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Books

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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  • Used Book in Good Condition

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Geometric Formulas (Quick Study: Academic)

Geometric Formulas (Quick Study: Academic) Lowest new price: $5.49
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Author: Inc. BarCharts
Brand: QuickStudy

6-page laminated guide includes:
·general terms
·lines
·line segments
·rays
·angles
·transversal line angles
·polygons
·circles
·theorems & relationships
·postulates
·geometric formulas

Features:

  • Geometric Formulas Reference Guide Quickstudy Academic

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Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)

Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics) Lowest new price: $15.99
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Author: Manfredo P. do Carmo

One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems.
The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.

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Geometry Part 2 (Quickstudy Reference Guides - Academic)

Geometry Part 2 (Quickstudy Reference Guides - Academic) Lowest new price: $4.00
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Author: Inc. BarCharts
Brand: QuickStudy

Part 2 of our coverage of the fundamental structure of geometry.

 

Features:

  • Geometry Part 2 Quickstudy Reference Guides Academic

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Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218)

Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218) Lowest new price: $69.99
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Author: John Lee
Brand: Brand: Springer

This book is an introductory graduate-level 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 first-order 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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Geometry Part 1 (Quickstudy Reference Guides - Academic)

Geometry Part 1 (Quickstudy Reference Guides - Academic) Lowest new price: $4.95
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Author: Inc. BarCharts
Brand: QuickStudy

Coverage of the fundamental structure of geometry.

Part 1 of two guides on geometry.

 

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  • Used Book in Good Condition

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Riemannian Geometry

Riemannian Geometry Lowest new price: $37.40
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Author: Manfredo Perdigao do Carmo
Brand: Manfredo P Do Carmo

Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year 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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  • Riemannian Geometry

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Differential Geometry (Dover Books on Mathematics)

Differential Geometry (Dover Books on Mathematics) Lowest new price: $10.86
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Author: Erwin Kreyszig
Brand: Erwin Kreyszig

This outstanding textbook by a distinguished mathematical scholar introduces the differential geometry of curves and surfaces in three-dimensional Euclidean space. The subject is presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the geometric significance and theoretical and practical importance of the different concepts, methods and results involved.
The first chapters of the book focus on the basic concepts and facts of analytic geometry, the theory of space curves, and the foundations of the theory of surfaces, including problems closely related to the first and second fundamental forms. The treatment of the theory of surfaces makes full use of the tensor calculus.
The later chapters address geodesics, mappings of surfaces, special surfaces, and the absolute differential calculus and the displacement of Levi-Cività. Problems at the end of each section (with solutions at the end of the book) will help students  meaningfully review the material presented, and familiarize themselves with the manner of reasoning in differential geometry.

Features:

  • Differential Geometry

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Benjamin Harrison: The American Presidents Series: The 23rd President, 1889-1893

Benjamin Harrison: The American Presidents Series: The 23rd President, 1889-1893 Lowest new price: $21.96
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Author: Charles W. Calhoun
Brand: Calhoun, Charles W./ Schesliner, Arthur M., Jr. (EDT)

The scion of a political dynasty ushers in the era of big government

Politics was in Benjamin Harrison's blood. His great-grandfather signed the Declaration and his grandfather, William Henry Harrison, was the ninth president of the United States. Harrison, a leading Indiana lawyer, became a Republican Party champion, even taking a leave from the Civil War to campaign for Lincoln. After a scandal-free term in the Senate-no small feat in the Gilded Age-the Republicans chose Harrison as their presidential candidate in 1888. Despite losing the popular vote, he trounced the incumbent, Grover Cleveland, in the electoral college.

In contrast to standard histories, which dismiss Harrison's presidency as corrupt and inactive, Charles W. Calhoun sweeps away the stereotypes of the age to reveal the accomplishments of our twenty-third president. With Congress under Republican control, he exemplified the activist president, working feverishly to put the Party's planks into law and approving the first billion-dollar peacetime budget. But the Democrats won Congress in 1890, stalling his legislative agenda, and with the First Lady ill, his race for reelection proceeded quietly. (She died just before the election.) In the end, Harrison could not beat Cleveland in their unprecedented rematch.

With dazzling attention to this president's life and the social tapestry of his times, Calhoun compellingly reconsiders Harrison's legacy.

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Introduction to Differential Geometry of Space Curves and Surfaces: Differential Geometry of Curves and Surfaces

Introduction to Differential Geometry of Space Curves and Surfaces: Differential Geometry of Curves and Surfaces Lowest new price: $14.53
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Author: Taha Sochi

This book is about differential geometry of space curves and surfaces. The formulation and presentation are largely based on a tensor calculus approach. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. The book is furnished with an index, extensive sets of exercises and many cross references, which are hyperlinked for the ebook users, to facilitate linking related concepts and sections. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references.

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