Introduction To Differential Geometry

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Introduction to Differential Geometry

Joel W. Robbin,Dietmar A. Salamon
Introduction to Differential Geometry Book PDF

Author : Joel W. Robbin,Dietmar A. Salamon
Publisher : Springer Nature
Page : 426 pages
File Size : 51,9 Mb
Release : 2022-01-12
Category : Mathematics
ISBN : 9783662643402

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Introduction to Differential Geometry by Joel W. Robbin,Dietmar A. Salamon Pdf

This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.

An Introduction to Differential Geometry

T. J. Willmore
An Introduction to Differential Geometry Book PDF

Author : T. J. Willmore
Publisher : Courier Corporation
Page : 336 pages
File Size : 55,6 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486282107

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An Introduction to Differential Geometry by T. J. Willmore Pdf

This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.

Introduction to Smooth Manifolds

John M. Lee
Introduction to Smooth Manifolds Book PDF

Author : John M. Lee
Publisher : Springer Science & Business Media
Page : 646 pages
File Size : 45,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9780387217529

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Introduction to Smooth Manifolds by John M. Lee Pdf

Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why

Elementary Differential Geometry

A.N. Pressley
Elementary Differential Geometry Book PDF

Author : A.N. Pressley
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 51,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781447136965

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Elementary Differential Geometry by A.N. Pressley Pdf

Pressley assumes the reader knows the main results of multivariate calculus and concentrates on the theory of the study of surfaces. Used for courses on surface geometry, it includes intersting and in-depth examples and goes into the subject in great detail and vigour. The book will cover three-dimensional Euclidean space only, and takes the whole book to cover the material and treat it as a subject in its own right.

First Steps in Differential Geometry

Andrew McInerney
First Steps in Differential Geometry Book PDF

Author : Andrew McInerney
Publisher : Springer Science & Business Media
Page : 420 pages
File Size : 50,7 Mb
Release : 2013-07-09
Category : Mathematics
ISBN : 9781461477327

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First Steps in Differential Geometry by Andrew McInerney Pdf

Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.

Introduction to Differential Geometry of Space Curves and Surfaces

Taha Sochi
Introduction to Differential Geometry of Space Curves and Surfaces Book PDF

Author : Taha Sochi
Publisher : Taha Sochi
Page : 252 pages
File Size : 40,8 Mb
Release : 2022-09-14
Category : Mathematics
ISBN : 8210379456XXX

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Introduction to Differential Geometry of Space Curves and Surfaces by Taha Sochi Pdf

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.

Introduction to Differential Geometry for Engineers

Brian F. Doolin,Clyde F. Martin
Introduction to Differential Geometry for Engineers Book PDF

Author : Brian F. Doolin,Clyde F. Martin
Publisher : Courier Corporation
Page : 178 pages
File Size : 51,9 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486281940

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Introduction to Differential Geometry for Engineers by Brian F. Doolin,Clyde F. Martin Pdf

This outstanding guide supplies important mathematical tools for diverse engineering applications, offering engineers the basic concepts and terminology of modern global differential geometry. Suitable for independent study as well as a supplementary text for advanced undergraduate and graduate courses, this volume also constitutes a valuable reference for control, systems, aeronautical, electrical, and mechanical engineers.The treatment's ideas are applied mainly as an introduction to the Lie theory of differential equations and to examine the role of Grassmannians in control systems analysis. Additional topics include the fundamental notions of manifolds, tangent spaces, vector fields, exterior algebra, and Lie algebras. An appendix reviews concepts related to vector calculus, including open and closed sets, compactness, continuity, and derivative.

An Introduction to Differential Geometry with Applications to Elasticity

Philippe G. Ciarlet
An Introduction to Differential Geometry with Applications to Elasticity Book PDF

Author : Philippe G. Ciarlet
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 41,7 Mb
Release : 2006-06-28
Category : Technology & Engineering
ISBN : 9781402042485

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An Introduction to Differential Geometry with Applications to Elasticity by Philippe G. Ciarlet Pdf

curvilinear coordinates. This treatment includes in particular a direct proof of the three-dimensional Korn inequality in curvilinear coordinates. The fourth and last chapter, which heavily relies on Chapter 2, begins by a detailed description of the nonlinear and linear equations proposed by W.T. Koiter for modeling thin elastic shells. These equations are “two-dimensional”, in the sense that they are expressed in terms of two curvilinear coordinates used for de?ning the middle surface of the shell. The existence, uniqueness, and regularity of solutions to the linear Koiter equations is then established, thanks this time to a fundamental “Korn inequality on a surface” and to an “in?nit- imal rigid displacement lemma on a surface”. This chapter also includes a brief introduction to other two-dimensional shell equations. Interestingly, notions that pertain to di?erential geometry per se,suchas covariant derivatives of tensor ?elds, are also introduced in Chapters 3 and 4, where they appear most naturally in the derivation of the basic boundary value problems of three-dimensional elasticity and shell theory. Occasionally, portions of the material covered here are adapted from - cerpts from my book “Mathematical Elasticity, Volume III: Theory of Shells”, published in 2000by North-Holland, Amsterdam; in this respect, I am indebted to Arjen Sevenster for his kind permission to rely on such excerpts. Oth- wise, the bulk of this work was substantially supported by two grants from the Research Grants Council of Hong Kong Special Administrative Region, China [Project No. 9040869, CityU 100803 and Project No. 9040966, CityU 100604].

Introduction to Differential Geometry

Luther Pfahler Eisenhart
Introduction to Differential Geometry Book PDF

Author : Luther Pfahler Eisenhart
Publisher : Princeton University Press
Page : 315 pages
File Size : 41,9 Mb
Release : 2015-12-08
Category : Mathematics
ISBN : 9781400877867

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Introduction to Differential Geometry by Luther Pfahler Eisenhart Pdf

Book 3 in the Princeton Mathematical Series. Originally published in 1950. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Fundamentals of Differential Geometry

Serge Lang
Fundamentals of Differential Geometry Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 553 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461205418

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Fundamentals of Differential Geometry by Serge Lang Pdf

This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER

Differential Geometry

Loring W. Tu
Differential Geometry Book PDF

Author : Loring W. Tu
Publisher : Springer
Page : 347 pages
File Size : 44,9 Mb
Release : 2017-06-01
Category : Mathematics
ISBN : 9783319550848

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Differential Geometry by Loring W. Tu Pdf

This text presents a graduate-level 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 self-contained, 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 far-fetched to argue that differential geometry should be in every mathematician's arsenal.

Differential Geometry

Wolfgang Kühnel
Differential Geometry Book PDF

Author : Wolfgang Kühnel
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 55,9 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821839881

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Differential Geometry by Wolfgang Kühnel Pdf

Our first knowledge of differential geometry usually comes from the study of the curves and surfaces in I\!\!R^3 that arise in calculus. Here we learn about line and surface integrals, divergence and curl, and the various forms of Stokes' Theorem. If we are fortunate, we may encounter curvature and such things as the Serret-Frenet formulas. With just the basic tools from multivariable calculus, plus a little knowledge of linear algebra, it is possible to begin a much richer and rewarding study of differential geometry, which is what is presented in this book. It starts with an introduction to the classical differential geometry of curves and surfaces in Euclidean space, then leads to an introduction to the Riemannian geometry of more general manifolds, including a look at Einstein spaces. An important bridge from the low-dimensional theory to the general case is provided by a chapter on the intrinsic geometry of surfaces. The first half of the book, covering the geometry of curves and surfaces, would be suitable for a one-semester undergraduate course. The local and global theories of curves and surfaces are presented, including detailed discussions of surfaces of rotation, ruled surfaces, and minimal surfaces. The second half of the book, which could be used for a more advanced course, begins with an introduction to differentiable manifolds, Riemannian structures, and the curvature tensor. Two special topics are treated in detail: spaces of constant curvature and Einstein spaces. The main goal of the book is to get started in a fairly elementary way, then to guide the reader toward more sophisticated concepts and more advanced topics. There are many examples and exercises to help along the way. Numerous figures help the reader visualize key concepts and examples, especially in lower dimensions. For the second edition, a number of errors were corrected and some text and a number of figures have been added.

Introduction to Numerical Linear Algebra and Optimisation

Philippe G. Ciarlet,Bernadette Miara,Jean-Marie Thomas
Introduction to Numerical Linear Algebra and Optimisation Book PDF

Author : Philippe G. Ciarlet,Bernadette Miara,Jean-Marie Thomas
Publisher : Cambridge University Press
Page : 456 pages
File Size : 40,5 Mb
Release : 1989-08-25
Category : Computers
ISBN : 0521339847

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Introduction to Numerical Linear Algebra and Optimisation by Philippe G. Ciarlet,Bernadette Miara,Jean-Marie Thomas Pdf

The purpose of this book is to give a thorough introduction to the most commonly used methods of numerical linear algebra and optimisation. The prerequisites are some familiarity with the basic properties of matrices, finite-dimensional vector spaces, advanced calculus, and some elementary notations from functional analysis. The book is in two parts. The first deals with numerical linear algebra (review of matrix theory, direct and iterative methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimisation (general algorithms, linear and nonlinear programming). The author has based the book on courses taught for advanced undergraduate and beginning graduate students and the result is a well-organised and lucid exposition. Summaries of basic mathematics are provided, proofs of theorems are complete yet kept as simple as possible, and applications from physics and mechanics are discussed. Professor Ciarlet has also helpfully provided over 40 line diagrams, a great many applications, and a useful guide to further reading. This excellent textbook, which is translated and revised from the very successful French edition, will be of great value to students of numerical analysis, applied mathematics and engineering.

An Introduction to Manifolds

Loring W. Tu
An Introduction to Manifolds Book PDF

Author : Loring W. Tu
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 55,9 Mb
Release : 2010-10-05
Category : Mathematics
ISBN : 9781441974006

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An Introduction to Manifolds by Loring W. Tu Pdf

Manifolds, the higher-dimensional 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 point-set 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 one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Applied Differential Geometry

William L. Burke
Applied Differential Geometry Book PDF

Author : William L. Burke
Publisher : Cambridge University Press
Page : 440 pages
File Size : 45,6 Mb
Release : 1985-05-31
Category : Mathematics
ISBN : 0521269296

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Applied Differential Geometry by William L. Burke Pdf

This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.