*Differential Forms in Analysis, Geometry, and Physics*

**Author**: Ilka Agricola,Thomas Friedrich

**Publisher:**American Mathematical Soc.

**ISBN:**0821829513

**Category:**Mathematics

**Page:**343

**View:**7328

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# Search Results for: global-analysis-differential-forms-in-analysis-geometry-and-physics-graduate-studies-in-mathematics

*Differential Forms in Analysis, Geometry, and Physics*

**Author**: Ilka Agricola,Thomas Friedrich

**Publisher:** American Mathematical Soc.

**ISBN:** 0821829513

**Category:** Mathematics

**Page:** 343

**View:** 7328

This book introduces the reader to the world of differential forms and their uses in geometry, analysis, and mathematical physics. It begins with a few basic topics, partly as review, then moves on to vector analysis on manifolds and the study of curves and surfaces in $3$-space. Lie groups and homogeneous spaces are discussed, providing the appropriate framework for introducing symmetry in both mathematical and physical contexts. The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics. There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics.

**Author**: Werner Ballmann

**Publisher:** Birkhäuser

**ISBN:** 3034809832

**Category:** Mathematics

**Page:** 169

**View:** 5578

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 Gauß equations and the version of Gauß'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.

**Author**: Andreas Knauf

**Publisher:** Springer

**ISBN:** 3662557746

**Category:** Science

**Page:** 683

**View:** 1301

As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.
*Differentialformen in Analysis, Geometrie und Physik*

**Author**: Ilka Agricola,Thomas Friedrich

**Publisher:** Springer-Verlag

**ISBN:** 3834896721

**Category:** Mathematics

**Page:** 313

**View:** 4749

Dieses Lehrbuch eignet sich als Fortsetzungskurs in Analysis nach den Grundvorlesungen im ersten Studienjahr. Die Vektoranalysis ist ein klassisches Teilgebiet der Mathematik mit vielfältigen Anwendungen, zum Beispiel in der Physik. Das Buch führt die Studierenden in die Welt der Differentialformen und Analysis auf Untermannigfaltigkeiten des Rn ein. Teile des Buches können auch sehr gut für Vorlesungen in Differentialgeometrie oder Mathematischer Physik verwendet werden. Der Text enthält viele ausführliche Beispiele mit vollständigem Lösungsweg, die zur Übung hilfreich sind. Zahlreiche Abbildungen veranschaulichen den Text. Am Ende jedes Kapitels befinden sich weitere Übungsaufgaben. In der ersten Auflage erschien das Buch unter dem Titel "Globale Analysis". Der Text wurde an vielen Stellen überarbeitet. Fast alle Bilder wurden neu erstellt. Inhaltliche Ergänzungen wurden u. a. in der Differentialgeometrie sowie der Elektrodynamik vorgenommen.

**Author**: Josef Dick,Frances Y. Kuo,Henryk Woźniakowski

**Publisher:** Springer

**ISBN:** 3319724568

**Category:** Mathematics

**Page:** 1309

**View:** 9814

This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.

**Author**: Demeter Krupka,David Saunders

**Publisher:** Elsevier

**ISBN:** 9780080556734

**Category:** Mathematics

**Page:** 1244

**View:** 9802

This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics. This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics - Written by world-experts in the field - Up-to-date contents

**Author**: Bo-Yu Hou,Bo-Yuan Hou

**Publisher:** World Scientific Publishing Company

**ISBN:** 9813105097

**Category:** Mathematics

**Page:** 560

**View:** 4050

This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8–10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.

**Author**: Harley Flanders

**Publisher:** Courier Corporation

**ISBN:** 0486139611

**Category:** Mathematics

**Page:** 240

**View:** 9335

A graduate-level text utilizing exterior differential forms in the analysis of a variety of mathematical problems in the physical and engineering sciences. Includes 45 illustrations. Index.

**Author**: Hung Nguyen-Schäfer,Jan-Philip Schmidt

**Publisher:** Springer

**ISBN:** 3662484978

**Category:** Technology & Engineering

**Page:** 376

**View:** 9439

This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world. The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: • 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 The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics. Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.
*Proceedings of the 5th International Workshop on Complex Structures and Vector Fields : St. Konstantin, Bulgaria, 3-9 September 2000*

**Author**: Stancho Dimiev,Kouei Sekigawa

**Publisher:** World Scientific

**ISBN:** 9812810145

**Category:** Mathematics

**Page:** 220

**View:** 9219

This workshop brought together specialists in complex analysis, differential geometry, mathematical physics and applications for stimulating cross-disciplinary discussions. The lectures presented ranged over various current topics in those fields. The proceedings will be of value to graduate students and researchers in complex analysis, differential geometry and theoretical physics, and also related fields. Contents: Length Spectrum of Geodesic Spheres in Non-Flat Complex and Quaternionic Space Forms (T Adachi); Canal Hypersurfaces of Second Type (G Ganchev); Weierstrass Formula for Super Minimal J-Holomorphic Curves of a 6-Dimensional Sphere and Its Applications (H Hashimoto); Real Hypersurfaces of Kaehler Manifold (Sixteen Classes) (M Hristov); Almost Hermitian Manifolds of Poinwise Constant Antiholomorphic Sectional Curvature (O Kassabov & G Ganchev); The Quotient Space of the Complex Projective Plane Under Conjugation is a 4-Sphere (K Kikuchi); On a Generalization of CMC OCo 1 Surfaces Theory (M Kokubu); The Deligne-Simpson Problem (V Kostov); and other papers. Readership: Graduate students and researchers in mathematics and mathematical physics."
*An Introduction for Mathematical Physicists*

**Author**: D. Martin

**Publisher:** Elsevier

**ISBN:** 0857099639

**Category:** Mathematics

**Page:** 424

**View:** 9385

This account of basic manifold theory and global analysis, based on senior undergraduate and post-graduate courses at Glasgow University for students and researchers in theoretical physics, has been proven over many years. The treatment is rigorous yet less condensed than in books written primarily for pure mathematicians. Prerequisites include knowledge of basic linear algebra and topology. Topology is included in two appendices because many courses on mathematics for physics students do not include this subject. Provides a comprehensive account of basic manifold theory for post-graduate students Introduces the basic theory of differential geometry to students in theoretical physics and mathematics Contains more than 130 exercises, with helpful hints and solutions
*Mit einem Ausblick auf die Seiberg-Witten-Theorie*

**Author**: Thomas Friedrich

**Publisher:** Springer-Verlag

**ISBN:** 3322803023

**Category:** Mathematics

**Page:** 207

**View:** 652

Dieses Buch entstand nach einer einsemestrigen Vorlesung an der Humboldt-Universität Berlin im Studienjahr 1996/ 97 und ist eine Einführung in die Theorie der Spinoren und Dirac-Operatoren über Riemannschen Mannigfaltigkeiten. Vom Leser werden nur die grundlegenden Kenntnisse der Algebra und Geometrie im Umfang von zwei bis drei Jahren eines Mathematik- oder Physikstudiums erwartet. Ein Anhang gibt eine Einführung in das aktuelle Gebiet der Seiberg-Witten-Theorie.

**Author**: Tai Alexis Melcher

**Publisher:** N.A

**ISBN:** N.A

**Category:**

**Page:** 240

**View:** 8046

**Author**: David Bachman

**Publisher:** Springer Science & Business Media

**ISBN:** 0817683046

**Category:** Mathematics

**Page:** 156

**View:** 9925

This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.
*An Introduction*

**Author**: Theodore Frankel

**Publisher:** Cambridge University Press

**ISBN:** 1139505610

**Category:** Mathematics

**Page:** N.A

**View:** 9385

This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.

**Author**: Alexander I. Bobenko

**Publisher:** Springer

**ISBN:** 3662504472

**Category:** Mathematics

**Page:** 439

**View:** 9532

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture. This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.
*A Guided Tour for Graduate Students*

**Author**: Michael Stone,Paul Goldbart

**Publisher:** Cambridge University Press

**ISBN:** 0521854032

**Category:** Science

**Page:** 806

**View:** 1893

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics - differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study.

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** American literature

**Page:** N.A

**View:** 2291

**Author**: Peterson's Guides Staff

**Publisher:** Petersons

**ISBN:** 9780768924022

**Category:** Reference

**Page:** 751

**View:** 1994

Offers information on entrance and degree requirements, expenses and financial aid, programs of study, and faculty research specialties.

**Author**: M. Karoubi,C. Leruste

**Publisher:** Cambridge University Press

**ISBN:** 9780521317146

**Category:** Mathematics

**Page:** 363

**View:** 1771

In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.

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