In this book international expert authors provide solutions for modern fundamental problems including the complexity of computing of critical points for set-valued mappings, the behaviour of solutions of ordinary differential equations, partial differential equations and difference equations, or the development of an abstract theory of global attractors for multi-valued impulsive dynamical systems.
In the past thirty years, differential geometry has undergone an enormous change with infusion of topology, Lie theory, complex analysis, algebraic geometry and partial differential equations.
This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a self-contained and accessible manner.
Differential Geometry offers a concise introduction to some basic notions of modern differential geometry and their applications to solid mechanics and physics.
Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.
This volume is based on the lectures given at the First Inter University Graduate School on Gravitation and Cosmology organized by IUCAA, Pune, in 1989.
Despite the fundamental role played by Reshetnyak's work in the theory of surfaces of bounded integral curvature, the proofs of his results were only available in his original articles, written in Russian and often hard to find.
Hans Duistermaat, an influential geometer-analyst, made substantial contributions to the theory of ordinary and partial differential equations, symplectic, differential, and algebraic geometry, minimal surfaces, semisimple Lie groups, mechanics, mathematical physics, and related fields.
The most immediate one-dimensional variation problem is certainly the problem of determining an arc of curve, bounded by two given and having a smallest possible length.
Providing an up-to-date overview of the geometry of manifolds with non-negative sectional curvature, this volume gives a detailed account of the most recent research in the area.
During the last ten years a powerful technique for the study of partial differential equations with regular singularities has developed using the theory of hyperfunctions.
This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields.
This book is devoted to the development of geometrie methods for studying and revealing geometrie aspects of the theory of differential equations with quadratie right-hand sides (Riccati-type equations), which are closely related to the calculus of variations and optimal control theory.
Deep connections exist between harmonic and applied analysis and the diverse yet connected topics of machine learning, data analysis, and imaging science.
Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, Numerical Analysis, Theoretical Physics, Control Theory, sub-Riemannian Geometry), this monograph is intended to: fully enable readers (graduates or specialists, mathematicians, physicists or applied scientists, acquainted with Algebra or not) to understand and apply the statements and numerous corollaries of the main result, provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of view and notation, provide a thorough historical background of the results, together with unknown facts about the effective early contributions by Schur, Poincare, Pascal, Campbell, Baker, Hausdorff and Dynkin, give an outlook on the applications, especially in Differential Geometry (Lie group theory) and Analysis (PDEs of subelliptic type) and quickly enable the reader, through a description of the state-of-art and open problems, to understand the modern literature concerning a theorem which, though having its roots in the beginning of the 20th century, has not ceased to provide new problems and applications.
Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education.
Anschauliche Geometrie - wohl selten ist ein Mathematikbuch seinem Titel so gerecht geworden wie dieses außergewöhnliche Werk von Hilbert und Cohn-Vossen.
This 4-th edition of the leading reference volume on distance metrics is characterized by updated and rewritten sections on some items suggested by experts and readers, as well a general streamlining of content and the addition of essential new topics.
