Автор: Gross Название: Manifolds, Vector Fields, and Differential Forms ISBN: 3031254082 ISBN-13(EAN): 9783031254086 Издательство: Springer Рейтинг: Цена: 45690.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This textbook serves as an introduction to modern differential geometry at a level accessible to advanced undergraduate and master's students. It places special emphasis on motivation and understanding, while developing a solid intuition for the more abstract concepts. In contrast to graduate level references, the text relies on a minimal set of prerequisites: a solid grounding in linear algebra and multivariable calculus, and ideally a course on ordinary differential equations. Manifolds are introduced intrinsically in terms of coordinate patches glued by transition functions. The theory is presented as a natural continuation of multivariable calculus; the role of point-set topology is kept to a minimum. Questions sprinkled throughout the text engage students in active learning, and encourage classroom participation. Answers to these questions are provided at the end of the book, thus making it ideal for independent study. Material is further reinforced with homework problems ranging from straightforward to challenging. The book contains more material than can be covered in a single semester, and detailed suggestions for instructors are provided in the Preface.
Автор: Lee, John M. Название: Introduction to riemannian manifolds ISBN: 3319917544 ISBN-13(EAN): 9783319917542 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet`s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
Автор: Tu, Loring W. Название: Introduction to manifolds ISBN: 1441973990 ISBN-13(EAN): 9781441973993 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 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.
Автор: Lee John M. Название: Introduction to Riemannian Manifolds ISBN: 3030801063 ISBN-13(EAN): 9783030801069 Издательство: Springer Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Thisbookisdesignedasatextbookforaone-quarterorone-semestergr- uate course on Riemannian geometry, for students who are familiar with topological and di?erentiable manifolds. It focuses on developing an in- mate acquaintance with the geometric meaning of curvature. In so doing, it introduces and demonstrates the uses of all the main technical tools needed for a careful study of Riemannian manifolds. I have selected a set of topics that can reasonably be covered in ten to ?fteen weeks, instead of making any attempt to provide an encyclopedic treatment of the subject. The book begins with a careful treatment of the machineryofmetrics, connections, andgeodesics, withoutwhichonecannot claim to be doing Riemannian geometry. It then introduces the Riemann curvature tensor, and quickly moves on to submanifold theory in order to give the curvature tensor a concrete quantitative interpretation. From then on, all e?orts are bent toward proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet theorem (expressing thetotalcurvatureofasurfaceintermsofitstopologicaltype), theCartan- Hadamard theorem (restricting the topology of manifolds of nonpositive curvature), Bonnet's theorem (giving analogous restrictions on manifolds of strictly positive curvature), and a special case of the Cartan-Ambrose- Hicks theorem (characterizing manifolds of constant curvature). Many other results and techniques might reasonably claim a place in an introductory Riemannian geometry course, but could not be included due to time constraints.
Автор: Nicolas Boumal Название: An Introduction to Optimization on Smooth Manifolds ISBN: 1009166174 ISBN-13(EAN): 9781009166171 Издательство: Cambridge Academ Рейтинг: Цена: 105600.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Optimization on Riemannian manifolds-the result of smooth geometry and optimization merging into one elegant modern framework-spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing. This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade for conducting research and for numerical implementations sprinkled throughout the book.
Автор: Nicolas Boumal Название: An Introduction to Optimization on Smooth Manifolds ISBN: 1009166158 ISBN-13(EAN): 9781009166157 Издательство: Cambridge Academ Рейтинг: Цена: 44350.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Optimization on Riemannian manifolds-the result of smooth geometry and optimization merging into one elegant modern framework-spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing. This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade for conducting research and for numerical implementations sprinkled throughout the book.
Автор: Sinha Rajinikant Название: Smooth Manifolds ISBN: 8132221036 ISBN-13(EAN): 9788132221036 Издательство: Springer Рейтинг: Цена: 55890.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book offers an introduction to the theory of smooth manifolds, helping students to familiarize themselves with the tools they will need for mathematical research on smooth manifolds and differential geometry.
Автор: Claudio Gorodski Название: Smooth Manifolds ISBN: 3030497747 ISBN-13(EAN): 9783030497743 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Невозможна поставка. Описание: This concise and practical textbook presents the essence of the theory on smooth manifolds. A key concept in mathematics, smooth manifolds are ubiquitous: They appear as Riemannian manifolds in differential geometry;
Автор: Lafontaine, Jacques Название: Introduction to differential manifolds ISBN: 3319207342 ISBN-13(EAN): 9783319207346 Издательство: Springer Рейтинг: Цена: 55890.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces.Its ambition is to give solid foundations.
Автор: Rajnikant Sinha Название: Smooth Manifolds ISBN: 813222955X ISBN-13(EAN): 9788132229551 Издательство: Springer Рейтинг: Цена: 55890.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book offers an introduction to the theory of smooth manifolds, helping students to familiarize themselves with the tools they will need for mathematical research on smooth manifolds and differential geometry.
Автор: Shen Yi-Bing Et Al Название: Introduction To Modern Finsler Geometry ISBN: 9814713163 ISBN-13(EAN): 9789814713160 Издательство: World Scientific Publishing Цена: 42240.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds.
In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.
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