Differential Topology

First Steps

Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 0486150038

Category: Mathematics

Page: 144

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DIVKeeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. 1968 edition. /div

An Introduction to Algebraic Topology

Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 0486152952

Category: Mathematics

Page: 208

View: 3564

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This self-contained treatment begins with three chapters on the basics of point-set topology, after which it proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. 1961 edition.

Differential Manifolds

Author: Antoni A. Kosinski

Publisher: Courier Corporation

ISBN: 048631815X

Category: Mathematics

Page: 288

View: 1338

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Introductory text for advanced undergraduates and graduate students presents systematic study of the topological structure of smooth manifolds, starting with elements of theory and concluding with method of surgery. 1993 edition.

Algebraic Topology

Homology and Cohomology

Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 0486462390

Category: Mathematics

Page: 272

View: 896

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Surveys several algebraic invariants, including the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.

Differential Geometry and Topology

With a View to Dynamical Systems

Author: Keith Burns,Marian Gidea

Publisher: CRC Press

ISBN: 9781584882534

Category: Mathematics

Page: 400

View: 5242

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Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field.

Topology and Geometry for Physicists

Author: Charles Nash,Siddhartha Sen

Publisher: Courier Corporation

ISBN: 0486318362

Category: Mathematics

Page: 320

View: 3662

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Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. "Thoroughly recommended" by The Physics Bulletin, this volume's physics applications range from condensed matter physics and statistical mechanics to elementary particle theory. Its main mathematical topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory.

A First Course in Functional Analysis

Author: Martin Davis

Publisher: Courier Corporation

ISBN: 0486315819

Category: Mathematics

Page: 128

View: 5102

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Designed for undergraduate mathematics majors, this self-contained exposition of Gelfand's proof of Wiener's theorem explores set theoretic preliminaries, normed linear spaces and algebras, functions on Banach spaces, homomorphisms on normed linear spaces, and more. 1966 edition.

Differential Geometry

Author: Erwin Kreyszig

Publisher: Courier Corporation

ISBN: 9780486667218

Category: Mathematics

Page: 352

View: 8569

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Text from preface: "This book provides an introduction to the differential geometry of curves and surfaces in three-dimensional Euclidean space"

Introduction to Differentiable Manifolds

Author: Louis Auslander,Robert E. MacKenzie

Publisher: Courier Corporation

ISBN: 048615808X

Category: Mathematics

Page: 224

View: 2490

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This text presents basic concepts in the modern approach to differential geometry. Topics include Euclidean spaces, submanifolds, and abstract manifolds; fundamental concepts of Lie theory; fiber bundles; and multilinear algebra. 1963 edition.

Tensor Analysis on Manifolds

Author: Richard L. Bishop,Samuel I. Goldberg

Publisher: Courier Corporation

ISBN: 0486139239

Category: Mathematics

Page: 288

View: 2193

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DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div

First Steps in Differential Geometry

Riemannian, Contact, Symplectic

Author: Andrew McInerney

Publisher: Springer Science & Business Media

ISBN: 1461477328

Category: Mathematics

Page: 410

View: 5261

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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.

Topology

An Introduction with Application to Topological Groups

Author: George McCarty

Publisher: Courier Corporation

ISBN: 0486450821

Category: Mathematics

Page: 288

View: 347

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This stimulating introduction employs the language of point set topology to define and discuss topological groups. It examines set-theoretic topology and its applications in function spaces as well as homotopy and the fundamental group. Well-chosen exercises and problems serve as reinforcements. 1967 edition. Includes 99 illustrations.

Ordinary Differential Equations

An Elementary Textbook for Students of Mathematics, Engineering, and the Sciences

Author: Morris Tenenbaum,Harry Pollard

Publisher: Courier Corporation

ISBN: 0486649407

Category: Mathematics

Page: 808

View: 8270

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Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

Differential Geometry

Author: Heinrich W. Guggenheimer

Publisher: Courier Corporation

ISBN: 0486157202

Category: Mathematics

Page: 400

View: 7859

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This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.

Real Variables with Basic Metric Space Topology

Author: Robert B. Ash

Publisher: Courier Corporation

ISBN: 0486151492

Category: Mathematics

Page: 224

View: 6894

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Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993 edition.

Principles of Topology

Author: Fred H. Croom

Publisher: Courier Dover Publications

ISBN: 0486801543

Category: Mathematics

Page: 336

View: 9763

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Originally published: Philadelphia: Saunders College Publishing, 1989; slightly corrected.

Technical Calculus with Analytic Geometry

Author: Peter Kuhfittig

Publisher: Cengage Learning

ISBN: 1133945198

Category: Mathematics

Page: 544

View: 6254

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Written for today’s technology student, TECHNICAL CALCULUS WITH ANALYTIC GEOMETRY prepares you for your future courses! With an emphasis on applications, this mathematics text helps you learn calculus skills that are particular to technology. Clear presentation of concepts, detailed examples, marginal annotations, and step-by-step procedures enhance your understanding of difficult concepts. Notations that are frequently encountered in technology are used throughout to help you prepare for further courses in your career. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

A First Course in Geometric Topology and Differential Geometry

Author: Ethan D. Bloch

Publisher: Springer Science & Business Media

ISBN: 9780817638405

Category: Mathematics

Page: 421

View: 2056

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The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level.

Differential Topology

Author: Victor Guillemin,Alan Pollack

Publisher: American Mathematical Soc.

ISBN: 0821851934

Category: Mathematics

Page: 222

View: 6191

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Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea--transversality--the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincaré-Hopf index theorem, and Stokes theorem. The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance. The book is suitable for either an introductory graduate course or an advanced undergraduate course.