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Books
Differential Geometry
A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd Edition
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Author: Michael Spivak
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Spivak's 5 volume set is a classic and overall the best and most thorough treatment of differential geometry
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 Used Book in Good Condition
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 A Comprehensive Introduction to Differential Geometry, Vol. 2, 3rd Edition
 A Comprehensive Introduction to Differential Geometry, Vol. 3, 3rd Edition
 A Comprehensive Introduction to Differential Geometry, Vol. 4, 3rd Edition
 A Comprehensive Introduction to Differential Geometry, Vol. 5, 3rd Edition
 Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus
 Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218)
 Algebraic Topology
 Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)
 Physics for Mathematicians, Mechanics I
 Differential Topology (AMS Chelsea Publishing)


Introduction to Tensor Analysis and the Calculus of Moving Surfaces
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Author: Pavel Grinfeld
Brand: Springer

This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20^{th} century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated GaussBonnet theorem.
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An Introduction to Manifolds (Universitext)
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Author: Loring W. Tu

Manifolds, the higherdimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite pointset topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a onesemester graduate or advanced undergraduate course, as well as by students engaged in selfstudy. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
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The Wheel Of Time: The Shamans Of Mexico Their Thoughts About Life Death And The Universe
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Author: Carlos Castaneda
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Worldrenowned bestselling author Carlos Castaneda's Selection of his wrtings on the shamans of ancient Mexico.
Originally drawn to Yaqui Indian spiritual leader don Juan Matus for his knowledge of mindaltering plants, bestselling author Carlos Castaneda soon immersed himself in the sorcerer’s magical world entirely. Ten years after his first encounter with the shaman, Castaneda examines his field notes and comes to understand what don Juan knew all along—that these plants are merely a means to understanding the alternative realities that one cannot fully embrace on one’s own. In Journey to Ixtlan, Carlos Castaneda introduces readers to this new approach for the first time and explores, as he comes to experience it himself, his own final voyage into the teachings of don Juan, sharing with us what it is like to truly “stop the world” and perceive reality on his own terms.
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 The Wheel of Time: The Shamans of Ancient Mexico, Their Thoughts About Life, Death and the Universe
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Differential Geometry: Connections, Curvature, and Characteristic Classes (Graduate Texts in Mathematics)
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Author: Loring W. Tu

This text presents a graduatelevel introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more selfcontained, sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too farfetched to argue that differential geometry should be in every mathematician's arsenal.
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A Comprehensive Introduction to Differential Geometry, Vol. 2, 3rd Edition
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Author: Michael Spivak
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Book by Michael Spivak, Spivak, Michael
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 Used Book in Good Condition
Similar Products:
 A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd Edition
 A Comprehensive Introduction to Differential Geometry, Vol. 3, 3rd Edition
 A Comprehensive Introduction to Differential Geometry, Vol. 4, 3rd Edition
 A Comprehensive Introduction to Differential Geometry, Vol. 5, 3rd Edition
 Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus
 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)
 Physics for Mathematicians, Mechanics I
 Gravitation
 Algebraic Topology


Differential Geometry of Spray and Finsler Spaces
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Author: Zhongmin Shen
Brand: Brand: Springer

In this book we study sprays and Finsler metrics. Roughly speaking, a spray on a manifold consists of compatible systems of secondorder ordinary differential equations. A Finsler metric on a manifold is a family of norms in tangent spaces, which vary smoothly with the base point. Every Finsler metric determines a spray by its systems of geodesic equations. Thus, Finsler spaces can be viewed as special spray spaces. On the other hand, every Finsler metric defines a distance function by the length of minimial curves. Thus Finsler spaces can be viewed as regular metric spaces. Riemannian spaces are special regular metric spaces. In 1854, B. Riemann introduced the Riemann curvature for Riemannian spaces in his groundbreaking Habilitationsvortrag. Thereafter the geometry of these special regular metric spaces is named after him. Riemann also mentioned general regular metric spaces, but he thought that there were nothing new in the general case. In fact, it is technically much more difficult to deal with general regular metric spaces. For more than half century, there had been no essential progress in this direction until P. Finsler did his pioneering work in 1918. Finsler studied the variational problems of curves and surfaces in general regular metric spaces. Some difficult problems were solved by him. Since then, such regular metric spaces are called Finsler spaces. Finsler, however, did not go any further to introduce curvatures for regular metric spaces. He switched his research direction to set theory shortly after his graduation.
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Elementary Differential Geometry (Springer Undergraduate Mathematics Series)
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Author: A.N. Pressley
Brand: Andrew Pressley

Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on nonEuclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book.  Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature.
 Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com
ul
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 Elementary Differential Geometry
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Beyond Einstein: Perspectives on Geometry, Gravitation, and Cosmology in the Twentieth Century (Einstein Studies)
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Beyond Einstein: Perspectives on Geometry, Gravitation, and Cosmology explores the rich interplay between mathematical and physical ideas by studying the interactions of major actors and the roles of important research communities over the course of the last century.


The Geometry of Physics: An Introduction
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Author: Theodore Frankel
Brand: Brand: Cambridge University Press

This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles, and Chern forms that are helpful for a deeper understanding of both classical and modern physics and engineering. It is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study.
A main addition introduced in this Third Edition is the inclusion of an Overview, which can be read before starting the text. This appears at the beginning of the text, before Chapter 1. Many of the geometric concepts developed in the text are previewed here and these are illustrated by their applications to a single extended problem in engineering, namely the study of the Cauchy stresses created by a small twist of an elastic cylindrical rod about its axis.
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