Geometry from a Differentiable Viewpoint PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Geometry from a Differentiable Viewpoint PDF full book. Access full book title Geometry from a Differentiable Viewpoint by John McCleary. Download full books in PDF and EPUB format.
Author: John McCleary
Publisher: Cambridge University Press
ISBN: 0521116074
Category : Mathematics
Languages : en
Pages : 375
Get Book Here
Book Description
A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.
Author: John McCleary
Publisher: Cambridge University Press
ISBN: 9780521424806
Category : Mathematics
Languages : en
Pages : 338
Get Book Here
Book Description
This book offers a new treatment of differential geometry which is designed to make the subject approachable for advanced undergraduates.
Author: John McCleary
Publisher: Cambridge University Press
ISBN: 0521116074
Category : Mathematics
Languages : en
Pages : 375
Get Book Here
Book Description
A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.
Author: John Willard Milnor
Publisher: Princeton University Press
ISBN: 9780691048338
Category : Mathematics
Languages : en
Pages : 80
Get Book Here
Book Description
This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.
Author: Morris W. Hirsch
Publisher: Springer Science & Business Media
ISBN: 146849449X
Category : Mathematics
Languages : en
Pages : 230
Get Book Here
Book Description
"A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology....There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text." —MATHEMATICAL REVIEWS
Author: Torsten Wedhorn
Publisher: Springer
ISBN: 3658106336
Category : Mathematics
Languages : en
Pages : 366
Get Book Here
Book Description
This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.
Author: Victor Guillemin
Publisher: American Mathematical Soc.
ISBN: 0821851934
Category : Mathematics
Languages : en
Pages : 242
Get Book Here
Book Description
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: William L. Burke
Publisher: Cambridge University Press
ISBN: 9780521269292
Category : Mathematics
Languages : en
Pages : 440
Get Book Here
Book Description
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.
Author: Christian Bär
Publisher: Cambridge University Press
ISBN: 0521896711
Category : Mathematics
Languages : en
Pages : 335
Get Book Here
Book Description
This easy-to-read introduction takes the reader from elementary problems through to current research. Ideal for courses and self-study.
Author: Joel W. Robbin
Publisher: Springer Nature
ISBN: 3662643405
Category : Mathematics
Languages : en
Pages : 426
Get Book Here
Book Description
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: Shigeyuki Morita
Publisher: American Mathematical Soc.
ISBN: 9780821810453
Category : Mathematics
Languages : en
Pages : 356
Get Book Here
Book Description
Since the times of Gauss, Riemann, and Poincare, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms. The book by Morita is a comprehensive introduction to differential forms. It begins with a quick introduction to the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results concerning them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated is a detailed description of the Chern-Weil theory. The book can serve as a textbook for undergraduate students and for graduate students in geometry.
