This work treats the fundamentals of differential geometry - manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry.

Presents two essential and apparently unrelated subjects that include, microlocal analysis and the theory of pseudo-differential operators, a basic tool in the study of partial differential equations and in analysis on manifolds; and the Nash-Moser theorem

Fourier analysis encompasses a variety of perspectives and techniques. This volume presents the real variable methods of Fourier analysis introduced by Calderon and Zygmund. The text was born from a graduate course taught at the Universidad Autonoma de Madrid and incorporates lecture notes from a course taught by Jose Luis Rubio de Francia at the same university. Motivated by the study of Fourier series and integrals, classical topics are introduced, such as the Hardy-Littlewood maximal function and the Hilbert transform. The remaining portions of the text are devoted to the study of singular...

Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds. This book unifies Riemannian geometry with modern complex analysis, as well as with algebra and number theory.

Defines simplicial homology and cohomology, with various examples and applications. This book introduces Kolmogorov-Alexander multiplication in cohomology. It deals with the applications of simplicial homology and cohomology to obstruction theory, in parti

This is an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. The Lebesgue integral and its essential properties are first developed in detail. The other three integrals are all generalizations of the Lebesgue integral that satisfy the ideal version of the Fundamental Theorem of Calculus: if F is differentiable on the interval a, b], then F ]1 integrable on a, b] and f ]b a = F(b) - F(a). One of the book's unique features is that the Denjoy, Perron, and Henstock integrals are each developed carefully from their...

This title is written as a book of impressions'' of a journey through the theory of complex algebraic curves. A cursory glance at the subjects visited reveals an apparently eclectic selection, from conics and cubics to theta functions, Jacobians, and questions of moduli, but by the end of the book, the theme of theta functions becomes clear, culminating in the Schottky problem. The author's intent was to motivate further study and to stimulate mathematical activity.

This book bridges the gap between the many elementary introductions to set theory that are available today and the more advanced, specialized monographs. The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.

This text offers a comprehensive and reader-friendly exposition of the theory of linear operators on Banach spaces and Banach lattices using their topological and order structures and properties. Abramovich and Aliprantis give a presentation that includes many contemporary developments in operator theory and also draws together results which are spread over the vast literature.

Covers key topics of numerical methods. This book includes such topics as interpolation, the fast Fourier transform, iterative methods for solving systems of linear and nonlinear equations, numerical methods for solving ODEs, numerical methods for matrix eigenvalue problems, approximation theory, and computer arithmetic.