mathematics and its application in modern physics. It aims to fill the gap between the basic courses and the highly technical and specialized courses which both mathematics and physics students require in their advanced training, while simultaneously trying to promote, at an early stage, a better appreciation and understanding of each other's discipline. The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics. The existing material from the first edition has been reworked and extended in some sections to provide extra clarity, with additional problems. Four new chapters on Lie groups and fibre bundles have been included, leading to an exposition of gauge theory and the standard model of elementary particle physics. Mathematical rigour combined with an informal style makes this a very accessible book and will provide the reader with an enjoyable panorama of interesting mathematics and physics.