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Books
Differential Geometry
Geometry Part 1 (Quickstudy: Academic)
Lowest new price: $1.83
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List price: $4.95
Author: Inc. BarCharts
Brand: QuickStudy

Coverage of the fundamental structure of geometry.
Part 1 of two guides on geometry.
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Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218)
Lowest new price: $63.39
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Author: John Lee
Brand: Brand: Springer

This book is an introductory graduatelevel textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard’s theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of firstorder partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.
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 Used Book in Good Condition
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Differential Geometry (Dover Books on Mathematics)
Lowest new price: $9.97
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List price: $16.95
Author: Erwin Kreyszig

An introductory textbook on the differential geometry of curves and surfaces in threedimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods and results involved. With problems at the end of each section, and solutions listed at the end of the book. Includes 99 illustrations.
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A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd Edition
Lowest new price: $47.50
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Author: Michael Spivak
Brand: Brand: Publish or Perish

Book by Michael Spivak, Spivak, Michael
Features:
 Used Book in Good Condition
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Geometry Part 2 (Quickstudy: Academic)
Lowest new price: $2.13
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List price: $5.95
Author: Inc. BarCharts
Brand: QuickStudy
Model: FBA283672

Part 2 of our coverage of the fundamental structure of geometry.
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Riemannian Geometry
Lowest new price: $30.00
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Author: Manfredo P. do Carmo

Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for firstyear graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text. A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight into the subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject.
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Geometric Formulas (Quickstudy: Academic)
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List price: $5.95
Author: Inc. BarCharts
Brand: QuickStudy

6page laminated guide includes: ·general terms ·lines ·line segments ·rays ·angles ·transversal line angles ·polygons ·circles ·theorems & relationships ·postulates ·geometric formulas
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Introduction to Tensor Analysis and the Calculus of Moving Surfaces
Lowest new price: $50.81
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List price: $69.99
Author: Pavel Grinfeld

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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Differential Geometry of Curves and Surfaces
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List price: $103.00
Author: Manfredo P. Do Carmo

This volume covers local as well as global differential geometry of curves and surfaces. 
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Manifolds, Tensors, and Forms: An Introduction for Mathematicians and Physicists
Lowest new price: $60.09
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Author: Paul Renteln

Providing a succinct yet comprehensive treatment of the essentials of modern differential geometry and topology, this book's clear prose and informal style make it accessible to advanced undergraduate and graduate students in mathematics and the physical sciences. The text covers the basics of multilinear algebra, differentiation and integration on manifolds, Lie groups and Lie algebras, homotopy and de Rham cohomology, homology, vector bundles, Riemannian and pseudoRiemannian geometry, and degree theory. It also features over 250 detailed exercises, and a variety of applications revealing fundamental connections to classical mechanics, electromagnetism (including circuit theory), general relativity and gauge theory. Solutions to the problems are available for instructors at www.cambridge.org/9781107042193.
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