《数学物理方法》课程教学资源（教案讲义）数学物理分类主题词.pdf_大学文库

1 1J Diophantine approximation, transcendental number theory 丢番图逼近论,超越数论 1 1K Probabilistic theory: distribution modulol; metric theory of algorithms 概率论:分布模,算法的度量 IL Exponential sums and character sums,指数和与特征和 11M Zata and L-functions: analytic theory,函数和L函数:解析理论 l| N Multiplicative number theory,乘法数论 l! P Additive number theory, partitions,加法数论,划分 IIR Algebraic number theory: global fields,代数数论:整体域 11S Algebraic number theory: local and p-adic fields 代数数论:局部域,p进位域 l1 T Finite fields and commutative rings,有限域与交换环 U Connections with logic,与逻辑的联系 11Y Computational number theory,计算数论 l1 Z Miscellaneous applications of number theory,数论的各种应用 l2 Field theory and polynomials,域论与多项式 12 D Real and complex fields,实数与复数域 12 E General field theory,普通域论 12 F Field extensions,域的扩张 l2 G Homological methods( field theory),同调方法(域论) 12 H Differential and difference algebra,微分和差分代数 l2 J Topological fields,拓扑域 12 K Generalizations of fields,域的推广 12 L Connections with logic,与逻辑的联系 12Y Computational aspects of field theory and polynomials 域论的计算方面与多项式 13 Commutative rings and algebras,交换环与代数 13 A General commutative ring theory,普通交换环论 13 B Ring extensions and related topics,环的扩张及其相关课题 l3 Theory of modules and ideals,模论与理想 13 D Homological methods,同调方法 13 E Chain conditions, finiteness conditions,链条件,有限性条件 13 Arithmetic rings and other special rings,算术环与其它特殊环 l3 G Integral domains,整环 13 H Local rings and semilocal rings,局部环和半局部环 13 I Topological rings and modules,拓扑环与模 13L Applications of logic to commutative algebra 逻辑在交换代数中的应用 13 FInite commutative rings,有限交换环 13 N Differential algebra,微分代数 13 P Computational aspects of commutative algebra,交换代数的计算方面 14 Algebraic geometry,代数几何 14 A Foundations,基础 l4 B Local theory,局部理论

l4 C Cycles and subschemes,圈与子格式? 14 D Families, fibrations,族,纤维 l4F(Co) homology theory,(余)同调论 l4 G Arithmetic problems, Diophantine geometry,算术问题,丢番图几何 14 H Curves,曲线 l4 J Surfaces and higher- dimensional varieties,表面与高维情形 14 ABelian varieties and schemes,阿贝尔情形与格式? l4 ALgebraic groups,代数群 l4 M Special varieties,特殊情形 l4 N Projective and enumerative geometry,射影几何与枚举几何 l4 P Real algebraic and real analytic geometry,实代数几何与实解析几何 l4 Q Computational aspects in algebraic geometry,代数几何的计算方面 14 R Affine geometry,仿射几何 15 Linear and multilinear algebra; matrix theory, 线性与多线性代数;矩阵理论 l6 Associative rings and algebras,结合环与代数 l6 B General and miscellaneous,概论与各个方面 l6 D Modules, bimodules and ideals,模,双模和理想 l6 E Homological methods,同调方法 16 G Representation theory of rings and algebras,环与代数的表示理论 1 6H Orders and arithmetic, separable, Azumaya algebras 序和代数的、可分的、 Azumaya代数 16 K Division rings and semisimple Artin rings,可除环与半单(纯)阿廷环 l6 L Local rings and generalizations,局部环及其推广 16P Chain conditions, growth conditions, and other forms of finiteness 链条件,生长条件,及有限性的其它形式 16 R Rings with polynomial identity,带有多项式恒等式的环 16S Rings and algebras arising under various constructions 各种不同结构中产生的环与代数 l6 U Conditions on elements,关于元素的条件 l6 W Rings and algebras with additional structure,带附加结构的环与代数 l6 Y Generalizations,推丿 17 Nonassociative rings and algebras,非结合环与代数 17 A General nonassociative rings,非结合环概论 17 B Lie algebras and Lie superalgebras,李代数与李超代数 17 Jordan algebras,约当代数 17 D Other nonassociative rings and algebras,其它非结合环与代数 l8 Category theory; homological algebra,范畴理论;同调代数 l8 A General theory of categories and functors,范畴与函子概论 I8 B Special categories,特殊范畴 l8 Categories and theories,范畴与理论 l8 D Categories with structure,带结构的范畴 l8 e abelian categories,阿贝尔范畴 l8 F Categories and geometry,范畴与几何

l8 G Homological algebra,同调代数 19K- theory,K-理论 19A Grothendieck groups and Ko, Grothendieck #f FKo 19 B Whitehead groups and K1, Whitehead群和K1 l9 D Higher algebraic K-theory,高阶代数K-理论 19EK- theory in geometry,几何中的K-理论 19 K-theory in number theory,数论中的K-理论 19GK- theory of form,形式的K-理论 19 j Obstructions from topology,由拓扑学引起的障碍 19 K K-theory and operator algebras,K-理论与算符代数 19 L Topological K-theory,拓扑K-理论 20 Group theory and generalizations,群论及其推广 20 A Foundations,基础 20 B Permutation groups,置换群 20 C Representation theory of groups,群的表示理论 20 D Abstract finite groups,抽象有限群 20E Structure and classification of infinite or finite groups 有限或无限群的结构与分类 20 F Special aspects of infinite or finite groups,有限或无限群的特殊方面 20 G Linear algebraic groups( classical groups),线性代数群(经典群) 20 H Other groups of matrices,其它矩阵群 20J Connections with homological algebra and category theory 与同调代数和范畴理论的联系 20 K Abelian groups,阿贝尔群 20 M Semigroups,半单(纯)群 20 N Other generalizations of groups,群的其它推广 22 Topological groups, Lie groups,拓朴群,李群 22 A Topological and differentiable algebraic systems,拓扑和可微代数系统 22 C Compact groups,紧致群 22 d Locally compact groups and their algebras,局部紧致群及其代数 22 E Lie groups,李群 22 F Noncompact transformation groups,非紧致变换群 26 Real functions,实函数 26 A Functions of one variable,单变量函数 26 B Functions of several variables,多变量函数 26 C Polynomials, rational functions,多项式,有理函数 26Dneqμ ualities,不等式 26 E Miscellaneous topics,各种相关课题 28 Measure and integration,测度与积分 28 A Classical measure theory,经典测度理论 28B set functions, measures and integrals with values in abstract spaces 集合函数,取值在抽象空间的测度和积分 28C Set functions and measures on spaces with additional structure 集合函数,带有附加结构的空间的测度

28 D Measure-theoretic ergodic theory,测度理论的各态遍历理论 28 E Miscellaneous topics in measure theory,测度理论中的各种课题 30 Functions of a complex variable,单复变函数 30 A General properties,一般性质 30 B Series expansions,级数展开 theory,几何函数理论 30D Entire and meromorphic functions, and related topics 整函数和亚纯函数,及其相关课题 30E Miscellaneous topics of analysis in the complex domain 复数区域微积分的各种课题 30 F Riemann surfaces,黎曼面 30 G Generalized function theory,广义函数理论 30 H spaces and algebras of analytic functions,解析函数的空间和代数 3 I Potential theory,位势理论 31ATwo- dimensional theory,二维理论 31 B Higher-dimensional theory,高维理论 3 IC Other generalizations,其它推广 3 D Axiomatic potential theory,公理化位势理论 32 Several complex variables and analytic spaces,多复变数和解析空间 32A Holomorphic functions of several complex variables 多复变数的全纯函数 32 B Local analytic geometry,局部解析几何 32 C Analytic spaces,解析空间 32 E holomorphic convexity,全纯凸性 32 Geometric convexity,几何凸性 32 G Deformations of analytic structures,解析结构的变形 32 H holomorphic mappings and correspondences,全纯映射和对应性 32 J Compact analytic spaces,紧致解析空间 32 K Generalizations of analytic space,解析空间的推丿 32 L Holomorphic fiber spaces,全纯纤维空间 32M Complex spaces with a group of automorphisms 带有自同构群的复空间 32 Q Complex manifolds,复流形 32 S Singularities,奇点 32 PSeudoconvex domains,伪凸区域 32 U Pluripotential theory, Pluri-位势理论 32 V CR manifolds,CR流形 32 W Differential operators in several variables,多变量微分算符 33 Special functions,特殊函数 33 B Elementary classical functions,初等经典函数 3 C Hypergeometric functions,超几何函数 33 D Basic hypergeometric functions,基本超几何函数 33 E Other special functions,其它特殊函数 33 F Computational aspects,计算方面

34 Ordinary differential equations,常微分方程 34 A General theory,一般理论 34 B Boundary value problems,边值问题 34 C Qualitative theory,定性理论 34 d Stability theory,稳定性理论 34 E Asymptotic theory,渐近理论 34 F Equations and systems with randomness,带随机性的方程与系统 34 G Differential equations in abstract spaces,抽象空间的微分方程 34 H Control problems控制问题 34K Functional-differential and differential-difference equations 泛函微分和微分-差分方程 34 L Ordinary differential operators,常微分算符 34 M Differential equations in the complex domain,复区域中的微分方程 35 Partial diferential equations,偏微分方程 35 A General theory,一般理论 3 B Qualitative properties of solutions,解的定性性质 3 C Representations of solutions,解的表示 35D Generalized solutions of partial differential equations 偏微分方程的广义解 35E Equations and systems with constant coefficients 带常系数的方程和系统 35 F General first-order equations and systems,一般一阶方程和系统 35 G General higher- order equations and systems,一般高阶方程和系统 35 H Close-to- -elliptic equations,近椭圆型方程 35 J Partial differential equations of elliptic type,椭圆型偏微分方程 3 K parabolic equations and systems,抛物线型方程和系统 3 L Partial differential equations of hyperbolic type,抛物线型偏微分方程 35M Partial differential equations of special type(mixed, composite, etc. 特殊类型(混合、复合等)的偏微分方程 35 OVerdetermined systems,超定系统 35P Spectral theory and eigenvalue problems for partial differential operators, th 微分算符的谱理论和本征值问题 35Q Equations of mathematical physics and other areas of application 数学物理方程和其它方面的应用 35R Miscellaneous topics involving partial differential equations 涉及偏微分方程的各种课题 35S Pseudodifferential operators and other generalizations of partial differential 37D2 perators,伪微分算符和偏微分算符的其它推广 mical systems and ergodic theory,动力系统和各态遍历理论 37 A Ergodic theory,各态遍历理论 37 B Topological dynamics,拓扑动力学 37C Smooth dynamical systems: general theor 光滑动力学系统:一般理论 37D Dynamical systems with hyperbolic behavior

带双曲行为的动力学系统 37ELow- dimensional dynamics systems,低维动力学系统 37 F Complex dynamical systems,复动力学系统 37 GLocal and nonlocal bifurcation theory,局部与非局部的分叉理论 37 H Random dynamical systems,随机动力学系统 37J Finite-dimensional Hamiltonian, Lagrangian, contact and nonholonomic systems,有限维哈密顿、拉格郎日、紧致、与非和乐的系统 37 K Infinite- dimensional Hamiltonian systems,无限维哈密顿系统 37L Infinite-dimensional dissipative dynamical systems 无限维耗散动力学系统 37M Approximation methods and numerical treatment of dynamical systems 动力学系统的近似方法和数值处理 37 N Applications,应用 39 Difference and functional equations,差分与函数方程 39 A Difference equations,差分方程 39 B Functional equations and inequalities,函数方程和表达式 40Seqμ uences, series, summability,数列,级数,可求和性 40A Convergence and divergence of infinite limiting processes 无穷极限过程的收敛与发散 40 B Multiple sequences and series,多重序列与级数 40 C General summability methods,一般可求和性方法 40 D Direct theorems on summability,关于可求和性的直接定理 40 E Inversion theorem,逆定理 40 F Absolute and strong summability,绝对和强可求和性 40 H Functional analytic methods in summability,可求和性的泛函分析方法 Approximations and expansions,近似与展开 42 Fourier analysis,傅立叶分析 42 A Fourier analysis in one variable,单变量傅立叶分析 4 B Fourier analysis in several variables,多变量傅立叶分析 42 C Nontrigonometric Fourier analysis,非三角函数的傅立叶分析 43 Abstract harmonic analysis,抽象调和分析 44 ntegral transforms, operational calculus,积分变换,运算微积 45 Integral equations积分方程 45 A Linear integral equations,线性积分方程 45 B Fredholm integral ecμ uations,弗雷德霍姆积分方程 45 D Volterra integral equations, Volterra积分方程 45 E Singular integral equations,奇异积分方程 45 G Nonlinear integral equations,非线性积分方程 4 H Miscellaneous special kernels,各种特殊的积分核 45 J Integro- ordinary differential equations,积分常微分方程 4 K Integro- partial differential equations,积分偏微分方程 45 L Theoretical approximation of solutions,解的理论近似 45N Abstract integral equations, integral equations in abstract spaces 抽象积分方程,抽象空间中的积分方程

45 P Integral operators,积分算符 45 Q Inverse problems,逆问题 46 Functional analysis,泛函分析 46A Topological linear spaces and related structures 拓扑线性空间及其相关问题 46B Normed linear spaces and Banach spaces; Banach lattices 赋范线性空间和 Banach空间, Banach格 46C Inner product spaces and their generalizations, Hilbert spaces 内积空间及其推广,希尔伯特空间 46 E Linear function spaces and their duals,线性函数空间及其对偶空间 46F Distributions, generalized functions, distribution spaces 分布,广义函数,分布空间 46G Measures, integration, derivative, holomorphy(all involving infinite- dimensional spaces),测度,积分,导数,全形 46H Topological algebras, normed rings and algebras, Banach algebras 拓扑代数,赋范环和代数, Banach代数 46J Commutative Banach algebras and commutative topological algebras 交换 Banach代数和交换拓扑代数 46K Topological (rings and)algebras with an involution 带对合的拓扑(环和)代数 46 L Selfadjoint operator algebras,自对偶算符代数 46M Methods of category theory in functional analysis 泛函分析中的范畴理论方法 46 N Miscellaneous applications of functional analysis,泛函分析的各种应用 46S Other(nonclassical) types of functional analysis 泛函分析的其它(非经典)类型 46 T Nonlinear functional analysis,非线性泛函分析 47 Operator theory,算符理论 47 A General theory of linear operators,线性算符的一般理论 47 B Special classes of linear operators,线性算符的特殊类型 47C Individual linear operators as elements of algebraic systems 作为代数系统的元素的单个线性算符 47D Groups and semigroups of linear operators, their generalizations and applications,线性算符的群和半群,它们的推广和应用 4 E Ordinary differential operators,常微分算符 4 7F Partial differential operators,偏微分算符 47G Integral, integro-differential, and pseudodifferential operators 积分算符,积分-微分算符和伪微分算符 47 H Nonlinear operators and their properties,非线性算符及其性质 47J Equations and inequalities involving nonlinear operators 涉及非线性算符的方程和不等式 47 L Linear spaces and algebras of operators,算符的线性空间和代数 47 N Miscellaneous applications of operator theory,算符理论的各种应用 47S Other(nonclassical) types of operator theory

算符理论的其它(非经典)类型 49 Calculus of variations and optimal control; optimization,变分法和优选法, 49 J Existence theories,存在性理论 49K Necessary conditions and sufficient conditions for optimality 最优性的充要条件 49L Hamilton-Jacobi theories, including dynamic programming 哈密顿一雅可比理论,包括动力学程序设计 49 M Methods of successive approximations,成功的近似方法 49 N Miscellaneous topics,各种课题 49 Q Manifolds,流形 49R Variational methods for eigenvalues of operators 算符本征值的变分方法 49 S Variational principles of physics,物理中的变分原理 5 I Geometry,几何学 5 IA Linear incidence geometry,线性关联几何 5 B Nonlinear incidence geometry,非线性关联几何 5 D Geometric closure systems,几何的封闭系统 51E Finite geometry and special incidence structures 有限几何与特殊关联结构 5 I F Metric geometry,度量几何 5 K Distance geometry,距离几何 M Real and complex geometry,实几何与复几何 51 N Analytic and descriptive geometry,解析的与画法几何 52 Convex and discrete geometry,凸几何与离散几何 52 A General convexity,一般凸性 52 B Polytopes and polyhedra,多胞形与多面体 52 C Discrete geometry,离散几何 53 Differential geometry,微分几何 53 A Classical differential geometry,经典微分几何 53 B Local differential geometry,局部微分几何 53 C Global differential geometry,整体微分几何 53 D Symplectic geometry, contact geometry,辛几何,接触几何 4 General topology,一般拓朴 54 A Generalities,通论 54 B Basic constructions,基本结构 54C Maps and general types of spaces defined by maps 映射和由映射定义的空间的一般类型 54 D Fairly general properties,适当的一般性质 54 E Spaces with richer structures,带有更多结构的空间 54 F Special properties,特殊性质 54 G Peculiar spaces,特殊空间 54H Connections with other structures, applications 与其它结构的联系,应用 54 J Nonstandard topology,非标准拓扑

55 Algebraic topology,代数拓朴 55 M Classical topics,经典课题 55 N Homology and cohomology theories,同调与余同调理论 55 P Homotopy theory,同伦理论 55 Q Homotopy groups,同伦群 55 R Fiber spaces and bundles,纤维空间与纤维丛 55 OPerations and obstructions,算符与障碍 55U Applied homological algebra and category theory 实用同调代数与范畴理论 57 Manifolds and cell complexes,流形与胞腔复形 57MLow- dimensional topology,低维拓扑 57 N Topological manifolds,拓扑流形 57 P Generalized manifolds,广义流形 57 Q PL-topology,PL一流形 57 R Differential topology,微分拓扑 57 S Topological transformation groups,拓扑变换群 57T Homology and homotopy of topological groups and related structures 拓扑群的同调和同伦及其相关结构 s8 Global analysis, analysis on manifolds,整体分析,流形上的分析 58 A General theory of differentiable manifolds,微分流形的一般理论 58 B Infinite-dimensional manifolds,无限维流形 58C Calculus on manifolds; nonlinear operators 流形上的微积分;非线性算符 58 D Spaces and manifolds of mappings,映射的空间与流形 58E Variational problems in infinite-dimensional spaces 无限维空间中的变分问题 58H Pseudogroups, differentiable groupoids and general structures on manifolds 伪群,可微广群和流形上的一般结构 58J Partial differential equations on manifolds; differential operators 流形上的偏微分方程;微分算符 58K Theory of singularities and catastrophe theory 奇异点理论与 catastrophe理论 60 Probability theory and stochastic processes 概率论和随机过程 60 A Foundations of probability theory,概率论基础 60B Probability theory on algebraic and topological structures 代数和拓扑结构上的概率论 60 C Combinatorial probability,组合概率 60D Ceometric probability, stochastic geometry, random sets 几何概率,随机几何,随机集合 60 E Distribution theory,分布理论 60 F Limit theorems,极限定理 60 G Stochastic processes,随机过程 60 H stochastic analysis,随机分析 60 J Markov processes,马尔柯夫过程