Basic Elements Of Differential Geometry And Topology

Author : S.P. Novikov
Publisher : Springer Science & Business Media
ISBN 13 : 9401578958
Total Pages : 500 pages
Book Rating : 4.50/5 ( download)

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Download or read book Basic Elements of Differential Geometry and Topology written by S.P. Novikov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et moi ..., si j'avait su comment en revenir, je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Matht"natics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics seNe as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series

Author : S.P. Novikov
Publisher : Springer
ISBN 13 : 9789401578967
Total Pages : 490 pages
Book Rating : 4.66/5 ( download)

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Download or read book Basic Elements of Differential Geometry and Topology written by S.P. Novikov and published by Springer. This book was released on 2013-01-09 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Anant R. Shastri
Publisher : CRC Press
ISBN 13 : 1439831637
Total Pages : 319 pages
Book Rating : 4.32/5 ( download)

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Download or read book Elements of Differential Topology written by Anant R. Shastri and published by CRC Press. This book was released on 2011-03-04 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived from the author's course on the subject, Elements of Differential Topology explores the vast and elegant theories in topology developed by Morse, Thom, Smale, Whitney, Milnor, and others. It begins with differential and integral calculus, leads you through the intricacies of manifold theory, and concludes with discussions on algebraic topol

Author : Richard S. Millman
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 288 pages
Book Rating : 4.81/5 ( download)

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Download or read book Elements of Differential Geometry written by Richard S. Millman and published by Prentice Hall. This book was released on 1977 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is intended for an advanced undergraduate (having taken linear algebra and multivariable calculus). It provides the necessary background for a more abstract course in differential geometry. The inclusion of diagrams is done without sacrificing the rigor of the material. For all readers interested in differential geometry.

Author : Barrett O'Neill
Publisher : Academic Press
ISBN 13 : 148326811X
Total Pages : 422 pages
Book Rating : 4.18/5 ( download)

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Download or read book Elementary Differential Geometry written by Barrett O'Neill and published by Academic Press. This book was released on 2014-05-12 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.

Author : Loring W. Tu
Publisher : Springer
ISBN 13 : 3319550845
Total Pages : 347 pages
Book Rating : 4.48/5 ( download)

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Download or read book Differential Geometry written by Loring W. Tu and published by Springer. This book was released on 2017-06-01 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Wang Rong
Publisher : World Scientific
ISBN 13 : 9814495808
Total Pages : 222 pages
Book Rating : 4.06/5 ( download)

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Download or read book An Introduction To Differential Geometry And Topology In Mathematical Physics written by Wang Rong and published by World Scientific. This book was released on 1999-01-18 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an outline of the developments of differential geometry and topology in the twentieth century, especially those which will be closely related to new discoveries in theoretical physics.

Author : Joel W. Robbin
Publisher : Springer Nature
ISBN 13 : 3662643405
Total Pages : 426 pages
Book Rating : 4.02/5 ( download)

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Download or read book Introduction to Differential Geometry written by Joel W. Robbin and published by Springer Nature. This book was released on 2022-01-12 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Victor Guillemin
Publisher : American Mathematical Soc.
ISBN 13 : 0821851934
Total Pages : 242 pages
Book Rating : 4.37/5 ( download)

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Download or read book Differential Topology written by Victor Guillemin and published by American Mathematical Soc.. This book was released on 2010 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Erwin Kreyszig
Publisher : Courier Corporation
ISBN 13 : 0486318621
Total Pages : 384 pages
Book Rating : 4.22/5 ( download)

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Download or read book Differential Geometry written by Erwin Kreyszig and published by Courier Corporation. This book was released on 2013-04-26 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.