Manifold Theory: An Introduction for Mathematical Physicists

ISBN-13: 9781898563846 / Angielski / Miękka / 2002 / 424 str.

D. Martin

Opis

This account of basic manifold theory and global analysis, based on senior undergraduate and post-graduate courses at Glasgow University for students and researchers in theoretical physics, has been proven over many years. The treatment is rigorous yet less condensed than in books written primarily for pure mathematicians. Prerequisites include knowledge of basic linear algebra and topology. Topology is included in two appendices because many courses on mathematics for physics students do not include this subject.

• Provides a comprehensive account of basic manifold theory for post-graduate students
• Introduces the basic theory of differential geometry to students in theoretical physics and mathematics
• Contains more than 130 exercises, with helpful hints and solutions

Recenzje

This blend of local coordinate methods and intrinsic differential geometry enables workers to read and do calculations in relativity and high energy particle research. It provides foundations for study in gauge theory, differential geometry and differential topology., Mathematical Reviews
Dr Martin's very readable differential geometry text for graduate students in physics could also be used for independent study., American Mathematical Monthly
Accessible and clear, students will appreciate the numerous examples., Zentralblatt fur Didaktik der Mathematik

Spis treści

Vector spaces; Tensor algebra; Differential manifolds; Vector and tensor fields on a manifold; Exterior differential forms; Differentiation on a manifold; Pseudo-Riemannian and Riemannian manifolds; Symplectic manifolds; Lie groups; Integration on a manifold; Fibre bundles; Complex linear algebra and almost complex manifolds.