Libros de Geometría, página 16 de 23

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

One of two volumes which lay the foundations for understanding differential geometry. This work familiarizes readers with various techniques of computation.

Andrzej KrasinskiThis unique volume provides a comprehensive survey of our understanding of the Universe based on the exact solutions of the theory of relativity. More precisely, it describes those models that fit with astronomical observations of galaxy clusters, cosmic voids and other key features of our Universe. This authoritative account achieves two important goals. First, it collects all independently derived cosmological solutions since the birth of relativity in 1915, and clearly shows how they are interrelated. Second, it presents a coherent overview of the physical properties of these inhomogeneous models. It demonstrates, for instance, that the formation of voids and the interaction of the cosmic microwave background radiation with matter in the Universe can be explained by exact solutions of the Einstein equations, without the need for approximations. This book will be of particular interest to graduates and researchers in gravity, relativity and theoretical cosmology as well as historians of science.

Alexander Altland, Ben SimonsPrimer, including problems and solutions, for graduate level courses on theoretical quantum condensed matter physics.

Partha GhoseTechnological advances have made it possible to perform experiments, once considered to be purely gedanken, which test the counterintuitive and bizarre consequences of quantum theory. This book provides simple accounts of these experiments and an understanding of what they aim to prove and why this is important. After introducing the main theoretical concepts and problems with the foundations of quantum mechanics, early chapters discuss experiments in the areas of wave-particle duality, cavity quantum electrodynamics and quantum non-demolition measurement. The text then examines investigation of certain predictions including the Aharanov-Bohm effect, before tackling the problem of macroscopic quantum coherence. Later chapters consider methods of testing the quantum Zeno paradox, collapse, macroscopic quantum jumps, tunnelling times and Einstein-Bell non-locality. Introductions to the theory behind types of measuring devices such as micromasers and those based on the concept of quantum non-demolition are also given. Detailed references are included. Up to date and accessible Suitable as an introduction for graduate students

Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does not go beyond the level of standard introductory undergraduate mathematics courses.

Paul M. BellanThis rigorous explanation of plasmas is relevant to diverse plasma applications such as controlled fusion, astrophysical plasmas, solar physics, magnetospheric plasmas, and plasma thrusters. More thorough than previous texts, it exploits new powerful mathematical techniques to develop deeper insights into plasma behavior. After developing the basic plasma equations from first principles, the book explores single particle motion with particular attention to adiabatic invariance. The author then examines types of plasma waves and the issue of Landau damping. Magnetohydrodynamic equilibrium and stability are tackled with emphasis on the topological concepts of magnetic helicity and self-organization. Advanced topics follow, including magnetic reconnection, nonlinear waves, and the Fokker-Planck treatment of collisions. The book concludes by discussing unconventional plasmas such as non-neutral and dusty plasmas. Written for beginning graduate students and advanced undergraduates, this text emphasizes the fundamental principles that apply across many different contexts. Applicable to many different plasma contexts Uses mathematical tools to obtain deeper insights into understanding of behaviour in complex, realistic geometries Contains new, modern topics such as self-organisation, topology of magnetic fields, non-neutral plasmas and dusty plasmas

Carlo RovelliBook presenting the loop and spinfoam approach to quantum gravity, for graduates and researchers. Quantum gravity is perhaps the most important open problem in fundamental physics. It is the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

Discípulo aventajado de Gauss, Riemann fue un matemático excepcional que marcó un antes y un después. Su particular visión de las matemáticas, unida a su interés por la física, le llevó a adentrarse en terrenos desconocidos en su tiempo. Guiado por su intuición y un perfeccionismo extremo, Riemann marcó el camino a seguir a muchos matemáticos. Hoy en día, conceptos como superficie de Riemann, variedades riemannianas, género de una superficie o integral son parte fundamental en los estudios de matemáticas, pero no debemos olvidar que no fue siempre así.

The second edition featured a new chapter with a systematic development of variational problems from quantum field theory, in particular the Seiberg-Witten and Ginzburg-Landau functionals. This third edition gives a new presentation of Morse theory and Floer homology that emphasises the geometric aspects and integrates it into the context of Riemannian geometry and geometric analysis. It also gives a new presentation of the geometric aspects of harmonic maps: This uses geometric methods from the theory of geometric spaces of nonpositive curvature and, at the same time, sheds light on these, as an excellent example of the integration of deep geometric insights and powerful analytical tools. These new materials are based on a course at the University of Leipzig, entitled Geometry and Physics, attended by graduate students, postdocs and researchers from other areas of mathematics. Much of this material appears for the first time in a textbook.

Este libro presenta una interesante ocasion al estudiante para aplicar los conocimientos adquiridos en el estudio del Algebra Lineal.Se parte de la base que el lector conoce las propiedades más elementales de la GEometria Euclipea y, aunque hemos intentado justificar los pasos previos a las aplicaciones practicas, en cualquier caso los conocimientos ya adquiridos seran de gran utilidad para el estudio de esta materia.

Este texto está dedicado a la geometría analítica elemental del plano y del espacio, insistiendo en la distinción natural entre las nociones vectoriales, las afines y las euclídes. Tras recordar brevemente las operaciones basicas de escalares y vectores se explica el calculo vectorial en el que se basa la geometria analitica: combinaciones lineales, bases y coordenadas, productos escalar, vectorial y mixto; nociones, todas ellas, que sirven para calcular modulos, areas y volumenes.

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

La necesidad de representar con claridad y sencillez formas y supeficies de dimensiones verticales mucho más pequeñas que las horizontales, motivó la aparación del sistema acotado, como caso particular del diedrico, sustituyendo la proyeccion vertical o alzado del punto, por su altura o ''cota'' respecto al plano horizontal de proyeccion o de referencia.