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Differential Geometry And Its Applications
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Book Synopsis Differential Geometry and Its Applications by : John Oprea
Download or read book Differential Geometry and Its Applications written by John Oprea and published by MAA. This book was released on 2007-09-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the differential geometry of surfaces and its relevance to engineering and the sciences.
Book Synopsis Geometry and Complexity Theory by : J. M. Landsberg
Download or read book Geometry and Complexity Theory written by J. M. Landsberg and published by Cambridge University Press. This book was released on 2017-09-28 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical importance. Algebraic geometry and representation theory provide fertile ground for advancing work on these problems and others in complexity. This introduction to algebraic complexity theory for graduate students and researchers in computer science and mathematics features concrete examples that demonstrate the application of geometric techniques to real world problems. Written by a noted expert in the field, it offers numerous open questions to motivate future research. Complexity theory has rejuvenated classical geometric questions and brought different areas of mathematics together in new ways. This book will show the beautiful, interesting, and important questions that have arisen as a result.
Book Synopsis An Introduction to Noncommutative Differential Geometry and Its Physical Applications by : J. Madore
Download or read book An Introduction to Noncommutative Differential Geometry and Its Physical Applications written by J. Madore and published by Cambridge University Press. This book was released on 1999-06-24 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thoroughly revised introduction to non-commutative geometry.
Book Synopsis Information Geometry and Its Applications by : Shun-ichi Amari
Download or read book Information Geometry and Its Applications written by Shun-ichi Amari and published by Springer. This book was released on 2016-02-02 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.
Book Synopsis Basic Elements of Differential Geometry and Topology by : S.P. Novikov
Download or read book Basic Elements of Differential Geometry and Topology written by S.P. Novikov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et moi ..., si j'avait su comment en revenir, je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Matht"natics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics seNe as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series
Book Synopsis Differential Geometry, Calculus of Variations, and Their Applications by : George M. Rassias
Download or read book Differential Geometry, Calculus of Variations, and Their Applications written by George M. Rassias and published by CRC Press. This book was released on 1985-10-01 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a series of papers on some of the longstanding research problems of geometry, calculus of variations, and their applications. It is suitable for advanced graduate students, teachers, research mathematicians, and other professionals in mathematics.
Book Synopsis Differential Geometry with Applications to Mechanics and Physics by : Yves Talpaert
Download or read book Differential Geometry with Applications to Mechanics and Physics written by Yves Talpaert and published by CRC Press. This book was released on 2000-09-12 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.
Book Synopsis Differential Geometry of Varieties with Degenerate Gauss Maps by : Maks A. Akivis
Download or read book Differential Geometry of Varieties with Degenerate Gauss Maps written by Maks A. Akivis and published by Springer Science & Business Media. This book was released on 2004 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.
Book Synopsis Differential Geometry of Curves and Surfaces by : Kristopher Tapp
Download or read book Differential Geometry of Curves and Surfaces written by Kristopher Tapp and published by Springer. This book was released on 2016-09-30 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it.
Book Synopsis New Horizons In Differential Geometry And Its Related Fields by : Toshiaki Adachi
Download or read book New Horizons In Differential Geometry And Its Related Fields written by Toshiaki Adachi and published by World Scientific. This book was released on 2022-04-07 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents recent developments in geometric structures on Riemannian manifolds and their discretizations. With chapters written by recognized experts, these discussions focus on contact structures, Kähler structures, fiber bundle structures and Einstein metrics. It also contains works on the geometric approach on coding theory.For researchers and students, this volume forms an invaluable source to learn about these subjects that are not only in the field of differential geometry but also in other wide related areas. It promotes and deepens the study of geometric structures.
Book Synopsis Differential Geometry and Statistics by : M.K. Murray
Download or read book Differential Geometry and Statistics written by M.K. Murray and published by CRC Press. This book was released on 1993-04-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions, there has been interest among statisticians in the application of differential geometry to statistics. This interest has increased rapidly in the last couple of decades with the work of a large number of researchers. Until now an impediment to the spread of these ideas into the wider community of statisticians has been the lack of a suitable text introducing the modern coordinate free approach to differential geometry in a manner accessible to statisticians. Differential Geometry and Statistics aims to fill this gap. The authors bring to this book extensive research experience in differential geometry and its application to statistics. The book commences with the study of the simplest differentiable manifolds - affine spaces and their relevance to exponential families, and goes on to the general theory, the Fisher information metric, the Amari connections and asymptotics. It culminates in the theory of vector bundles, principal bundles and jets and their applications to the theory of strings - a topic presently at the cutting edge of research in statistics and differential geometry.
Book Synopsis Introduction to Differential Geometry with Applications to Navier-Stokes Dynamics by : Troy L Story
Download or read book Introduction to Differential Geometry with Applications to Navier-Stokes Dynamics written by Troy L Story and published by iUniverse. This book was released on 2005 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Differential Geometry with applications to Navier-Stokes Dynamics is an invaluable manuscript for anyone who wants to understand and use exterior calculus and differential geometry, the modern approach to calculus and geometry. Author Troy Story makes use of over thirty years of research experience to provide a smooth transition from conventional calculus to exterior calculus and differential geometry, assuming only a knowledge of conventional calculus. Introduction to Differential Geometry with applications to Navier-Stokes Dynamics includes the topics: Geometry, Exterior calculus, Homology and co-homology, Applications of differential geometry and exterior calculus to: Hamiltonian mechanics, geometric optics, irreversible thermodynamics, black hole dynamics, electromagnetism, classical string fields, and Navier-Stokes dynamics.
Book Synopsis Geometric Control Theory by : Velimir Jurdjevic
Download or read book Geometric Control Theory written by Velimir Jurdjevic and published by Cambridge University Press. This book was released on 1997 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric control theory is concerned with the evolution of systems subject to physical laws but having some degree of freedom through which motion is to be controlled. This book describes the mathematical theory inspired by the irreversible nature of time evolving events. The first part of the book deals with the issue of being able to steer the system from any point of departure to any desired destination. The second part deals with optimal control, the question of finding the best possible course. An overlap with mathematical physics is demonstrated by the Maximum principle, a fundamental principle of optimality arising from geometric control, which is applied to time-evolving systems governed by physics as well as to man-made systems governed by controls. Applications are drawn from geometry, mechanics, and control of dynamical systems. The geometric language in which the results are expressed allows clear visual interpretations and makes the book accessible to physicists and engineers as well as to mathematicians.
Book Synopsis Geometry and its Applications in Arts, Nature and Technology by : Georg Glaeser
Download or read book Geometry and its Applications in Arts, Nature and Technology written by Georg Glaeser and published by Springer Nature. This book was released on 2020-12-18 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book returns geometry to its natural habitats: the arts, nature and technology. Throughout the book, geometry comes alive as a tool to unlock the understanding of our world. Assuming only familiarity with high school mathematics, the book invites the reader to discover geometry through examples from biology, astronomy, architecture, design, photography, drawing, engineering and more. Lavishly illustrated with over 1200 figures, all of the geometric results are carefully derived from scratch, with topics from differential, projective and non-Euclidean geometry, as well as kinematics, introduced as the need arises. The mathematical results contained in the book range from very basic facts to recent results, and mathematical proofs are included although not necessary for comprehension. With its wide range of geometric applications, this self-contained volume demonstrates the ubiquity of geometry in our world, and may serve as a source of inspiration for architects, artists, designers, engineers, and natural scientists. This new edition has been completely revised and updated, with new topics and many new illustrations.
Book Synopsis Fundamentals of Differential Geometry by : Serge Lang
Download or read book Fundamentals of Differential Geometry written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER
Book Synopsis Differential Geometry in the Large by : Owen Dearricott
Download or read book Differential Geometry in the Large written by Owen Dearricott and published by Cambridge University Press. This book was released on 2020-10-22 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2019 'Australian-German Workshop on Differential Geometry in the Large' represented an extraordinary cross section of topics across differential geometry, geometric analysis and differential topology. The two-week programme featured talks from prominent keynote speakers from across the globe, treating geometric evolution equations, structures on manifolds, non-negative curvature and Alexandrov geometry, and topics in differential topology. A joy to the expert and novice alike, this proceedings volume touches on topics as diverse as Ricci and mean curvature flow, geometric invariant theory, Alexandrov spaces, almost formality, prescribed Ricci curvature, and Kähler and Sasaki geometry.
Book Synopsis Differential Geometry by : Erwin Kreyszig
Download or read book Differential Geometry written by Erwin Kreyszig and published by Courier Corporation. This book was released on 2013-04-26 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.
