Introduction to Differential Geometry with Tensor Applications, De
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: Itskov, Mikhail Название: Tensor algebra and tensor analysis for engineers ISBN: 3319988050 ISBN-13(EAN): 9783319988054 Издательство: Springer Рейтинг: Цена: 9083.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This is the fifth and revised edition of a well-received textbook that aims at bridging the gap between the engineering course of tensor algebra on the one hand and the mathematical course of classical linear algebra on the other hand. In accordance with the contemporary way of scientific publication, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. As such, this new edition also discusses such modern topics of solid mechanics as electro- and magnetoelasticity. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this textbook addresses graduate students as well as scientists working in this field and in particular dealing with multi-physical problems. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.
Автор: Joachim Weickert; Hans Hagen Название: Visualization and Processing of Tensor Fields ISBN: 3642439268 ISBN-13(EAN): 9783642439261 Издательство: Springer Рейтинг: Цена: 23058.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Matrix-valued data sets - so-called second order tensor fields - have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state of the art in the visualization and processing of tensor fields.
Автор: Mikhail Itskov Название: Tensor Algebra and Tensor Analysis for Engineers ISBN: 3642448186 ISBN-13(EAN): 9783642448188 Издательство: Springer Рейтинг: Цена: 9794.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book provides a comprehensive exposition of tensor analysis. It presents modern developments in the theory of isotropic and anisotropic tensor functions and includes numerous exercises with solutions.
Автор: Eisenhart Luther Pfahler Название: Introduction to Differential Geometry ISBN: 0691653453 ISBN-13(EAN): 9780691653457 Издательство: Wiley Рейтинг: Цена: 23408.00 р. 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: 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: 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.
General Basis and Bra-Ket Notation.- Tensor Analysis.- Elementary Differential Geometry.- Differential Forms.- Applications of Tensors and Differential Geometry.- Tensors and Bra-Ket Notation in Quantum Mechanics.- Appendices.
Описание: This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors, differential geometry, and differential forms; and to apply them to the physical and engineering world. Many methods and applications are given in CFD, continuum mechanics, electrodynamics in special relativity, cosmology in the Minkowski four-dimensional spacetime, and relativistic and non-relativistic quantum mechanics. Tensors, differential geometry, differential forms, and Dirac notation are very useful advanced mathematical tools in many fields of modern physics and computational engineering. They are involved in special and general relativity physics, quantum mechanics, cosmology, electrodynamics, computational fluid dynamics (CFD), and continuum mechanics. The target audience of this all-in-one book primarily comprises graduate students in mathematics, physics, engineering, research scientists, and engineers.
Описание: This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics on tensors, Riemannian geometry and geometric approach to partial differential equations. Application of approximate transformation groups to the equations of general relativity in the de Sitter space simplifies the subject significantly.
Описание: This introduction to tensor calculus features over 150 exercises. It uses an informal approach, focuses on concrete objects, and appeals to the reader`s intuition with regard to fundamental concepts, such as the Euclidean space, surface, and length.
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