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.
Автор: Needham Tristan Название: Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts ISBN: 0691203709 ISBN-13(EAN): 9780691203706 Издательство: Wiley Рейтинг: Цена: 44350.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: An inviting, intuitive, and visual exploration of differential geometry and formsVisual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton's geometrical methods to provide geometrical explanations of the classical results.
In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss's famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein's field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell's equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan's method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms.
Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.
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: Eisenhart Luther Pfahler Название: Introduction to Differential Geometry ISBN: 0691627460 ISBN-13(EAN): 9780691627465 Издательство: Wiley Рейтинг: Цена: 54910.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Book 3 in the Princeton Mathematical Series.
Originally published in 1950. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
This book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis. Once the background material is established, the applications mainly deal with the following meaningful settings:
ODE theory;
Maximum Principles (weak, strong and propagation principles);
Lie groups (with an emphasis on the construction of Lie groups).
This book also provides an introduction to the basic theory of Geometrical Analysis, with a new foundational presentation based on Ordinary Differential Equation techniques, in a unitary and self-contained way.
The book also contains:
58 figures;
182 exercises;
3 Appendices;
a Further Reading section.
Автор: Andrei Agrachev, Davide Barilari, Ugo Boscain Название: A Comprehensive Introduction to Sub-Riemannian Geometry ISBN: 110847635X ISBN-13(EAN): 9781108476355 Издательство: Cambridge Academ Рейтинг: Цена: 185850.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This comprehensive introduction to sub-Riemannian geometry proceeds from classical topics to cutting-edge theory and applications. The only prerequisites are calculus, linear algebra and differential equations. It can be used for graduate courses in Riemannian or sub-Riemannian geometry, or as a reference for researchers in several disciplines.
Автор: Eisenhart Luther Pfahler Название: Introduction to Differential Geometry ISBN: 0691653453 ISBN-13(EAN): 9780691653457 Издательство: Wiley Рейтинг: Цена: 156050.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Book 3 in the Princeton Mathematical Series. Originally published in 1950. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting
Автор: Janina Kotus, Mariusz Urbanski Название: Meromorphic Dynamics: Volume 2: Elliptic Functions with an Introduction to the Dynamics of Meromorphic Functions ISBN: 1009215973 ISBN-13(EAN): 9781009215978 Издательство: Cambridge Academ Рейтинг: Цена: 137280.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This text, the second of two volumes, builds on the foundational material on ergodic theory and geometric measure theory provided in Volume I, and applies all the techniques discussed to describe the beautiful and rich dynamics of elliptic functions. The text begins with an introduction to topological dynamics of transcendental meromorphic functions, before progressing to elliptic functions, discussing at length their classical properties, measurable dynamics and fractal geometry. The authors then look in depth at compactly non-recurrent elliptic functions. Much of this material is appearing for the first time in book or paper form. Both senior and junior researchers working in ergodic theory and dynamical systems will appreciate what is sure to be an indispensable reference.
Автор: Shen Yi-Bing Et Al Название: Introduction To Modern Finsler Geometry ISBN: 9814704903 ISBN-13(EAN): 9789814704908 Издательство: World Scientific Publishing Рейтинг: Цена: 69690.00 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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