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Starting from an undergraduate level, this book systematically develops the basics of  • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustra

Differential Geometry and Mathematical Physics

??From Kinetic Models to Hydrodynamics serves as an introduction to the asymptotic methods necessary to obtain hydrodynamic equations from a fundamental description using kinetic theory models and the Boltzmann equation.  The work is a survey of an active research area, which aims to bridge time and length scales from the particle-like description inherent in Boltzmann equation theory to a fully established “continuum” approach typical of macroscopic laws of physics.The author sheds light on a new method—using invariant manifolds—which addresses a functional equation for the nonequilibrium single-particle distribution function.  This method allows one to find exact and thermodynamically consistent expressions for: hydrodynamic modes; transport coefficient expressions for hydrodynamic modes; and transport coefficients of a fluid beyond the traditional hydrodynamic limit.  The invariant manifold method paves the way to establish a needed bridge between Boltzmann equation theory and a par

From Kinetic Models to Hydrodynamics

ENbook.pl

This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds.

Differential Geometry and Lie Groups | Gallier Jean | Twarda

pThis book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields.ppAlthough this second edition has the same basic structure as the first edition, it has been extensively revised and clarified not a single page has been left untouched. The major changes include a new introduction to CW complexes replacing most of the material on simplicial complexes in Chapter 5 expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps and a new section on paracompactness.p

Introduction to Topological Manifolds | Lee John | Twarda | Twarda

pThis is an introduction to geometric algebra in n-dimensional Euclidean space and its application to manifolds and to calculus on manifolds. The treatment is moderately rigorous and is suitable for advanced undergraduates and beginning graduate students in mathematics though it should also be accessible to well-prepared students in physics, engineering, computer science, statistics, etc. Preparation in linear algebra and multivariable analysis as encountered in calculus as well as a modest amount of mathematical maturity should be sufficient.p

An Introduction to Geometric Algebra and Geometric Calculus | Taylor Michael D. | Paperback | Twarda

This new edition of FUNCTIONS OF SEVERAL VARIABLES is an extensive revision. Like the first edition it presents a thorough introduction to differential and integral calculus, including the integration of differential forms on manifolds.

Functions of Several Variables | Fleming Wendell | Twarda | Twarda

This text on contact topology is the first comprehensive introduction to the subject, including recent striking applications in geometric and differential topology Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology where the focus mainly on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums.

An Introduction to Contact Topology | Geiges Hansjrg | Twarda | Twarda

This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point.pThe first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor.p pAn additional chapter goes beyond the scope of a one semester lecture course and deals wit

Introduction to Differential Geometry | Robbin Joel W. | Paperback | Twarda

Introduction.- Chapter 1. Differentiation in R n.- Chapter 2. Linear Operators in Banach Spaces.- Chapter 3. Differentiation in Banach Spaces.- Chapter 4. Vector Fields.- Chapter 5. Vectors Integration, Potential Theory.- Chapter 6. Differential Forms, Stoke's Theorem.- Chapter 7. Applications to the Stoke's Theorem.- Appendix A. Basics of Analysis.- Appendix B. Differentiable Manifolds, Lie Groups.- Appendix C. Tensor Algebra.- Bibliography.- Index.br

Differentiability in Banach Spaces, Differential Forms and Applications | Doria Celso Melchiades | Paperback | Twarda

Rational homotopy is a very powerful tool for differential topology and geometry. This text aims to provide graduates and researchers with the tools necessary for the use of rational homotopy in geometry. Algebraic Models in Geometry has been written for topologists who are drawn to geometrical problems amenable to topological methods and also for geometers who are faced with problems requiring topological approaches and thus need a simple and concrete introduction to rational homotopy. This is essentially a book of applications. Geodesics, curvature, embeddings of manifolds, blow-ups, complex and Khler manifolds, symplectic geometry, torus actions, configurations and arrangements are all covered. The chapters related to these subjects act as an introduction to the topic, a survey, and a guide to the literature. But no matter what the particular subject is, the central theme of the book persists namely, there is a beautiful connection between geometry and rational homotopy which both s

Algebraic Models in Geometry | Felix Yves | Paperback | Twarda

This introductory book offers a unique and unified overview of symplectic geometry, highlighting the differential properties of symplectic manifolds. It consists of six chapters Some Algebra Basics, Symplectic Manifolds, Cotangent Bundles, Symplectic G-spaces, Poisson Manifolds, and A Graded Case, concluding with a discussion of the differential properties of graded symplectic manifolds of dimensions 0, n. It is a useful reference resource for students and researchers interested in geometry, group theory, analysis and differential equations.This book is also inspiring in the emerging field of Geometric Science of Information, in particular the chapter on Symplectic G-spaces, where Jean-Louis Koszul develops Jean-Marie Souriau's tools related to the non-equivariant case of co-adjoint action on Souriau's moment map through Souriau's Cocycle, opening the door to Lie Group Machine Learning with Souriau-Fisher metric.

Introduction to Symplectic Geometry | Koszul Jean | Louis | Twarda | Twarda

Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give an introduction to these topics, and to describe recent progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersection theory and algebraic geometry.

Schubert Varieties and Degeneracy Loci | Fulton William | Paperback | Twarda

pConstructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds. This introduction to the subject can be regarded as a textbook on modern algebraic topology, treating the cohomology of spaces with sheaf as opposed to constant coefficients. The author helps readers progress quickly from the basic theory to current research questions, thoroughly supported along the way by examples and exercises.p

Sheaves in Topology | Dimca Alexandru | Twarda | Twarda

This independent account of modern ideas in differential geometry shows how they can be used to understand and extend classical results in integral geometry. The authors explore the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, although their work can be extended to more general spaces. Each chapter features open problems, making the volume a suitable learning aid for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.

The Geometry of Total Curvature on Complete Open Surfaces | Shiohama Katsuhiro | Twarda | Twarda

This two-volume introduction to differential geometry, part of Wiley's popular iClassics Libraryi, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide. bVolume 1b presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The bsecond volumeb continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.

Foundations of Differential Geometry, Volume 2 | Kobayashi Shoshichi | Paperback | Twarda

This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory with the latter being treated in a more theoretical way than is usual in geometry. The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.

Hodge Theory and Complex Algebraic Geometry I | Voisin Claire | Twarda

Thisbookisdesignedasatextbookforaone-quarterorone-semestergr- uate course on Riemannian geometry, for students who are familiar with topological and dierentiable 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 eorts are bent toward proving the four most fundamental theorems relating curvature an

Introduction to Riemannian Manifolds | Lee John M. | Twarda | Twarda

pPresenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them. p pThe book's four chapters are based on lectures given by leading researchers in the field of geometric analysis and low-dimensional geometrytopology, respectively offering an introduction to the differentiable sphere theorem G. Besson, the geometrization of 3-manifolds M. Boileau, the singularities of 3-dimensional Ricci flows C. Sinestrari, and Kahler-Ricci flow G. Tian. The lectures will be particularly valuable to young researchers interested in differential manifolds.p

Ricci Flow and Geometric Applications | Benedetti Riccardo | Twarda

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pHow can music withstand the death and destruction brought on by war Global conflicts of the 20th century fundamentally transformed not only national boundaries, power relations, and global economies, but also the arts and culture of every nation involved. An important, unacknowledged aspect of these conflicts is that they have unique musical soundtracks. iMusic in World War IIi explores how music and sound took on radically different dimensions in the United States and Europe before, during, and after World War II. Additionally, the collection examines the impact of radio and film as the disseminators of the war's musical soundtrack. Contributors contend that the European and American soundtrack of World War II was largely one of escapism rather than the lofty, solemn, heroic, and celebratory mode of war music in the past. Furthermore, they explore the variety of experiences of populations forced from their homes and interned in civilian and POW camps in Europe and the United States, 

Music in World War II | Potter Pamela M. | Twarda

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