作者：王怀玉著
页数：730
出版社：科学出版社
出版日期：2017
ISBN：9787030520791
电子书格式：pdf/epub/txt
内容简介
《物理学中的数学方法（英文版）》主要适用于物理、工程研究生，也适用于高年级学生和学生。 《物理学中的数学方法（英文版）》包括以下几个领域的知识：Hilbert空间，微分函数的微分方程，狄拉克函数，数学物理中的格林函数，积分方程，数论在物理学中的应用，基础多维空间和非欧几里得空间中的方程。 《物理学中的数学方法（英文版）》解释了这些概念，并详细推导了公式，包含大量的练习有益于读者。
目录
IntroductionPrefaceChapter 1 Variational Method1．1． Functional and Its Extremal Problems1．1．1． The conception of functional1．1．2． The extremes of functionals1．2． The Variational of Functionals and the Simplest Euler Equation1．2．1． The variational of functionals1．2．2． The simplest Euler equation1．3． The Cases of Multifunctions and Multivariates1．3．1． Multifunctions1．3．2． Multivariates1．4． Functional Extremes under Certain Conditions1．4．1． Isoperimetric problem1．4．2． Geodesic problem1．5． Natural Boundary Conditions1．6． Variational Principle1．6．1． Variational principle of classical mechanics1．6．2． Variational principle of quantummechanics1．7． The Applications of the Variational Method in Physics1．7．1． The applications in classical physics1．7．2． The applications in quantum mechanicsExercisesChapter 2 Hilbert Space2．1． Linear Space， Inner Product Spaceand Hilbert Space2．1．1． Linear space2．1．2． Inner product space2．1．3． Hilbert space2．2． Operators in Inner Product Spaces2．2．1． Operators and adjoint operators2．2．2． Self-adjoint operators2．2．3． The alternative theorem for the solutions of linear algebraic equations2．3． Complete Set of Orthonormal Functions2．3．1． Three kinds of convergences2．3．2． The completeness of a set of functions2．3．3． N-dimensional space and Hilbert function space2．3．4． Orthogonal polynomials2．4． Polynomial Approximation2．4．1． Weierstrass theorem2．4．2． Polynomial approximationExercisesChapter 3 Linear Ordinary Differential Equations of Second Order3．1． General Theory3．1．1． The existence and uniqueness of solutions3．1．2． The structure of solutions of homogeneous equations3．1．3． The solutions of inhomogeneous equations3．2． Sturm-Liouville Eigenvalue Problem3．2．1． The form of Sturm-LiouviUe equations……
Chapter 4 Bessel FunctionsChapter 5 The Dirac Delta FunctionChapter 6 Green’s FunctionChapter 7 NormChapter 8 Integral EquationsChapter 9 Application of Number Theory in Inverse Problems in PhysicsChapter 10 Fundamental Equations in Spaces with Arbitrary DimensionsReferencesAnswers of Selected ExercisesAuthor IndexSubject Index
Chapter 4 Bessel FunctionsChapter 5 The Dirac Delta FunctionChapter 6 Green’s FunctionChapter 7 NormChapter 8 Integral EquationsChapter 9 Application of Number Theory in Inverse Problems in PhysicsChapter 10 Fundamental Equations in Spaces with Arbitrary DimensionsReferencesAnswers of Selected ExercisesAuthor IndexSubject Index
