Автор: Gross Название: Manifolds, Vector Fields, and Differential Forms ISBN: 3031254082 ISBN-13(EAN): 9783031254086 Издательство: Springer Рейтинг: Цена: 6854.00 р. 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: Tu, Loring W. Название: Introduction to manifolds ISBN: 1441973990 ISBN-13(EAN): 9781441973993 Издательство: Springer Рейтинг: Цена: 6986.00 р. 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 Название: Introduction to smooth manifolds ISBN: 1489994750 ISBN-13(EAN): 9781489994752 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Поставка под заказ.
Автор: Lee John M. Название: Introduction to Riemannian Manifolds ISBN: 3030801063 ISBN-13(EAN): 9783030801069 Издательство: Springer Цена: 6986.00 р. 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: Stern Название: Introduction to Geometry and Topology ISBN: 3034809824 ISBN-13(EAN): 9783034809825 Издательство: Springer Рейтинг: Цена: 6288.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book provides an introduction to topology, differential topology, and differential geometry. It is based on manuscripts refined through use in a variety of lecture courses. The first chapter covers elementary results and concepts from point-set topology. An exception is the Jordan Curve Theorem, which is proved for polygonal paths and is intended to give students a first glimpse into the nature of deeper topological problems. The second chapter of the book introduces manifolds and Lie groups, and examines a wide assortment of examples. Further discussion explores tangent bundles, vector bundles, differentials, vector fields, and Lie brackets of vector fields. This discussion is deepened and expanded in the third chapter, which introduces the de Rham cohomology and the oriented integral and gives proofs of the Brouwer Fixed-Point Theorem, the Jordan-Brouwer Separation Theorem, and Stokes's integral formula. The fourth and final chapter is devoted to the fundamentals of differential geometry and traces the development of ideas from curves to submanifolds of Euclidean spaces. Along the way, the book discusses connections and curvature--the central concepts of differential geometry. The discussion culminates with the Gau? equations and the version of Gau?'s theorema egregium for submanifolds of arbitrary dimension and codimension. This book is primarily aimed at advanced undergraduates in mathematics and physics and is intended as the template for a one- or two-semester bachelor's course.
Автор: Nicolas Boumal Название: An Introduction to Optimization on Smooth Manifolds ISBN: 1009166158 ISBN-13(EAN): 9781009166157 Издательство: Cambridge Academ Рейтинг: Цена: 6653.00 р. 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: 1009166174 ISBN-13(EAN): 9781009166171 Издательство: Cambridge Academ Рейтинг: Цена: 15840.00 р. 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: Majumdar, Manjusha Bhattacharyya, Arindam Название: Introduction to smooth manifolds ISBN: 9819905672 ISBN-13(EAN): 9789819905676 Издательство: Springer Рейтинг: Цена: 7685.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Rajnikant Sinha Название: Smooth Manifolds ISBN: 813222955X ISBN-13(EAN): 9788132229551 Издательство: Springer Рейтинг: Цена: 8384.00 р. 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: Majumdar Название: An Introduction to Smooth Manifolds ISBN: 9819905648 ISBN-13(EAN): 9789819905645 Издательство: Springer Рейтинг: Цена: 7685.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Targeted to graduate students of mathematics, this book discusses major topics like the Lie group in the study of smooth manifolds. It is said that mathematics can be learned by solving problems and not only by just reading it. To serve this purpose, this book contains a sufficient number of examples and exercises after each section in every chapter. Some of the exercises are routine ones for the general understanding of topics. The book also contains hints to difficult exercises. Answers to all exercises are given at the end of each section. It also provides proofs of all theorems in a lucid manner. The only pre-requisites are good working knowledge of point-set topology and linear algebra.
Автор: Sinha Rajinikant Название: Smooth Manifolds ISBN: 8132221036 ISBN-13(EAN): 9788132221036 Издательство: Springer Рейтинг: Цена: 8384.00 р. 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.
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