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Books
Differential Geometry
A Geometric Approach to Differential Forms
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Author: David Bachman
Brand: imusti

This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.
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Shapes and Diffeomorphisms (Applied Mathematical Sciences, Vol. 171)
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Author: Laurent Younes
Brand: Brand: Springer

Shapes are complex objects to apprehend, as mathematical entities, in terms that also are suitable for computerized analysis and interpretation. This volume provides the background that is required for this purpose, including different approaches that can be used to model shapes, and algorithms that are available to analyze them. It explores, in particular, the interesting connections between shapes and the objects that naturally act on them, diffeomorphisms. The book is, as far as possible, selfcontained, with an appendix that describes a series of classical topics in mathematics (Hilbert spaces, differential equations, Riemannian manifolds) and sections that represent the state of the art in the analysis of shapes and their deformations. A direct application of what is presented in the book is a branch of the computerized analysis of medical images, called computational anatomy.
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 Used Book in Good Condition
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Problems And Solutions In Differential Geometry, Lie Series, Differential Forms, Relativity And Applications
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Author: WilliHans Steeb

This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easytodigest manner, with the materials of the volume being selfcontained. In particular, curves, surfaces, Riemannian and pseudoRiemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrixvalued differential forms, Maurer–Cartan form, and the Lie derivative are covered.
Readers will find useful applications to special and general relativity, Yang–Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry.
Readership: Graduate students, lecturers and researchers in differential geometry and its applications.
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A Comprehensive Introduction to Differential Geometry, Vol. 4, 3rd Edition
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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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 A Comprehensive Introduction to Differential Geometry, Vol. 5, 3rd Edition
 A Comprehensive Introduction to Differential Geometry, Vol. 3, 3rd Edition
 A Comprehensive Introduction to Differential Geometry, Vol. 2, 3rd Edition
 A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd Edition
 Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus
 Physics for Mathematicians, Mechanics I
 Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)
 Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218)
 Combined Answer Book For Calculus Third and Fourth Editions
 Calculus, 4th edition


Differential Forms and the Geometry of General Relativity
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List price: $59.95
Author: Tevian Dray

Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity. The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of "index gymnastics" as much as possible. The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.
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SpaceTime Algebra
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Author: David Hestenes

This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about farreaching change in the future. At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. These same techniques, in the form of the ‘Geometric Algebra’, can be applied in many areas of engineering, robotics and computer science, with no changes necessary – it is the same underlying mathematics, and enables physicists to understand topics in engineering, and engineers to understand topics in physics (including aspects in frontier areas), in a way which no other single mathematical system could hope to make possible. There is another aspect to Geometric Algebra, which is less tangible, and goes beyond questions of mathematical power and range. This is the remarkable insight it gives to physical problems, and the way it constantly suggests new features of the physics itself, not just the mathematics. Examples of this are peppered throughout ‘SpaceTime Algebra’, despite its short length, and some of them are effectively still research topics for the future. From the Foreward by Anthony Lasenby
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A Panoramic View of Riemannian Geometry
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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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Differential Geometry and Symmetric Spaces (AMS Chelsea Publishing)
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Author: Sigurdur Helgason
Brand: Brand: American Mathematical Society

Sigurdur Helgason's Differential Geometry and Symmetric Spaces was quickly recognized as a remarkable and important book. For many years, it was the standard text both for Riemannian geometry and for the analysis and geometry of symmetric spaces. Several generations of mathematicians relied on it for its clarity and careful attention to detail. Although much has happened in the field since the publication of this book, as demonstrated by Helgason's own threevolume expansion of the original work, this single volume is still an excellent overview of the subjects. For instance, even though there are now many competing texts, the chapters on differential geometry and Lie groups continue to be among the best treatments of the subjects available. There is also a welldeveloped treatment of Cartan's classification and structure theory of symmetric spaces. The last chapter, on functions on symmetric spaces, remains an excellent introduction to the study of spherical functions, the theory of invariant differential operators, and other topics in harmonic analysis. This text is rightly called a classic. Sigurdur Helgason was awarded the Steele Prize for Groups and Geometric Analysis and the companion volume, Differential Geometry, Lie Groups and Symmetric Spaces.
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 Used Book in Good Condition


Differential Forms and Applications (Universitext)
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Author: Manfredo P. Do Carmo
Brand: Brand: Springer

An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames expounded by E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. This is then collated in the last chapter to present Chern's proof of the GaussBonnet theorem for compact surfaces.
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An Introduction to Differential Geometry (Dover Books on Mathematics)
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Author: T. J. Willmore
Brand: Willmore T J

A solid introduction to the methods of differential geometry and tensor calculus, this volume is suitable for advanced undergraduate and graduate students of mathematics, physics, and engineering. Rather than a comprehensive account, it offers an introduction to the essential ideas and methods of differential geometry. Part 1 begins by employing vector methods to explore the classical theory of curves and surfaces. An introduction to the differential geometry of surfaces in the large provides students with ideas and techniques involved in global research. Part 2 introduces the concept of a tensor, first in algebra, then in calculus. It covers the basic theory of the absolute calculus and the fundamentals of Riemannian geometry. Worked examples and exercises appear throughout the text.
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 An Introduction to Differential Geometry
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