Introduction to Mathematical Physics
Introduction to Mathematical Physics
复制标题
数学物理导论
DOI：
10.1002/9783527618859
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
M. T. Vaughn
中科院分区：
文献类型：
--
作者：
M. T. Vaughn
1无穷数列与级数。1.1实数与复数。1.2无穷数列与乘积的收敛性。1.3函数的数列与级数。1.4渐近级数。2有限维向量空间。2.1线性向量空间。2.2线性算子。2.3特征向量与特征值。2.4算子的函数。2.5线性动力系统。3物理中的几何。3.1流形与坐标。3.2向量、微分形式和张量。3.3微积分流形。3.4度量张量和距离。3.5动力系统和向量场。3.6流体力学。4复变量函数。4.1解析函数的初等性质。4.2复平面积分。4.3解析函数。4.4残数演算：应用。4.5周期函数傅立叶级数。5微分方程：解析方法。5.1微分方程系统。5.2一阶微分方程。5.3线性微分方程。5.4线性二阶方程。5.5勒让德方程。5.6贝塞尔方程。6希尔伯特空间。6.1无限维向量空间。6.2函数空间测度理论。6.3傅立叶级数。6.4傅立叶积分积分变换。6.5正交多项式。6.6 Haar函数小波。7希尔伯特空间上的线性算子。7.1某些希尔伯特空间精妙之处。7.2 Hilbert空间上线性算子的一般性质。7.3 Hilbert空间上线性算子的谱。7.4线性微分算子。7.5线性积分算子。绿函数。8偏微分方程。8.1线性一阶方程。8.2拉普拉斯二阶方程和线性二阶方程。8.3时变偏微分方程。8.4非线性偏微分方程。9有限群。9.1群的一般性质。9.2某些有限群。9.3对称群SN9.4组表示。9.5对称组SN表示。9.6离散无限群。10李群与李代数。10.1李群。10.2李代数。10.3李代数的表示。索引。
1 Infinite Sequences and Series. 1.1 Real and Complex Numbers. 1.2 Convergence of Infinite Series and Products. 1.3 Sequences and Series of Functions. 1.4 Asymptotic Series. 2 Finite-Dimensional Vector Spaces. 2.1 Linear Vector Spaces. 2.2 Linear Operators. 2.3 Eigenvectors and Eigenvalues. 2.4 Functions of Operators. 2.5 Linear Dynamical Systems. 3 Geometry in Physics. 3.1 Manifolds andCoordinates. 3.2 Vectors, Differential Forms, and Tensors. 3.3 Calculuson Manifolds. 3.4 Metric Tensor and Distance. 3.5 Dynamical Systems and Vector Fields. 3.6 Fluid Mechanics. 4 Functions of a Complex Variable. 4.1 Elementary Properties of Analytic Functions. 4.2 Integration in theComplex Plane. 4.3 Analytic Functions. 4.4 Calculus of Residues: Applications. 4.5 Periodic Functions Fourier Series. 5 Differential Equations: Analytical Methods. 5.1 Systems of Differential Equations. 5.2 First-Order Differential Equations. 5.3 Linear Differential Equations. 5.4 Linear Second-Order Equations. 5.5 Legendre's Equation. 5.6 Bessel's Equation. 6 Hilbert Spaces. 6.1 Infinite-Dimensional Vector Spaces. 6.2 Function Spaces Measure Theory. 6.3 Fourier Series. 6.4 Fourier Integral Integral Transforms. 6.5 Orthogonal Polynomials. 6.6 Haar Functions Wavelets. 7 Linear Operators on Hilbert Space. 7.1 Some Hilbert Space Subtleties. 7.2 General Properties of Linear Operators on Hilbert Space. 7.3 Spectrum of Linear Operators on Hilbert Space. 7.4 Linear Differential Operators. 7.5 Linear Integral Operators Green Functions. 8 Partial Differential Equations. 8.1 LinearFirst-OrderEquations. 8.2 The Laplacian and Linear Second-Order Equations. 8.3 Time-Dependent Partial Differential Equations. 8.4 Nonlinear Partial Differential Equations. 9 Finite Groups. 9.1 General Properties of Groups. 9.2 Some Finite Groups. 9.3 The Symmetric Group SN. 9.4 Group Representations. 9.5 Representations of the Symmetric Group SN. 9.6 Discrete Infinite Groups. 10 Lie Groups and Lie Algebras. 10.1 Lie Groups. 10.2 Lie Algebras. 10.3 Representationsof Lie Algebras. Index.