PDF
本書有DRM加密保護,需使用HyRead閱讀軟體開啟
  • Mathematical methods for physics
  • 點閱:542
  • 作者: Felix Lee
  • 出版社:National Tsing Hua University Press
  • 出版年:c2009
  • ISBN:978-986-85667-0-5 ; 986-85667-0-3
  • 格式:PDF

This book is a written version of a lecture course that I have conducted over anumber of years at National Tsing Hua University on the subject of mathematical methods for physics. In response to student requests, once and again, the main purpose of the book is devoted to motivate students to feel free to study mathematics independently. The book is intended to provide advanced undergraduate and beginning graduate students in physical science with the most fundamental tools and important background which they will need in the advanced studies. It contains a lot of physical examples appearing in many remarkable reference books, or bursting out in my research career. All examples have been carried out step by step as clear as possible. Through the numerous illustrations readers may become familiar with the basic outlook of mathematical methods for physics, recognize the skillful techniques in general, and enable to apply or to extend to advanced problems.

  • Preface(第3頁)
  • Contents(第5頁)
  • 1 Functions of a Complex Variable(第9頁)
    • 1.1 A Brief Review of Analytic Functions(第9頁)
    • 1.2 Cauchy Residue Theorem and Its Applications(第23頁)
    • 1.3 Poisson's Integral and Mittag-Leffler's Expansion(第53頁)
    • 1.4 Evaluations of Inverse Laplace Transform(第58頁)
    • Exercise(第64頁)
  • 2 Conformal Mapping(第69頁)
    • 2.1 Examples of Conformal Mappings(第69頁)
    • 2.2 Transformation of Harmonic Functions(第78頁)
    • 2.3 Applications to Steady Temperatures(第81頁)
    • 2.4 Applications to Electrostatic Potential(第90頁)
    • 2.5 Schwarz-Christoffel Transformation(第101頁)
    • 2.6 Applications to Fluid Flow(第113頁)
    • Exercise(第124頁)
  • 3 Elliptic Functions(第129頁)
    • 3.1 Introduction(第129頁)
    • 3.2 Elliptic Integrals(第135頁)
    • 3.3 Parametric Equation of the Ellipse(第145頁)
    • 3.4 Reduction to the Standard Form(第157頁)
    • 3.5 Complex Argument(第169頁)
    • 3.6 Conformal Mapping(第174頁)
    • 3.7 Applications(第181頁)
    • Exercise(第196頁)
  • 4 Tensor Calculus(第201頁)
    • 4.1 Tensor Algebra(第201頁)
    • 4.2 Fundamental Tensor (Metric)(第207頁)
    • 4.3 Parallel Displacement(第213頁)
    • 4.4 Christoffel Symbols(第214頁)
    • 4.5 Covariant Differentiation(第221頁)
    • 4.6 Geodesics(第228頁)
    • 4.7 Frenet-Serret Formulas(第236頁)
    • 4.8 Riemann-Christoffel Tensors(第241頁)
    • 4.9 Gravity as a Metric Phenomenon(第255頁)
    • Exercise(第269頁)
  • 5 Sturm-Liouville Theory(第271頁)
    • 5.1 Adjoint and Hermitian Operators(第272頁)
    • 5.2 Properties of the Hermitian Operators(第279頁)
    • 5.3 Bessel Inequality and Schwarz Inequality(第284頁)
    • 5.4 Green Function(第290頁)
    • 5.5 Gram-Schmidt Orthogonalization(第317頁)
    • Exercise(第321頁)
  • 6 Gamma Function(第323頁)
    • 6.1 Definition and Properties of Gamma Functions (z)(第323頁)
    • 6.2 Integral Expression of (z)(第328頁)
    • 6.3 Cauchy and Saalschutz Extension of (z) with Re(z)<0(第332頁)
    • 6.4 Digamma Functions And Polygamma Functions(第333頁)
    • 6.5 Bernoulli Numbers And Bernoulli Functions(第339頁)
    • 6.6 Euler-Maclaurin Integration Formula(第342頁)
    • 6.7 Beta Function and Incomplete Functions(第346頁)
    • 6.8 Error Functions(第353頁)
    • 6.9 Dirichlet Integral(第357頁)
    • Exercise(第360頁)
  • 7 Bessel Functions(第365頁)
    • 7.1 Generating Function(第365頁)
    • 7.2 Recurrence Relations(第368頁)
    • 7.3 Integral Expressions of Bessel Function Jn(x)(第370頁)
    • 7.4 Bessel Functions J(x) with Noninteger(第371頁)
    • 7.5 Contour Expression of Bessel Functions(第380頁)
    • 7.6 Orthogonality of Bessel Functions(第383頁)
    • 7.7 The Second Kind Bessel Functions N(x)(第391頁)
    • 7.8 Hankel Functions H(1,2)(x)(第394頁)
    • 7.9 Saddle-Point Method (Steepest Descent)(第396頁)
    • 7.10 Wronskian Formulas(第401頁)
    • 7.11 Modified Bessel Functions(第403頁)
    • 7.12 Spherical Bessel Functions(第410頁)
    • 7.13 Modified Spherical Bessel Functions(第419頁)
    • Exercise(第421頁)
  • 8 Legendre Functions(第425頁)
    • 8.1 Generating Function(第425頁)
    • 8.2 Recurrence Relations(第429頁)
    • 8.3 Orthogonality(第433頁)
    • 8.4 Rodrigues Formula of Legendre Functions(第439頁)
    • 8.5 Legendre Functions of the Second Kind(第444頁)
    • 8.6 Laplace Integral Representation of Legendre Function(第450頁)
    • 8.7 Associated Legendre Functions(第452頁)
    • 8.8 Spherical Harmonic Functions(第462頁)
    • 8.9 Angular Momentum(第468頁)
    • 8.10 Addition Theorem(第474頁)
    • 8.11 Integrals of the Product of Three Spherical Harmonic Functions(第479頁)
    • Exercise(第481頁)
  • 9 Other Special Functions(第485頁)
    • 9.1 Hermite Functions(第485頁)
    • 9.2 Laguerre Functions(第502頁)
    • 9.3 Associated Laguerre Functions(第506頁)
    • 9.4 Chebyshev Polynomials(第514頁)
    • 9.5 Hypergeometric Functions(第526頁)
    • 9.6 Confluent Hypergeometric Functions(第535頁)
    • Exercise(第543頁)
  • 10 Fourier Series and Fourier Transform(第547頁)
    • 10.1 Fourier Series(第547頁)
    • 10.2 Complex Fourier Series(第561頁)
    • 10.3 Applications to Solving Differential Equations(第563頁)
    • 10.4 Fourier Integral(第569頁)
    • 10.5 Properties of Fourier Transform(第583頁)
    • 10.6 Dirac -Function(第601頁)
    • Exercise(第610頁)
  • 11 Laplace Transform(第615頁)
    • 11.1 Definition of Laplace Transform(第615頁)
    • 11.2 Properties of Laplace Transform(第618頁)
    • 11.3 Applications to Special Functions and Differential Equations(第630頁)
    • 11.4 Inverse Laplace Transform(第647頁)
    • 11.5 Operator Calculus(第656頁)
    • 11.6 Useful Integrals(第662頁)
    • Exercise(第669頁)
  • 12 Mellin and Hankel Transform(第673頁)
    • 12.1 Definition of Integral Transform(第673頁)
    • 12.2 Mellin Transform(第678頁)
    • 12.3 Properties of Mellin Transform(第687頁)
    • 12.4 Hankel Transform(第691頁)
    • 12.5 Properties of Hankel Transform(第702頁)
    • 12.6 Relation Between Hankel and Fourier Transforms(第707頁)
    • 12.7 Dual Integral Equations(第714頁)
    • 12.8 Finite Hankel Transform(第722頁)
    • Exercise(第738頁)
  • 13 Integral Equations(第741頁)
    • 13.1 Linear Differential Equations And Integral Equations(第742頁)
    • 13.2 Sturm-Liouville Equation into Integral Equation(第747頁)
    • 13.3 Integral Transforms(第759頁)
    • 13.4 Iteration Method(第767頁)
    • 13.5 Separable Kernels(第769頁)
    • 13.6 Eigenvalues and Eigenfunctions(第772頁)
    • 13.7 Variation-Iteration Method(第777頁)
    • 13.8 Two-Dimensional Green Function(第782頁)
    • 13.9 Three-Dimensional Green Function(第789頁)
    • 13.10 Applications to Heat, Wave, and Schrödinger Equations(第796頁)
    • Exercise(第807頁)
  • 14 Calculus of Variations(第813頁)
    • 14.1 Variational Calculus(第814頁)
    • 14.2 Hamiltonian Principle(第821頁)
    • 14.3 One Dependence, Several Independent Variables(第824頁)
    • 14.4 Several Dependent, Several Independent Variables(第827頁)
    • 14.5 Lagrangian Multipliers(第830頁)
    • 14.6 Variation Subject to Constraints(第835頁)
    • 14.7 Rayleigh-Ritz Method(第842頁)
    • 14.8 Variational Formulation of Eigenfunction Problems(第844頁)
    • 14. Eigenfunction Problems by the Ratio Method(第850頁)
    • Exercise(第855頁)
  • 15 Bibliography(第859頁)
  • Index(第861頁)
紙本書 NT$ 1600
單本電子書
NT$ 1120

還沒安裝 HyRead 3 嗎?馬上免費安裝~
QR Code