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Differential Geometry


LECTURES ON THE GEOMETRY OF MANIFOLDS (2ND EDITION)

LECTURES ON THE GEOMETRY OF MANIFOLDS (2ND EDITION) Lowest new price: $151.38
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Author: LIVIU I NICOLAESCU
Brand: Brand: World Scientific Pub Co Inc

The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.The book's guiding philosophy is, in the words of Newton, that “in learning the sciences examples are of more use than precepts”. We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue.While we present most of the local aspects of classical differential geometry, the book has a “global and analytical bias”. We develop many algebraic-topological techniques in the special context of smooth manifolds such as Poincaré duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss-Bonnet theorem.We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic Lpand Hölder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an in-depth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators.The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight.

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Curved Spaces: From Classical Geometries to Elementary Differential Geometry

Curved Spaces: From Classical Geometries to Elementary Differential Geometry Lowest new price: $168.76
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Author: P. M. H. Wilson
Brand: Brand: Cambridge University Press

This self-contained 2007 textbook presents an exposition of the well-known classical two-dimensional geometries, such as Euclidean, spherical, hyperbolic, and the locally Euclidean torus, and introduces the basic concepts of Euler numbers for topological triangulations, and Riemannian metrics. The careful discussion of these classical examples provides students with an introduction to the more general theory of curved spaces developed later in the book, as represented by embedded surfaces in Euclidean 3-space, and their generalization to abstract surfaces equipped with Riemannian metrics. Themes running throughout include those of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the link to topology provided by the Gauss-Bonnet theorem. Numerous diagrams help bring the key points to life and helpful examples and exercises are included to aid understanding. Throughout the emphasis is placed on explicit proofs, making this text ideal for any student with a basic background in analysis and algebra.

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An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics)

An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics) Lowest new price: $98.72
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Author: William M. Boothby

The second edition of An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject.

  • Line and surface integrals
  • Divergence and curl of vector fields

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A Comprehensive Introduction to Differential Geometry, Vol. 4, 3rd Edition

A Comprehensive Introduction to Differential Geometry, Vol. 4, 3rd Edition Lowest new price: $45.00
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Author: Michael Spivak

Spivak's 5 volume set is a classic and overall the best and most thorough treatment of differential geometry

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Modern Geometry ― Methods and Applications: Part I: The Geometry of Surfaces, Transformation Groups, and Fields (Graduate Texts in Mathematics) (Pt. 1)

Modern Geometry ― Methods and Applications: Part I: The Geometry of Surfaces, Transformation Groups, and Fields (Graduate Texts in Mathematics) (Pt. 1) Lowest new price: $34.00
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Author: B.A. Dubrovin
Brand: B A Dubrovin

This is the first volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This new edition offers substantial revisions, and the material is written in concrete language with terminology acceptable to physicists.

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  • Modern Geometry Methods and Applications Part I The Geometry of Surfaces Transformation Groups and Fields Graduate Texts in Mathematics Pt 1

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Multivariable Calculus and Differential Geometry (de Gruyter Textbook)

Multivariable Calculus and Differential Geometry (de Gruyter Textbook) Lowest new price: $42.03
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Author: Gerard Walschap

This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.

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A Panoramic View of Riemannian Geometry

A Panoramic View of Riemannian Geometry Lowest new price: $73.91
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Author: Marcel Berger
Brand: Brand: Springer

This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field.

From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS

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Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition (Textbooks in Mathematics)

Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition (Textbooks in Mathematics) Lowest new price: $97.47
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Author: Elsa Abbena

Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray’s famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and surfaces from existing ones. Since Gray’s death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions.

The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted.

Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.

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Michael Atiyah Collected Works: 7 Volume Set

Michael Atiyah Collected Works: 7 Volume Set Lowest new price: $953.97
List price: $1,505.00
Author: Michael Atiyah

Professor Atiyah is one of the greatest living mathematicians and is renowned in the mathematical world. He is a recipient of the Fields Medal, the mathematical equivalent of the Nobel Prize, and is still actively involved in the mathematics community. His huge number of published papers, focusing on the areas of algebraic geometry and topology, have here been collected into seven volumes, with the first five volumes divided thematically and the sixth and seventh arranged by date.

This seven volume set of the collected works of Professor Sir Michael Atiyah, includes:
Collected Works: Volume 1: Early Papers; General Papers
Collected Works: Volume 2: K-Theory
Collected Works: Volume 3: Index Theory: 1
Collected Works: Volume 4: Index Theory: 2
Collected Works: Volume 5: Gauge Theories
Collected Works: Volume 6: Publications between 1987 and 2002
New for 2014:
Collected Works: Volume 7: 2002-2013, including Sir Michael's work on skyrmions; K-theory and cohomology; geometric models of matter; curvature, cones and characteristic numbers; and reflections on the work of Riemann, Einstein and Bott.


Differential Geometry and its Applications (Classroom Resource Materials) (Mathematical Association of America Textbooks)

Differential Geometry and its Applications (Classroom Resource Materials) (Mathematical Association of America Textbooks) Lowest new price: $74.29
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Author: John Oprea
Brand: Brand: The Mathematical Association of America

Differential geometry has a long, wonderful history. It has found relevance in areas ranging from machinery design to the classification of four-manifolds to the creation of theories of nature's fundamental forces to the study of DNA. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes together geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors. It is also for students in engineering and the sciences. The mix of ideas offer students the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. Students will not only see geodesics on surfaces, but they will also observe the effect that an abstract result such as the Clairaut relation can have on geodesics. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.

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