Books in Differential geometry

Fractal Functions, Fractal Surfaces, and Wavelets

2nd Edition
August 9, 2016
Peter R. Massopust
English
Hardback
9 7 8 0 1 2 8 0 4 4 0 8 7
eBook
9 7 8 0 1 2 8 0 4 4 7 0 4

Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets. The book is based on Massopust’s work on and contributions to the theory of fractal interpolation, and the author uses a number of tools—including analysis, topology, algebra, and probability theory—to introduce readers to this exciting subject. Though much of the material presented in this book is relatively current (developed in the past decades by the author and his colleagues) and fairly specialized, an informative background is provided for those entering the field. With its coherent and comprehensive presentation of the theory of univariate and multivariate fractal interpolation, this book will appeal to mathematicians as well as to applied scientists in the fields of physics, engineering, biomathematics, and computer science. In this second edition, Massopust includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, further develops the connections to wavelets and wavelet sets, and deepens and extends the pedagogical content.

Elementary Differential Geometry, Revised 2nd Edition

2nd Edition
March 27, 2006
Barrett O'Neill
English
Hardback
9 7 8 0 1 2 0 8 8 7 3 5 4
eBook
9 7 8 0 0 8 0 5 0 5 4 2 8

Written primarily for students who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Revised 2nd Edition, provides an introduction to the geometry of curves and surfaces. The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard. This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text.

Initiation to Global Finslerian Geometry

1st Edition
Volume 68
January 18, 2006
Hassan Akbar-Zadeh
English
Hardback
9 7 8 0 4 4 4 5 2 1 0 6 4
eBook
9 7 8 0 0 8 0 4 6 1 7 0 0

After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, projective and conformal vector fields on the unitary tangent fibre bundle.Key features- Theory of connections of vectors and directions on the unitary tangent fibre bundle.- Complete list of Bianchi identities for a regular conection of directions.- Geometry of generalized Einstein manifolds.- Classification of Finslerian manifolds.- Affine, isometric, conformal and projective vector fields on the unitary tangent fibre bundle.

Handbook of Differential Geometry

1st Edition
November 29, 2005
Franki J.E. Dillen + 1 more
English
Hardback
9 7 8 0 4 4 4 5 2 0 5 2 4
eBook
9 7 8 0 0 8 0 4 6 1 2 0 5

In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent).All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas.

Minimal Surfaces of Codimension One

1st Edition
Volume 91
April 1, 2000
U. Massari + 1 more
English
eBook
9 7 8 0 0 8 0 8 7 2 0 2 5

This book gives a unified presentation of different mathematical tools used to solve classical problems like Plateau's problem, Bernstein's problem, Dirichlet's problem for the Minimal Surface Equation and the Capillary problem.The fundamental idea is a quite elementary geometrical definition of codimension one surfaces. The isoperimetric property of the Euclidean balls, together with the modern theory of partial differential equations are used to solve the 19th Hilbert problem. Also included is a modern mathematical treatment of capillary problems.

Generalized Classical Mechanics and Field Theory

1st Edition
Volume 112
April 1, 2000
M. de León + 1 more
English
eBook
9 7 8 0 0 8 0 8 7 2 2 3 0

The aim of this book is to discuss the present situation of Lagrangian and Hamiltonian formalisms involving higher order derivatives. The achievements of differential geometry in formulating a more modern and powerful treatment of these theories is described and an extensive review of the development of these theories in classical language is also given.

Handbook of Differential Geometry, Volume 1

1st Edition
December 16, 1999
F.J.E. Dillen + 1 more
English
Hardback
9 7 8 0 4 4 4 8 2 2 4 0 6
eBook
9 7 8 0 0 8 0 5 3 2 8 3 7

In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.

The Language of Shape

1st Edition
November 1, 1996
S. Hyde + 6 more
English
Hardback
9 7 8 0 4 4 4 8 1 5 3 8 5
eBook
9 7 8 0 0 8 0 5 4 2 5 4 6

This book develops the thesis that structure and function in a variety of condensed systems - from the atomic assemblies in inorganic frameworks and organic molecules, through molecular self-assemblies to proteins - can be unified when curvature and surface geometry are taken together with molecular shape and forces. An astonishing variety of synthetic and biological assemblies can be accurately modelled and understood in terms of hyperbolic surfaces, whose richness and beauty are only now being revealed by applied mathematicians, physicists, chemists and crystallographers. These surfaces, often close to periodic minimal surfaces, weave and twist through space, carving out interconnected labyrinths whose range of topologies and symmetries challenge the imaginative powers.The book offers an overview of these structures and structural transformations, convincingly demonstrating their ubiquity in covalent frameworks from zeolites used for cracking oil and pollution control to enzymes and structural proteins, thermotropic and lyotropic bicontinuous mesophases formed by surfactants, detergents and lipids, synthetic block copolymer and protein networks, as well as biological cell assemblies, from muscles to membranes in prokaryotic and eukaryotic cells. The relation between structure and function is analysed in terms of the previously neglected hidden variables of curvature and topology. Thus, the catalytic activity of zeolites and enzymes, the superior material properties of interpenetrating networks in microstructured polymer composites, the transport requirements in cells, the transmission of nerve signals and the folding of DNA can be more easily understood in the light of this.The text is liberally sprinkled with figures and colour plates, making it accessible to both the beginning graduate student and researchers in condensed matter physics and chemistry, mineralogists, crystallographers and biologists.

Topological Theory of Dynamical Systems

1st Edition
Volume 52
June 3, 1994
N. Aoki + 1 more
English
eBook
9 7 8 0 0 8 0 8 8 7 2 1 0

This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians. Although some of the topics discussed are relatively new, others are not: this book is not a collection of research papers, but a textbook to present recent developments of the theory that could be the foundations for future developments.This book contains a new theory developed by the authors to deal with problems occurring in diffentiable dynamics that are within the scope of general topology. To follow it, the book provides an adequate foundation for topological theory of dynamical systems, and contains tools which are sufficiently powerful throughout the book.Graduate students (and some undergraduates) with sufficient knowledge of basic general topology, basic topological dynamics, and basic algebraic topology will find little difficulty in reading this book.

Differential Topology and Quantum Field Theory

1st Edition
October 23, 1992
Charles Nash
English
Paperback
9 7 8 0 1 2 5 1 4 0 7 6 8

The remarkable developments in differential topology and how these recent advances have been applied as a primary research tool in quantum field theory are presented here in a style reflecting the genuinely two-sided interaction between mathematical physics and applied mathematics. The author, following his previous work (Nash/Sen: Differential Topology for Physicists, Academic Press, 1983), covers elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory. The explanatory approach serves to illuminate and clarify these theories for graduate students and research workers entering the field for the first time.

Life Sciences

Physical Sciences & Engineering

Social Sciences & Humanities

Health