DIFFERENTIABLE MANIFOLDS A First Course

The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses in differential topology and geometry. Differential Manifolds is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good grounding in general topology, calculus, and modern algebra. It is ideal for a full year Ph.D. qualifying course and sufficiently self contained for private study by non-specialists wishing to survey the topic. The themes of linearization, (re)integration, and global versus local are emphasized repeatedly; additional features include a treatment of the elements of multivariable calculus, an exploration of bundle theory, and a further development of Lie theory than is customary in textbooks at this level. Students, teachers, and professionals in mathematics and mathematical physics should find this a most stimulating and useful text.