Litgu.ru - Литературный Гуру

Название: Компактные группы Ли и их представления
Автор: Желобенко Д.П.
Издательство: М.: МЦНМО
Год: 2021
Формат: djvu
Страниц: 552
Размер: 13 mb
Язык: Русский

Книга содержит изложение теории представлений компактных групп Ли и родственных структур, в том числе полупростых комплексных групп и алгебр Ли. Центральное место в теории занимает известная теорема Петера— Вейля о рядах Фурье на компактных группах, ассоциированных с неприводимыми (конечномерными) представлениями этих групп. Значительное место в книге уделяется конкретному описанию неприводимых представлений простых компактных групп Ли. Изложение, выдержанное по правилу «от простого к сложному», позволяет читателю эффективно и быстро овладеть основами теории представлений. Для студентов и аспирантов физико-математических специальностей.

Название: Антарктида. История изучения ледяного континента
Автор: Иванов Д.В.
Издательство: Москва : АСТ: ОГИЗ
Год: 2025
Формат: djvu
Страниц: 160
Размер: 59 mb
Язык: Русский

Эта книга о наших соотечественниках, которые открывали и изучали последнее белое пятно на карте мира, ледяной континент, о котором еще несколько десятилетий назад не было известно почти ничего.
Особенностью издания являются многочисленные фотографии, картины, гравюры и зарисовки, рассказывающие о первопроходцах Антарктики.
Автор текста — журналист Дмитрий Иванов, много лет занимающийся изучением истории географических открытий.

Название: Астрономия: 11 класс
Автор: Воронцов-Вельяминов Б.А.
Издательство: М.: Просвещение
Год: 1989 - 18-е изд.
Cтраниц: 160
Формат: pdf
Размер: 32 мб
Язык: русский

Учебник Воронцова-Вельяминова является одним из лучших учебников по астрономии времен СССР. Целые поколения изучали в советской школе астрономию именно по этому учебнику. То, как он завораживал нас и заставлял себя прочитывать, вновь удаётся сделать немногим книгам.

Название: Global Analysis: Differential Forms in Analysis, Geometry, and Physics
Серия: Graduate Studies in Mathematics, 52
Автор: Ilka Agricola, Thomas Friedrich
Издательство: American Mathematical Society
Год: 2002
Формат: pdf/djvu
Страниц: 362
Размер: 10,2 Мб
Язык: английский

This text is based on graduate courses on analysis and differential geometry, covering the topic of differential forms from the perspective of analysis, differential geometry, and mathematical physics. Nine chapters explore differential and integral calculus for differential forms defined on open sets in Euclidean space, vector analysis on manifolds, Pfaffian systems, curves and surfaces in Euclidean 3-space, Lie groups and homogenous spaces, symplectic geometry and mechanics, elements of statistical mechanics and thermodynamics, and elements of electrodynamics.

Название: A Course in Metric Geometry
Серия: The Graduate Studies in Mathematics, 33
Автор: Dmitri Burago, Yuri Burago, Sergei Ivanov
Издательство: American Mathematical Society
Год: 2001
Формат: pdf
Страниц: 434
Размер: 11,3 Мб
Язык: английский

Metric geometry'' is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations.
The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Caratheodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with ""easy-to-touch'' mathematical objects using ""easy-to-visualize'' methods.
The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of the exposition.

Название: Прямые и обратные задачи механики упругих композитных пластин и оболочек вращения
Автор: Голушко С.К., Немировский Ю.В.
Издательство: М.: ФИЗМАТЛИТ
Год: 2008
Формат: pdf
Страниц: 430
Размер: 17 mb
Язык: Русский

В монографии представлены результаты исследований, выполненных авторами в области механики многослойных анизотропных пластин и оболочек. Получены новые решения задач расчета напряженно-деформированного состояния и определения нагрузок начального разрушения широкого класса различных элементов тонкостенных конструкций. Проведен сравнительный анализ поведения конструкций на основе классической и ряда уточненных теорий пластин и оболочек в геометрически линейной и нелинейной постановках. Представлен оригинальный метод и новые классы аналитических решений обратных задач рационального проектирования композитных пластин и оболочек.

Название: An Introduction to Modern Cosmology, 2nd and 3rd Editions
Автор: Andrew Liddle
Издательство: Wiley
Год: 2003 / 2015
Формат: pdf/djvu
Страниц: 189 / 201
Размер: 17,7 Мб
Язык: английский

An Introduction to Modern Cosmology Third Edition is an accessible account of modern cosmological ideas. The Big Bang Cosmology is explored, looking at its observational successes in explaining the expansion of the universe, the existence and properties of the cosmic microwave background, and the origin of light elements in the universe. Properties of the very early Universe are also covered, including the motivation for a rapid period of expansion known as cosmological inflation. The third edition brings this established undergraduate textbook up-to-date with the rapidly evolving observational situation.
This fully revised edition of a bestseller takes an approach which is grounded in physics with a logical flow of chapters leading the reader from basic ideas of the expansion described by the Friedman equations to some of the more advanced ideas about the early universe. It also incorporates up-to-date results from the Planck mission, which imaged the anisotropies of the Cosmic Microwave Background radiation over the whole sky. The Advanced Topic sections present subjects with more detailed mathematical approaches to give greater depth to discussions. Student problems with hints for solving them and numerical answers are embedded in the chapters to facilitate the reader’s understanding and learning.
Cosmology is now part of the core in many degree programs. This current, clear and concise introductory text is relevant to a wide range of astronomy programs worldwide and is essential reading for undergraduates and masters students, as well as anyone starting research in cosmology.

Название: A Basic Course in Partial Differential Equations
Серия: Graduate Studies in Mathematics, 120
Автор: Qing Han
Издательство: American Mathematical Society
Год: 2011
Формат: pdf/djvu
Страниц: 306
Размер: 12,4 Мб
Язык: английский

This is a textbook for an introductory graduate course on partial differential equations. Han focuses on linear equations of first and second order. An important feature of his treatment is that the majority of the techniques are applicable more generally. In particular, Han emphasizes a priori estimates throughout the text, even for those equations that can be solved explicitly. Such estimates are indispensable tools for proving the existence and uniqueness of solutions to PDEs, being especially important for nonlinear equations. The estimates are also crucial to establishing properties of the solutions, such as the continuous dependence on parameters. Han's book is suitable for students interested in the mathematical theory of partial differential equations, either as an overview of the subject or as an introduction leading to further study.

Название: A Course in Complex Analysis and Riemann Surfaces
Серия: Graduate Studies in Mathematics, 154
Автор: Wilhelm Schlag
Издательство: American Mathematical Society
Год: 2014
Формат: pdf/djvu
Страниц: 403
Размер: 26,8 Мб
Язык: английский

Schlag presents a textbook for a one-quarter first-year graduate course in analysis for mathematics majors that covers real analysis and measure theory, and functional analysis and applications. It also discusses elementary aspects of complex analysis such as the Cauchy integral theorem, the residue theorem, Laurent series, the Riemann mapping theorem, and more advanced material selected from Riemann surface theory. He does not try to complete with specialized textbooks or classic treatises on these topics, he says, but offers a fairly detailed yet fast-paced introduction to those parts of the theory of one complex variable that seem most useful in other areas of mathematics such as geometric group theory, dynamics, algebraic geometry, number theory, and functional analysis.

Название: Manifolds and Differential Geometry
Серия: Graduate Studies in Mathematics, 107
Автор: Jeffrey M. Lee
Издательство: American Mathematical Society
Год: 2009
Формат: pdf/djvu
Страниц: 688
Размер: 47,9 Мб
Язык: английский

Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hyper-surfaces in Euclidean space. There is also a section that derives the exterior calculus version of Maxwell's equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more than enough material for a year-long course on manifolds and geometry.