張量與黎曼幾何：微分方程應用（英文版） [Tensors and Riemannian Geometry with Applications to Differential Equations] 下載 mobi epub pdf 電子書 2024

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　　《張量與黎曼幾何：微分方程應用（英文版）》是作者在俄羅斯、法國、南非和瑞典多年講授黎曼幾何與張量課程講義的基礎上整理而成。《張量與黎曼幾何：微分方程應用（英文版）》通俗易懂、敘述清晰。通過閱讀《張量與黎曼幾何：微分方程應用（英文版）》，讀者將輕鬆掌握應用張量、黎曼幾何的理論以及幾何化的方法求解偏微分方程，尤其是利用近似重整化群理論將大大簡化de Sitter空間中廣義相對論方程的求解。 Nail H.Ibragimov教授為瑞典科學傢，被公認為是在微分方程對稱分析方麵世界上具有專業的專傢之一。他發起並構建瞭現代群分析理論和應用方麵很多新的發展。

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目錄

Preface
Part Ⅰ Tensors and Riemannian spaces
1 Preliminaries
1.1 Vectors in linear spaces
1.1.1 Three-dimensionalvectors
1.1.2 Generalcase
1.2 Index notation. Summation convention
Exercises
2 Conservation laws
2.1 Conservation laws in classical mechanics
2.1.1 Free fall of a body near the earth
2.1.2 Fall of a body in a viscous fluid
2.1.3 Discussion of Kepler's laws
2.2 General discussion of conservation laws
2.2.1 Conservationlaws for ODEs
2.2.2 Conservation laws for PDEs
2.3 Conserved vectors defined by symmetries
2.3.1 Infinitesimal symmetries of differential equations
2.3.2 Euler-Lagrange equations. Noether's theorem ...
2.3.3 Method of nonlinear self-adjointness
2.3.4 Short pulse equation
2.3.5 Linear equations
Exercises
3 Introduction of tensors and Riemannian spaces
3.1 Tensors
3.1.1 Motivation
3.1.2 Covariant and contravariant vectors
3.1.3 Tensor algebra
3.2 Riemannian spaces
3.2.1 Differential metric form
3.2.2 Geodesics. The Christoffel symbols
3.2.3 Covariant differentiation. The Riemann tensor
3.2.4 Flat spaces
3.3 Application to ODEs
Exercises
4 Motions in Riemannian spaces
4.1 Introduction
4.2 Isometric motions
4.2.1 Definition
4.2.2 Killing equations
4.2.3 Isometric motions on the plane
4.2.4 Maximal group of isometric motions
4.3 Conformal motions
4.3.l Definition
4.3.2 Generalized Killing equations
4.3.3 Conformally flat spaces
4.4 Generalized motions
4.4.l Generalized motions. their invariants and defect
4.4.2 Invariant family of spaces
Exercises

Part Ⅱ Riemannian spaces of second-order equations
5 Riemannian spaces associated with linear PDEs
5.1 Covariant form of second-order equations
5.2 Conformally invariant equations
Exercises
6 Geometry of linear hyperbolic equations
6.1 Generalities
6.1.1 Covariant form of determining equations
6.1.2 Equivalence transformations
6.1.3 Existence of conformally invariant equations
6.2 Spaces with nontrivial conformal group
6.2.1 Definition of nontrivial conformal group
6.2.2 Classification of four-dimensional spaces
6.2.3 Uniqueness theorem
6.2.4 On spaces with trivial conformal group
6.3 Standard form of second-order equations
6.3.1 Curved wave operator in V4 with nontrivial conformal group
6.3.2 Standard form of hyperbolic equations with nontrivial conformal group
……
Part Ⅲ Theory of relativity
Bibliography
Index
張量與黎曼幾何：微分方程應用（英文版） [Tensors and Riemannian Geometry with Applications to Differential Equations] 下載 mobi epub pdf txt 電子書 格式

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