Mathematics : Geometry

A genuine introduction to the geometry of lines and conics in the Euclidean plane. Example based and self contained, with numerous illustrations and several hundred worked examples and exercises. Ideal for undergraduate courses in mathematics, or for postgraduates in the engineering and physical sciences. more...

Price: $52.00

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings. more...

Price: $85.00

Symplectic geometry serves Hamiltonian dynamics and symplectic mappings occur as time-1-maps of Hamiltonian flows. Studies in the last few years have been done to show that certain things cannot be done by a symplectic mapping, such as mapping a ball into a thinner cylinder. Schlenk shows that certain other things can be done, through elementary an more...

Price: $99.95

In this unique book, written in a reasonably self-contained manner, the theory of linear connections is systematically presented as a natural part of differential calculus over commutative algebras. This not only makes easy and natural numerous generalizations of the classical theory and reveals various new aspects of it, but also shows in a clear and transparent manner the intrinsic structure of the associated differential calculus. The notion of a “fat manifold” introduced here then allows the reader to build a well-working analogy of this “connection calculus” with the usual one. more...

Price: $105.00

This book provides an in-depth discussion of the theory of finite packings and coverings by convex bodies. It contains various new results and arguments and provides a comprehensive treatment of problems whose interplay was not clearly understood before. Two-dimensional and higher-dimensional arrangements are discussed separately, arrangements of congruent convex bodies in Euclidean space are discussed, and the density of finite packing and covering by balls in Euclidean, spherical and hyperbolic spaces is considered. more...

Price: $68.00