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.

Concepts from Tensor Analysis and Differential Geometry

1st Edition
January 1, 1961
Tracy Y. Thomas
Richard Bellman
English
eBook
9 7 8 1 4 8 3 2 6 3 7 1 7

Concepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors. The book explains some interesting formal properties of a skew-symmetric tensor and the curl of a vector in a coordinate manifold of three dimensions. It also explains Riemann spaces, affinely connected spaces, normal coordinates, and the general theory of extension. The book explores differential invariants, transformation groups, Euclidean metric space, and the Frenet formulae. The text describes curves in space, surfaces in space, mixed surfaces, space tensors, including the formulae of Gaus and Weingarten. It presents the equations of two scalars K and Q which can be defined over a regular surface S in a three dimensional Riemannian space R. In the equation, the scalar K, which is an intrinsic differential invariant of the surface S, is known as the total or Gaussian curvature and the scalar U is the mean curvature of the surface. The book also tackles families of parallel surfaces, developable surfaces, asymptotic lines, and orthogonal ennuples. The text is intended for a one-semester course for graduate students of pure mathematics, of applied mathematics covering subjects such as the theory of relativity, fluid mechanics, elasticity, and plasticity theory.

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.

Methods of Differential Geometry in Analytical Mechanics

1st Edition
Volume 158
January 1, 1989
M. de León + 1 more
English
eBook
9 7 8 0 0 8 0 8 7 2 6 9 8

The differential geometric formulation of analytical mechanics not only offers a new insight into Mechanics, but also provides a more rigorous formulation of its physical content from a mathematical viewpoint.Topics covered in this volume include differential forms, the differential geometry of tangent and cotangent bundles, almost tangent geometry, symplectic and pre-symplectic Lagrangian and Hamiltonian formalisms, tensors and connections on manifolds, and geometrical aspects of variational and constraint theories.The book may be considered as a self-contained text and only presupposes that readers are acquainted with linear and multilinear algebra as well as advanced calculus.

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.

Introduction to Global Variational Geometry

1st Edition
Volume 23
January 1, 1980
Demeter Krupka
English
eBook
9 7 8 0 0 8 0 9 5 4 2 9 5

This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether’s theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles

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.

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.

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