Mathematical methods for physics:
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| Main Author: | |
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| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
2021
|
| Edition: | 45th anniversary edition |
| Subjects: | |
| Online Access: | TUM01 |
| Item Description: | Description based on publisher supplied metadata and other sources |
| Physical Description: | 1 Online-Ressource Illustrationen, Diagramme |
| ISBN: | 9781000261127 9781003037460 |
Staff View
MARC
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| 100 | 1 | |a Wyld, Henry William, Jr. |d 1928-2013 |e Verfasser |0 (DE-588)1246986086 |4 aut | |
| 245 | 1 | 0 | |a Mathematical methods for physics |c H.W. Wyld ; edited by Gary Powell |
| 250 | |a 45th anniversary edition | ||
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press |c 2021 | |
| 264 | 4 | |c © 2021 | |
| 300 | |a 1 Online-Ressource |b Illustrationen, Diagramme | ||
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| 500 | |a Description based on publisher supplied metadata and other sources | ||
| 505 | 8 | |a Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- List of Figures -- List of Tables -- Editor's Preface to the 45th Anniversary Edition -- Preface to the First Edition -- Section I Homogeneous Boundary Value Problems and Special Functions -- Chapter 1 The Partial Differential Equations of Mathematical Physics -- 1.1 Introduction -- 1.2 Heat Conduction and Diffusion -- 1.3 Quantum Mechanics -- 1.4 Waves on Strings and Membranes -- 1.5 Hydrodynamics and Aerodynamics -- 1.6 Acoustic Waves in a Compressible Fluid -- 1.7 Irrotational Flow in an Incompressible Fluid -- 1.8 Electrodynamics -- 1.8.1 Time Independent Phenomena -- 1.8.2 Vacuum Equations -- 1.8.3 General Case -- 1.9 Summary -- Problems -- Chapter 2 Separation of Variables and Ordinary Differential Equations -- 2.1 Introduction -- 2.2 Separation of Variables -- 2.3 Rectangular Coordinates (x, y, z) -- 2.4 Cylindrical Coordinates (r, θ, z) -- 2.5 Spherical Coordinates (r, θ, ?) -- 2.6 Series Solutions of Ordinary Differential Equations: Preliminaries -- 2.7 Expansion About a Regular Singular Point -- 2.8 Sturm-Liouville Eigenvalue Problem -- 2.9 Fourier Series and Integrals -- 2.10 Numerical Solution of Ordinary Differential Equations -- Problems -- Chapter 3 Spherical Harmonics and Applications -- 3.1 Introduction -- 3.2 Series Solution of Legendre's Equation-Legendre Polynomials -- 3.3 Properties of Legendre Polynomials -- 3.4 The Second Solution Ql(x) of Legendre's Equation -- 3.5 Associated Legendre Polynomials -- 3.6 Spherical Harmonics -- 3.7 The Spherical Harmonics Addition Theorem -- 3.8 Multipole Expansions -- 3.9 Laplace's Equation in Spherical Coordinates -- 3.9.1 Interior Problem I, r ≤ a with ψ(a, θ, ϕ)= u(θ, ϕ) given -- 3.9.2 Interior Problem II, r ≤ a with ∂ψ/∂rr=a = v(θ, ϕ) given -- 3.9.3 Exterior Problem, r ≥ a with ψ(a, θ, ϕ)= u(θ, ϕ) given | |
| 505 | 8 | |a 3.9.4 Exterior Problem, r ≥ a with ∂ψ/∂rr=a = v(θ, ϕ) given -- 3.9.5 Region Between Two Spheres, a ≤ r ≤ b with ψ(a, θ, ϕ)=u(θ, ϕ) and ψ(b, θ, ϕ)= v(θ, ϕ) given -- 3.9.6 Notes on Solving Other Boundary Conditions on Regions Between Two Spheres -- 3.10 Conducting Sphere in a Uniform External Electric Field -- 3.11 Flow of an Incompressible Fluid Around a Spherical Obstacle -- Problems -- Chapter 4 Bessel Functions and Applications -- 4.1 Introduction -- 4.2 Series Solutions of Bessel's Equation -- Bessel Functions -- 4.3 Neumann Functions -- 4.4 Small Argument and Asymptotic Expansions -- 4.5 Bessel Functions of Imaginary Argument -- 4.6 Laplace's Equation in Cylindrical Coordinates -- 4.7 Interior of a Cylinder of Finite Length -- 4.8 The Sturm-Liouville Eigenvalue Problem and Application of The Expansion Theorem -- 4.9 Interior of a Cylinder of Finite Length - Continued -- 4.10 Exterior of an Infinitely Long Cylinder -- 4.11 Cylinder in an External Field -- 4.12 Space between Two Infinite Planes -- 4.13 Fourier Bessel Transforms -- 4.14 Space between Two Infinite Planes - Continued -- Problems -- Chapter 5 Normal Mode Eigenvalue Problems -- 5.1 Introduction -- 5.2 Reduction of the Diffusion Equation and Wave Equation to an Eigenvalue Problem -- 5.3 The Vibrating String -- 5.4 The Vibrating Drumhead -- 5.5 Heat Conduction in a Cylinder of Finite Length -- 5.6 Particle in a Cylindrical Box (Quantum Mechanics) -- 5.7 Normal Modes of an Acoustic Resonant Cavity -- 5.8 Acoustic Wave Guide -- Problems -- Chapter 6 Spherical Bessel Functions and Applications -- 6.1 Introduction -- 6.2 Formulas for Spherical Bessel Functions in Terms of Elementary Functions -- 6.3 Eigenvalue Problem and Application of the Expansion Theorem -- 6.4 Expansion of Plane and Spherical Waves in Spherical Coordinates -- 6.5 The Emission of Spherical Waves | |
| 505 | 8 | |a 6.6 Scattering of Waves by a Sphere -- Problems -- Summary of Part I -- Section II Inhomogeneous Problems, Green's Functions, and Integral Equations -- Chapter 7 Dielectric and Magnetic Media -- 7.1 Introduction -- 7.2 Macroscopic Electrostatics in the Presence of Dielectrics -- 7.3 Boundary Value Problems in Dielectrics -- 7.3.1 Free Charge Distribution ρF Embedded in an Infinite Uniform Dielectric with a Constant Dielectric Constant ε -- 7.3.2 Point Charge in Front of a Semi-infinite Dielectric -- 7.3.3 Dielectric Sphere in a Uniform External Electric Field -- 7.4 Magnetostatics and the Multipole Expansion for the Vector Potential -- 7.5 Magnetic Media -- 7.6 Boundary Value Problems in Magnetic Media -- 7.6.1 Uniformly Magnetized Sphere, M Given -- 7.6.2 Magnetic Sphere in a Uniform External Magnetic Field -- 7.6.3 Long Straight Wire Carrying Current I Parallel to a Semi-infinite Slab of Material of Permeability μ -- Problems -- Chapter 8 Green's Functions: Part One -- 8.1 Introduction -- 8.2 Ordinary Differential Equations -- 8.3 General Theory, Various Boundary Conditions -- 8.4 The Bowed Stretched String -- 8.5 Expansion of Green's Function in Eigenfunctions -- 8.6 Poisson's Equation -- 8.7 Poisson's Equation for All Space -- 8.8 Electrostatics with Boundary Conditions on Surfaces at Finite Distances - The Image Method -- 8.9 Expansion of the Green's Function for the Interior of a Sphere in Series -- 8.10 The Helmholtz Equation - The Forced Drumhead -- 8.11 Eigenfunction Expansion of the Green's Function for the Helmholtz Equation -- Problems -- Chapter 9 Green's Functions: Part Two -- 9.1 Introduction -- 9.2 The Helmholtz Equation for Infinite Regions, Radiation, and the Wave Equation -- Sinusoidal Time Dependence -- 9.3 General Time Dependence -- 9.4 The Wave Equation | |
| 505 | 8 | |a 9.5 The Wave Equation for All Space, No Boundaries at Finite Distances -- 9.6 Field Due to a Point Source -- 9.6.1 Point Source Moving with Constant Velocity, v < -- c -- 9.6.2 Point Source Moving with Constant Velocity, v > -- c -- 9.7 The Diffusion Equation -- 9.8 The Diffusion Equation for All Space, No Boundaries at Finite Distances -- Problems -- Chapter 10 Integral Equations -- 10.1 Introduction -- 10.2 Quantum Theory of Scattering -- 10.3 Types of Integral Equations -- 10.3.1 First Kind -- 10.3.2 Second Kind -- 10.3.3 Volterra -- 10.3.4 Eigenvalue Problem -- 10.4 Integral Equations with Separable Kernels -- 10.5 Convolution Integral Equations -- 10.6 Iteration - Liouville-Neumann Series -- 10.7 Numerical Solution -- 10.8 Fredholm's Formulas -- 10.9 Conditions for Validity of Fredholm's Formulas -- 10.10 Hilbert-Schmidt Theory -- Problems -- Section III Complex Variable Techniques -- Chapter 11 Complex Variables -- Basic Theory -- 11.1 Introduction -- 11.2 Analytic Functions -- The Cauchy-Riemann Equations -- 11.3 Power Series -- 11.4 Multivalued Functions -- Cuts -- Riemann Sheets -- 11.5 Contour Integrals -- Cauchy's Theorem -- 11.6 Cauchy's Integral Formula -- 11.7 Taylor and Laurent Expansions -- 11.8 Analytic Continuation -- Problems -- Chapter 12 Evaluation of Integrals -- 12.1 Introduction -- 12.2 The Residue Theorem -- 12.3 Rational Functions (−∞, ∞) -- 12.4 Exponential Factors -- Jordan's Lemma -- 12.5 Integrals on the Range (0, ∞) -- 12.6 Angular Integrals -- 12.7 Transforming the Contour -- 12.8 Partial Fraction and Product Expansions -- Problems -- Chapter 13 Dispersion Relations -- 13.1 Introduction -- 13.2 Plemelj Formulas -- Dirac's Formula -- 13.3 Discontinuity Problem -- 13.4 Dispersion Relations -- Spectral Representations -- 13.5 Examples -- 13.6 Integral Equations with Cauchy Kernels -- Problems | |
| 505 | 8 | |a Chapter 14 Special Functions -- 14.1 Introduction -- 14.2 The Gamma Function -- 14.3 Asymptotic Expansions -- Stirling's Formula -- 14.4 The Hypergeometric Function -- 14.5 Legendre Functions -- 14.6 Bessel Functions -- 14.7 Asymptotic Expansions for Bessel Functions -- Problems -- Chapter 15 Integral Transforms in the Complex Plane -- 15.1 Introduction -- 15.2 The Calculation of Green's Functions by Fourier Transform Methods -- 15.2.1 The Helmholtz Equation -- 15.2.2 The Wave Equation -- 15.2.3 The Klein-Gordon Equation -- 15.3 One-Sided Fourier Transforms -- Laplace Transforms -- 15.4 Linear Differential Equations with Constant Coefficients -- 15.5 Integral Equations of Convolution Type -- 15.6 Mellin Transforms -- 15.7 Partial Differential Equations -- 15.8 The Wiener-Hopf Method -- 15.8.1 Potential Given on Semi-Infinite Plate -- 15.8.2 Diffraction by a Knife Edge -- Problems -- Bibliography -- Index | |
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| author | Wyld, Henry William, Jr. 1928-2013 |
| author2 | Powell, Gary |
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| author_GND | (DE-588)1246986086 |
| author_facet | Wyld, Henry William, Jr. 1928-2013 Powell, Gary |
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| author_sort | Wyld, Henry William, Jr. 1928-2013 |
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| contents | Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- List of Figures -- List of Tables -- Editor's Preface to the 45th Anniversary Edition -- Preface to the First Edition -- Section I Homogeneous Boundary Value Problems and Special Functions -- Chapter 1 The Partial Differential Equations of Mathematical Physics -- 1.1 Introduction -- 1.2 Heat Conduction and Diffusion -- 1.3 Quantum Mechanics -- 1.4 Waves on Strings and Membranes -- 1.5 Hydrodynamics and Aerodynamics -- 1.6 Acoustic Waves in a Compressible Fluid -- 1.7 Irrotational Flow in an Incompressible Fluid -- 1.8 Electrodynamics -- 1.8.1 Time Independent Phenomena -- 1.8.2 Vacuum Equations -- 1.8.3 General Case -- 1.9 Summary -- Problems -- Chapter 2 Separation of Variables and Ordinary Differential Equations -- 2.1 Introduction -- 2.2 Separation of Variables -- 2.3 Rectangular Coordinates (x, y, z) -- 2.4 Cylindrical Coordinates (r, θ, z) -- 2.5 Spherical Coordinates (r, θ, ?) -- 2.6 Series Solutions of Ordinary Differential Equations: Preliminaries -- 2.7 Expansion About a Regular Singular Point -- 2.8 Sturm-Liouville Eigenvalue Problem -- 2.9 Fourier Series and Integrals -- 2.10 Numerical Solution of Ordinary Differential Equations -- Problems -- Chapter 3 Spherical Harmonics and Applications -- 3.1 Introduction -- 3.2 Series Solution of Legendre's Equation-Legendre Polynomials -- 3.3 Properties of Legendre Polynomials -- 3.4 The Second Solution Ql(x) of Legendre's Equation -- 3.5 Associated Legendre Polynomials -- 3.6 Spherical Harmonics -- 3.7 The Spherical Harmonics Addition Theorem -- 3.8 Multipole Expansions -- 3.9 Laplace's Equation in Spherical Coordinates -- 3.9.1 Interior Problem I, r ≤ a with ψ(a, θ, ϕ)= u(θ, ϕ) given -- 3.9.2 Interior Problem II, r ≤ a with ∂ψ/∂rr=a = v(θ, ϕ) given -- 3.9.3 Exterior Problem, r ≥ a with ψ(a, θ, ϕ)= u(θ, ϕ) given 3.9.4 Exterior Problem, r ≥ a with ∂ψ/∂rr=a = v(θ, ϕ) given -- 3.9.5 Region Between Two Spheres, a ≤ r ≤ b with ψ(a, θ, ϕ)=u(θ, ϕ) and ψ(b, θ, ϕ)= v(θ, ϕ) given -- 3.9.6 Notes on Solving Other Boundary Conditions on Regions Between Two Spheres -- 3.10 Conducting Sphere in a Uniform External Electric Field -- 3.11 Flow of an Incompressible Fluid Around a Spherical Obstacle -- Problems -- Chapter 4 Bessel Functions and Applications -- 4.1 Introduction -- 4.2 Series Solutions of Bessel's Equation -- Bessel Functions -- 4.3 Neumann Functions -- 4.4 Small Argument and Asymptotic Expansions -- 4.5 Bessel Functions of Imaginary Argument -- 4.6 Laplace's Equation in Cylindrical Coordinates -- 4.7 Interior of a Cylinder of Finite Length -- 4.8 The Sturm-Liouville Eigenvalue Problem and Application of The Expansion Theorem -- 4.9 Interior of a Cylinder of Finite Length - Continued -- 4.10 Exterior of an Infinitely Long Cylinder -- 4.11 Cylinder in an External Field -- 4.12 Space between Two Infinite Planes -- 4.13 Fourier Bessel Transforms -- 4.14 Space between Two Infinite Planes - Continued -- Problems -- Chapter 5 Normal Mode Eigenvalue Problems -- 5.1 Introduction -- 5.2 Reduction of the Diffusion Equation and Wave Equation to an Eigenvalue Problem -- 5.3 The Vibrating String -- 5.4 The Vibrating Drumhead -- 5.5 Heat Conduction in a Cylinder of Finite Length -- 5.6 Particle in a Cylindrical Box (Quantum Mechanics) -- 5.7 Normal Modes of an Acoustic Resonant Cavity -- 5.8 Acoustic Wave Guide -- Problems -- Chapter 6 Spherical Bessel Functions and Applications -- 6.1 Introduction -- 6.2 Formulas for Spherical Bessel Functions in Terms of Elementary Functions -- 6.3 Eigenvalue Problem and Application of the Expansion Theorem -- 6.4 Expansion of Plane and Spherical Waves in Spherical Coordinates -- 6.5 The Emission of Spherical Waves 6.6 Scattering of Waves by a Sphere -- Problems -- Summary of Part I -- Section II Inhomogeneous Problems, Green's Functions, and Integral Equations -- Chapter 7 Dielectric and Magnetic Media -- 7.1 Introduction -- 7.2 Macroscopic Electrostatics in the Presence of Dielectrics -- 7.3 Boundary Value Problems in Dielectrics -- 7.3.1 Free Charge Distribution ρF Embedded in an Infinite Uniform Dielectric with a Constant Dielectric Constant ε -- 7.3.2 Point Charge in Front of a Semi-infinite Dielectric -- 7.3.3 Dielectric Sphere in a Uniform External Electric Field -- 7.4 Magnetostatics and the Multipole Expansion for the Vector Potential -- 7.5 Magnetic Media -- 7.6 Boundary Value Problems in Magnetic Media -- 7.6.1 Uniformly Magnetized Sphere, M Given -- 7.6.2 Magnetic Sphere in a Uniform External Magnetic Field -- 7.6.3 Long Straight Wire Carrying Current I Parallel to a Semi-infinite Slab of Material of Permeability μ -- Problems -- Chapter 8 Green's Functions: Part One -- 8.1 Introduction -- 8.2 Ordinary Differential Equations -- 8.3 General Theory, Various Boundary Conditions -- 8.4 The Bowed Stretched String -- 8.5 Expansion of Green's Function in Eigenfunctions -- 8.6 Poisson's Equation -- 8.7 Poisson's Equation for All Space -- 8.8 Electrostatics with Boundary Conditions on Surfaces at Finite Distances - The Image Method -- 8.9 Expansion of the Green's Function for the Interior of a Sphere in Series -- 8.10 The Helmholtz Equation - The Forced Drumhead -- 8.11 Eigenfunction Expansion of the Green's Function for the Helmholtz Equation -- Problems -- Chapter 9 Green's Functions: Part Two -- 9.1 Introduction -- 9.2 The Helmholtz Equation for Infinite Regions, Radiation, and the Wave Equation -- Sinusoidal Time Dependence -- 9.3 General Time Dependence -- 9.4 The Wave Equation 9.5 The Wave Equation for All Space, No Boundaries at Finite Distances -- 9.6 Field Due to a Point Source -- 9.6.1 Point Source Moving with Constant Velocity, v < -- c -- 9.6.2 Point Source Moving with Constant Velocity, v > -- c -- 9.7 The Diffusion Equation -- 9.8 The Diffusion Equation for All Space, No Boundaries at Finite Distances -- Problems -- Chapter 10 Integral Equations -- 10.1 Introduction -- 10.2 Quantum Theory of Scattering -- 10.3 Types of Integral Equations -- 10.3.1 First Kind -- 10.3.2 Second Kind -- 10.3.3 Volterra -- 10.3.4 Eigenvalue Problem -- 10.4 Integral Equations with Separable Kernels -- 10.5 Convolution Integral Equations -- 10.6 Iteration - Liouville-Neumann Series -- 10.7 Numerical Solution -- 10.8 Fredholm's Formulas -- 10.9 Conditions for Validity of Fredholm's Formulas -- 10.10 Hilbert-Schmidt Theory -- Problems -- Section III Complex Variable Techniques -- Chapter 11 Complex Variables -- Basic Theory -- 11.1 Introduction -- 11.2 Analytic Functions -- The Cauchy-Riemann Equations -- 11.3 Power Series -- 11.4 Multivalued Functions -- Cuts -- Riemann Sheets -- 11.5 Contour Integrals -- Cauchy's Theorem -- 11.6 Cauchy's Integral Formula -- 11.7 Taylor and Laurent Expansions -- 11.8 Analytic Continuation -- Problems -- Chapter 12 Evaluation of Integrals -- 12.1 Introduction -- 12.2 The Residue Theorem -- 12.3 Rational Functions (−∞, ∞) -- 12.4 Exponential Factors -- Jordan's Lemma -- 12.5 Integrals on the Range (0, ∞) -- 12.6 Angular Integrals -- 12.7 Transforming the Contour -- 12.8 Partial Fraction and Product Expansions -- Problems -- Chapter 13 Dispersion Relations -- 13.1 Introduction -- 13.2 Plemelj Formulas -- Dirac's Formula -- 13.3 Discontinuity Problem -- 13.4 Dispersion Relations -- Spectral Representations -- 13.5 Examples -- 13.6 Integral Equations with Cauchy Kernels -- Problems Chapter 14 Special Functions -- 14.1 Introduction -- 14.2 The Gamma Function -- 14.3 Asymptotic Expansions -- Stirling's Formula -- 14.4 The Hypergeometric Function -- 14.5 Legendre Functions -- 14.6 Bessel Functions -- 14.7 Asymptotic Expansions for Bessel Functions -- Problems -- Chapter 15 Integral Transforms in the Complex Plane -- 15.1 Introduction -- 15.2 The Calculation of Green's Functions by Fourier Transform Methods -- 15.2.1 The Helmholtz Equation -- 15.2.2 The Wave Equation -- 15.2.3 The Klein-Gordon Equation -- 15.3 One-Sided Fourier Transforms -- Laplace Transforms -- 15.4 Linear Differential Equations with Constant Coefficients -- 15.5 Integral Equations of Convolution Type -- 15.6 Mellin Transforms -- 15.7 Partial Differential Equations -- 15.8 The Wiener-Hopf Method -- 15.8.1 Potential Given on Semi-Infinite Plate -- 15.8.2 Diffraction by a Knife Edge -- Problems -- Bibliography -- Index |
| ctrlnum | (ZDB-30-PQE)EBC6377807 (ZDB-30-PAD)EBC6377807 (ZDB-89-EBL)EBL6377807 (OCoLC)1202451134 (DE-599)BVBBV047442147 |
| dewey-full | 530.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15 |
| dewey-search | 530.15 |
| dewey-sort | 3530.15 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| discipline_str_mv | Physik Mathematik |
| edition | 45th anniversary edition |
| format | Electronic eBook |
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Wyld ; edited by Gary Powell</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">45th anniversary edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boca Raton ; London ; New York</subfield><subfield code="b">CRC Press</subfield><subfield code="c">2021</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2021</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource</subfield><subfield code="b">Illustrationen, Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Description based on publisher supplied metadata and other sources</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- List of Figures -- List of Tables -- Editor's Preface to the 45th Anniversary Edition -- Preface to the First Edition -- Section I Homogeneous Boundary Value Problems and Special Functions -- Chapter 1 The Partial Differential Equations of Mathematical Physics -- 1.1 Introduction -- 1.2 Heat Conduction and Diffusion -- 1.3 Quantum Mechanics -- 1.4 Waves on Strings and Membranes -- 1.5 Hydrodynamics and Aerodynamics -- 1.6 Acoustic Waves in a Compressible Fluid -- 1.7 Irrotational Flow in an Incompressible Fluid -- 1.8 Electrodynamics -- 1.8.1 Time Independent Phenomena -- 1.8.2 Vacuum Equations -- 1.8.3 General Case -- 1.9 Summary -- Problems -- Chapter 2 Separation of Variables and Ordinary Differential Equations -- 2.1 Introduction -- 2.2 Separation of Variables -- 2.3 Rectangular Coordinates (x, y, z) -- 2.4 Cylindrical Coordinates (r, θ, z) -- 2.5 Spherical Coordinates (r, θ, ?) -- 2.6 Series Solutions of Ordinary Differential Equations: Preliminaries -- 2.7 Expansion About a Regular Singular Point -- 2.8 Sturm-Liouville Eigenvalue Problem -- 2.9 Fourier Series and Integrals -- 2.10 Numerical Solution of Ordinary Differential Equations -- Problems -- Chapter 3 Spherical Harmonics and Applications -- 3.1 Introduction -- 3.2 Series Solution of Legendre's Equation-Legendre Polynomials -- 3.3 Properties of Legendre Polynomials -- 3.4 The Second Solution Ql(x) of Legendre's Equation -- 3.5 Associated Legendre Polynomials -- 3.6 Spherical Harmonics -- 3.7 The Spherical Harmonics Addition Theorem -- 3.8 Multipole Expansions -- 3.9 Laplace's Equation in Spherical Coordinates -- 3.9.1 Interior Problem I, r ≤ a with ψ(a, θ, ϕ)= u(θ, ϕ) given -- 3.9.2 Interior Problem II, r ≤ a with ∂ψ/∂rr=a = v(θ, ϕ) given -- 3.9.3 Exterior Problem, r ≥ a with ψ(a, θ, ϕ)= u(θ, ϕ) given</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3.9.4 Exterior Problem, r ≥ a with ∂ψ/∂rr=a = v(θ, ϕ) given -- 3.9.5 Region Between Two Spheres, a ≤ r ≤ b with ψ(a, θ, ϕ)=u(θ, ϕ) and ψ(b, θ, ϕ)= v(θ, ϕ) given -- 3.9.6 Notes on Solving Other Boundary Conditions on Regions Between Two Spheres -- 3.10 Conducting Sphere in a Uniform External Electric Field -- 3.11 Flow of an Incompressible Fluid Around a Spherical Obstacle -- Problems -- Chapter 4 Bessel Functions and Applications -- 4.1 Introduction -- 4.2 Series Solutions of Bessel's Equation -- Bessel Functions -- 4.3 Neumann Functions -- 4.4 Small Argument and Asymptotic Expansions -- 4.5 Bessel Functions of Imaginary Argument -- 4.6 Laplace's Equation in Cylindrical Coordinates -- 4.7 Interior of a Cylinder of Finite Length -- 4.8 The Sturm-Liouville Eigenvalue Problem and Application of The Expansion Theorem -- 4.9 Interior of a Cylinder of Finite Length - Continued -- 4.10 Exterior of an Infinitely Long Cylinder -- 4.11 Cylinder in an External Field -- 4.12 Space between Two Infinite Planes -- 4.13 Fourier Bessel Transforms -- 4.14 Space between Two Infinite Planes - Continued -- Problems -- Chapter 5 Normal Mode Eigenvalue Problems -- 5.1 Introduction -- 5.2 Reduction of the Diffusion Equation and Wave Equation to an Eigenvalue Problem -- 5.3 The Vibrating String -- 5.4 The Vibrating Drumhead -- 5.5 Heat Conduction in a Cylinder of Finite Length -- 5.6 Particle in a Cylindrical Box (Quantum Mechanics) -- 5.7 Normal Modes of an Acoustic Resonant Cavity -- 5.8 Acoustic Wave Guide -- Problems -- Chapter 6 Spherical Bessel Functions and Applications -- 6.1 Introduction -- 6.2 Formulas for Spherical Bessel Functions in Terms of Elementary Functions -- 6.3 Eigenvalue Problem and Application of the Expansion Theorem -- 6.4 Expansion of Plane and Spherical Waves in Spherical Coordinates -- 6.5 The Emission of Spherical Waves</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">6.6 Scattering of Waves by a Sphere -- Problems -- Summary of Part I -- Section II Inhomogeneous Problems, Green's Functions, and Integral Equations -- Chapter 7 Dielectric and Magnetic Media -- 7.1 Introduction -- 7.2 Macroscopic Electrostatics in the Presence of Dielectrics -- 7.3 Boundary Value Problems in Dielectrics -- 7.3.1 Free Charge Distribution ρF Embedded in an Infinite Uniform Dielectric with a Constant Dielectric Constant ε -- 7.3.2 Point Charge in Front of a Semi-infinite Dielectric -- 7.3.3 Dielectric Sphere in a Uniform External Electric Field -- 7.4 Magnetostatics and the Multipole Expansion for the Vector Potential -- 7.5 Magnetic Media -- 7.6 Boundary Value Problems in Magnetic Media -- 7.6.1 Uniformly Magnetized Sphere, M Given -- 7.6.2 Magnetic Sphere in a Uniform External Magnetic Field -- 7.6.3 Long Straight Wire Carrying Current I Parallel to a Semi-infinite Slab of Material of Permeability μ -- Problems -- Chapter 8 Green's Functions: Part One -- 8.1 Introduction -- 8.2 Ordinary Differential Equations -- 8.3 General Theory, Various Boundary Conditions -- 8.4 The Bowed Stretched String -- 8.5 Expansion of Green's Function in Eigenfunctions -- 8.6 Poisson's Equation -- 8.7 Poisson's Equation for All Space -- 8.8 Electrostatics with Boundary Conditions on Surfaces at Finite Distances - The Image Method -- 8.9 Expansion of the Green's Function for the Interior of a Sphere in Series -- 8.10 The Helmholtz Equation - The Forced Drumhead -- 8.11 Eigenfunction Expansion of the Green's Function for the Helmholtz Equation -- Problems -- Chapter 9 Green's Functions: Part Two -- 9.1 Introduction -- 9.2 The Helmholtz Equation for Infinite Regions, Radiation, and the Wave Equation -- Sinusoidal Time Dependence -- 9.3 General Time Dependence -- 9.4 The Wave Equation</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">9.5 The Wave Equation for All Space, No Boundaries at Finite Distances -- 9.6 Field Due to a Point Source -- 9.6.1 Point Source Moving with Constant Velocity, v &lt -- c -- 9.6.2 Point Source Moving with Constant Velocity, v &gt -- c -- 9.7 The Diffusion Equation -- 9.8 The Diffusion Equation for All Space, No Boundaries at Finite Distances -- Problems -- Chapter 10 Integral Equations -- 10.1 Introduction -- 10.2 Quantum Theory of Scattering -- 10.3 Types of Integral Equations -- 10.3.1 First Kind -- 10.3.2 Second Kind -- 10.3.3 Volterra -- 10.3.4 Eigenvalue Problem -- 10.4 Integral Equations with Separable Kernels -- 10.5 Convolution Integral Equations -- 10.6 Iteration - Liouville-Neumann Series -- 10.7 Numerical Solution -- 10.8 Fredholm's Formulas -- 10.9 Conditions for Validity of Fredholm's Formulas -- 10.10 Hilbert-Schmidt Theory -- Problems -- Section III Complex Variable Techniques -- Chapter 11 Complex Variables -- Basic Theory -- 11.1 Introduction -- 11.2 Analytic Functions -- The Cauchy-Riemann Equations -- 11.3 Power Series -- 11.4 Multivalued Functions -- Cuts -- Riemann Sheets -- 11.5 Contour Integrals -- Cauchy's Theorem -- 11.6 Cauchy's Integral Formula -- 11.7 Taylor and Laurent Expansions -- 11.8 Analytic Continuation -- Problems -- Chapter 12 Evaluation of Integrals -- 12.1 Introduction -- 12.2 The Residue Theorem -- 12.3 Rational Functions (−∞, ∞) -- 12.4 Exponential Factors -- Jordan's Lemma -- 12.5 Integrals on the Range (0, ∞) -- 12.6 Angular Integrals -- 12.7 Transforming the Contour -- 12.8 Partial Fraction and Product Expansions -- Problems -- Chapter 13 Dispersion Relations -- 13.1 Introduction -- 13.2 Plemelj Formulas -- Dirac's Formula -- 13.3 Discontinuity Problem -- 13.4 Dispersion Relations -- Spectral Representations -- 13.5 Examples -- 13.6 Integral Equations with Cauchy Kernels -- Problems</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Chapter 14 Special Functions -- 14.1 Introduction -- 14.2 The Gamma Function -- 14.3 Asymptotic Expansions -- Stirling's Formula -- 14.4 The Hypergeometric Function -- 14.5 Legendre Functions -- 14.6 Bessel Functions -- 14.7 Asymptotic Expansions for Bessel Functions -- Problems -- Chapter 15 Integral Transforms in the Complex Plane -- 15.1 Introduction -- 15.2 The Calculation of Green's Functions by Fourier Transform Methods -- 15.2.1 The Helmholtz Equation -- 15.2.2 The Wave Equation -- 15.2.3 The Klein-Gordon Equation -- 15.3 One-Sided Fourier Transforms -- Laplace Transforms -- 15.4 Linear Differential Equations with Constant Coefficients -- 15.5 Integral Equations of Convolution Type -- 15.6 Mellin Transforms -- 15.7 Partial Differential Equations -- 15.8 The Wiener-Hopf Method -- 15.8.1 Potential Given on Semi-Infinite Plate -- 15.8.2 Diffraction by a Knife Edge -- Problems -- Bibliography -- Index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical physics</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematische Methode</subfield><subfield code="0">(DE-588)4155620-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematische Physik</subfield><subfield code="0">(DE-588)4037952-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Physik</subfield><subfield code="0">(DE-588)4045956-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Physik</subfield><subfield code="0">(DE-588)4045956-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Mathematische Methode</subfield><subfield code="0">(DE-588)4155620-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Mathematische Physik</subfield><subfield code="0">(DE-588)4037952-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Powell, Gary</subfield><subfield code="4">edt</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="a">Wyld, H. 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| id | DE-604.BV047442147 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:01:24Z |
| indexdate | 2024-07-10T09:12:16Z |
| institution | BVB |
| isbn | 9781000261127 9781003037460 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032844299 |
| oclc_num | 1202451134 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM |
| owner_facet | DE-91 DE-BY-TUM |
| physical | 1 Online-Ressource Illustrationen, Diagramme |
| psigel | ZDB-30-PQE ZDB-30-PQE TUM_PDA_PQE_Kauf |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Wyld, Henry William, Jr. 1928-2013 Verfasser (DE-588)1246986086 aut Mathematical methods for physics H.W. Wyld ; edited by Gary Powell 45th anniversary edition Boca Raton ; London ; New York CRC Press 2021 © 2021 1 Online-Ressource Illustrationen, Diagramme txt rdacontent c rdamedia cr rdacarrier Description based on publisher supplied metadata and other sources Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- List of Figures -- List of Tables -- Editor's Preface to the 45th Anniversary Edition -- Preface to the First Edition -- Section I Homogeneous Boundary Value Problems and Special Functions -- Chapter 1 The Partial Differential Equations of Mathematical Physics -- 1.1 Introduction -- 1.2 Heat Conduction and Diffusion -- 1.3 Quantum Mechanics -- 1.4 Waves on Strings and Membranes -- 1.5 Hydrodynamics and Aerodynamics -- 1.6 Acoustic Waves in a Compressible Fluid -- 1.7 Irrotational Flow in an Incompressible Fluid -- 1.8 Electrodynamics -- 1.8.1 Time Independent Phenomena -- 1.8.2 Vacuum Equations -- 1.8.3 General Case -- 1.9 Summary -- Problems -- Chapter 2 Separation of Variables and Ordinary Differential Equations -- 2.1 Introduction -- 2.2 Separation of Variables -- 2.3 Rectangular Coordinates (x, y, z) -- 2.4 Cylindrical Coordinates (r, θ, z) -- 2.5 Spherical Coordinates (r, θ, ?) -- 2.6 Series Solutions of Ordinary Differential Equations: Preliminaries -- 2.7 Expansion About a Regular Singular Point -- 2.8 Sturm-Liouville Eigenvalue Problem -- 2.9 Fourier Series and Integrals -- 2.10 Numerical Solution of Ordinary Differential Equations -- Problems -- Chapter 3 Spherical Harmonics and Applications -- 3.1 Introduction -- 3.2 Series Solution of Legendre's Equation-Legendre Polynomials -- 3.3 Properties of Legendre Polynomials -- 3.4 The Second Solution Ql(x) of Legendre's Equation -- 3.5 Associated Legendre Polynomials -- 3.6 Spherical Harmonics -- 3.7 The Spherical Harmonics Addition Theorem -- 3.8 Multipole Expansions -- 3.9 Laplace's Equation in Spherical Coordinates -- 3.9.1 Interior Problem I, r ≤ a with ψ(a, θ, ϕ)= u(θ, ϕ) given -- 3.9.2 Interior Problem II, r ≤ a with ∂ψ/∂rr=a = v(θ, ϕ) given -- 3.9.3 Exterior Problem, r ≥ a with ψ(a, θ, ϕ)= u(θ, ϕ) given 3.9.4 Exterior Problem, r ≥ a with ∂ψ/∂rr=a = v(θ, ϕ) given -- 3.9.5 Region Between Two Spheres, a ≤ r ≤ b with ψ(a, θ, ϕ)=u(θ, ϕ) and ψ(b, θ, ϕ)= v(θ, ϕ) given -- 3.9.6 Notes on Solving Other Boundary Conditions on Regions Between Two Spheres -- 3.10 Conducting Sphere in a Uniform External Electric Field -- 3.11 Flow of an Incompressible Fluid Around a Spherical Obstacle -- Problems -- Chapter 4 Bessel Functions and Applications -- 4.1 Introduction -- 4.2 Series Solutions of Bessel's Equation -- Bessel Functions -- 4.3 Neumann Functions -- 4.4 Small Argument and Asymptotic Expansions -- 4.5 Bessel Functions of Imaginary Argument -- 4.6 Laplace's Equation in Cylindrical Coordinates -- 4.7 Interior of a Cylinder of Finite Length -- 4.8 The Sturm-Liouville Eigenvalue Problem and Application of The Expansion Theorem -- 4.9 Interior of a Cylinder of Finite Length - Continued -- 4.10 Exterior of an Infinitely Long Cylinder -- 4.11 Cylinder in an External Field -- 4.12 Space between Two Infinite Planes -- 4.13 Fourier Bessel Transforms -- 4.14 Space between Two Infinite Planes - Continued -- Problems -- Chapter 5 Normal Mode Eigenvalue Problems -- 5.1 Introduction -- 5.2 Reduction of the Diffusion Equation and Wave Equation to an Eigenvalue Problem -- 5.3 The Vibrating String -- 5.4 The Vibrating Drumhead -- 5.5 Heat Conduction in a Cylinder of Finite Length -- 5.6 Particle in a Cylindrical Box (Quantum Mechanics) -- 5.7 Normal Modes of an Acoustic Resonant Cavity -- 5.8 Acoustic Wave Guide -- Problems -- Chapter 6 Spherical Bessel Functions and Applications -- 6.1 Introduction -- 6.2 Formulas for Spherical Bessel Functions in Terms of Elementary Functions -- 6.3 Eigenvalue Problem and Application of the Expansion Theorem -- 6.4 Expansion of Plane and Spherical Waves in Spherical Coordinates -- 6.5 The Emission of Spherical Waves 6.6 Scattering of Waves by a Sphere -- Problems -- Summary of Part I -- Section II Inhomogeneous Problems, Green's Functions, and Integral Equations -- Chapter 7 Dielectric and Magnetic Media -- 7.1 Introduction -- 7.2 Macroscopic Electrostatics in the Presence of Dielectrics -- 7.3 Boundary Value Problems in Dielectrics -- 7.3.1 Free Charge Distribution ρF Embedded in an Infinite Uniform Dielectric with a Constant Dielectric Constant ε -- 7.3.2 Point Charge in Front of a Semi-infinite Dielectric -- 7.3.3 Dielectric Sphere in a Uniform External Electric Field -- 7.4 Magnetostatics and the Multipole Expansion for the Vector Potential -- 7.5 Magnetic Media -- 7.6 Boundary Value Problems in Magnetic Media -- 7.6.1 Uniformly Magnetized Sphere, M Given -- 7.6.2 Magnetic Sphere in a Uniform External Magnetic Field -- 7.6.3 Long Straight Wire Carrying Current I Parallel to a Semi-infinite Slab of Material of Permeability μ -- Problems -- Chapter 8 Green's Functions: Part One -- 8.1 Introduction -- 8.2 Ordinary Differential Equations -- 8.3 General Theory, Various Boundary Conditions -- 8.4 The Bowed Stretched String -- 8.5 Expansion of Green's Function in Eigenfunctions -- 8.6 Poisson's Equation -- 8.7 Poisson's Equation for All Space -- 8.8 Electrostatics with Boundary Conditions on Surfaces at Finite Distances - The Image Method -- 8.9 Expansion of the Green's Function for the Interior of a Sphere in Series -- 8.10 The Helmholtz Equation - The Forced Drumhead -- 8.11 Eigenfunction Expansion of the Green's Function for the Helmholtz Equation -- Problems -- Chapter 9 Green's Functions: Part Two -- 9.1 Introduction -- 9.2 The Helmholtz Equation for Infinite Regions, Radiation, and the Wave Equation -- Sinusoidal Time Dependence -- 9.3 General Time Dependence -- 9.4 The Wave Equation 9.5 The Wave Equation for All Space, No Boundaries at Finite Distances -- 9.6 Field Due to a Point Source -- 9.6.1 Point Source Moving with Constant Velocity, v < -- c -- 9.6.2 Point Source Moving with Constant Velocity, v > -- c -- 9.7 The Diffusion Equation -- 9.8 The Diffusion Equation for All Space, No Boundaries at Finite Distances -- Problems -- Chapter 10 Integral Equations -- 10.1 Introduction -- 10.2 Quantum Theory of Scattering -- 10.3 Types of Integral Equations -- 10.3.1 First Kind -- 10.3.2 Second Kind -- 10.3.3 Volterra -- 10.3.4 Eigenvalue Problem -- 10.4 Integral Equations with Separable Kernels -- 10.5 Convolution Integral Equations -- 10.6 Iteration - Liouville-Neumann Series -- 10.7 Numerical Solution -- 10.8 Fredholm's Formulas -- 10.9 Conditions for Validity of Fredholm's Formulas -- 10.10 Hilbert-Schmidt Theory -- Problems -- Section III Complex Variable Techniques -- Chapter 11 Complex Variables -- Basic Theory -- 11.1 Introduction -- 11.2 Analytic Functions -- The Cauchy-Riemann Equations -- 11.3 Power Series -- 11.4 Multivalued Functions -- Cuts -- Riemann Sheets -- 11.5 Contour Integrals -- Cauchy's Theorem -- 11.6 Cauchy's Integral Formula -- 11.7 Taylor and Laurent Expansions -- 11.8 Analytic Continuation -- Problems -- Chapter 12 Evaluation of Integrals -- 12.1 Introduction -- 12.2 The Residue Theorem -- 12.3 Rational Functions (−∞, ∞) -- 12.4 Exponential Factors -- Jordan's Lemma -- 12.5 Integrals on the Range (0, ∞) -- 12.6 Angular Integrals -- 12.7 Transforming the Contour -- 12.8 Partial Fraction and Product Expansions -- Problems -- Chapter 13 Dispersion Relations -- 13.1 Introduction -- 13.2 Plemelj Formulas -- Dirac's Formula -- 13.3 Discontinuity Problem -- 13.4 Dispersion Relations -- Spectral Representations -- 13.5 Examples -- 13.6 Integral Equations with Cauchy Kernels -- Problems Chapter 14 Special Functions -- 14.1 Introduction -- 14.2 The Gamma Function -- 14.3 Asymptotic Expansions -- Stirling's Formula -- 14.4 The Hypergeometric Function -- 14.5 Legendre Functions -- 14.6 Bessel Functions -- 14.7 Asymptotic Expansions for Bessel Functions -- Problems -- Chapter 15 Integral Transforms in the Complex Plane -- 15.1 Introduction -- 15.2 The Calculation of Green's Functions by Fourier Transform Methods -- 15.2.1 The Helmholtz Equation -- 15.2.2 The Wave Equation -- 15.2.3 The Klein-Gordon Equation -- 15.3 One-Sided Fourier Transforms -- Laplace Transforms -- 15.4 Linear Differential Equations with Constant Coefficients -- 15.5 Integral Equations of Convolution Type -- 15.6 Mellin Transforms -- 15.7 Partial Differential Equations -- 15.8 The Wiener-Hopf Method -- 15.8.1 Potential Given on Semi-Infinite Plate -- 15.8.2 Diffraction by a Knife Edge -- Problems -- Bibliography -- Index Mathematical physics Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Physik (DE-588)4045956-1 s Mathematische Methode (DE-588)4155620-3 s DE-604 Mathematische Physik (DE-588)4037952-8 s Powell, Gary edt Erscheint auch als Wyld, H. W. Mathematical Methods for Physics Milton : Taylor & Francis Group,c2020 Druck-Ausgabe, Hardcover 978-0-367-47708-0 Erscheint auch als Druck-Ausgabe, Paperback 978-0-367-47973-2 |
| spellingShingle | Wyld, Henry William, Jr. 1928-2013 Mathematical methods for physics Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- List of Figures -- List of Tables -- Editor's Preface to the 45th Anniversary Edition -- Preface to the First Edition -- Section I Homogeneous Boundary Value Problems and Special Functions -- Chapter 1 The Partial Differential Equations of Mathematical Physics -- 1.1 Introduction -- 1.2 Heat Conduction and Diffusion -- 1.3 Quantum Mechanics -- 1.4 Waves on Strings and Membranes -- 1.5 Hydrodynamics and Aerodynamics -- 1.6 Acoustic Waves in a Compressible Fluid -- 1.7 Irrotational Flow in an Incompressible Fluid -- 1.8 Electrodynamics -- 1.8.1 Time Independent Phenomena -- 1.8.2 Vacuum Equations -- 1.8.3 General Case -- 1.9 Summary -- Problems -- Chapter 2 Separation of Variables and Ordinary Differential Equations -- 2.1 Introduction -- 2.2 Separation of Variables -- 2.3 Rectangular Coordinates (x, y, z) -- 2.4 Cylindrical Coordinates (r, θ, z) -- 2.5 Spherical Coordinates (r, θ, ?) -- 2.6 Series Solutions of Ordinary Differential Equations: Preliminaries -- 2.7 Expansion About a Regular Singular Point -- 2.8 Sturm-Liouville Eigenvalue Problem -- 2.9 Fourier Series and Integrals -- 2.10 Numerical Solution of Ordinary Differential Equations -- Problems -- Chapter 3 Spherical Harmonics and Applications -- 3.1 Introduction -- 3.2 Series Solution of Legendre's Equation-Legendre Polynomials -- 3.3 Properties of Legendre Polynomials -- 3.4 The Second Solution Ql(x) of Legendre's Equation -- 3.5 Associated Legendre Polynomials -- 3.6 Spherical Harmonics -- 3.7 The Spherical Harmonics Addition Theorem -- 3.8 Multipole Expansions -- 3.9 Laplace's Equation in Spherical Coordinates -- 3.9.1 Interior Problem I, r ≤ a with ψ(a, θ, ϕ)= u(θ, ϕ) given -- 3.9.2 Interior Problem II, r ≤ a with ∂ψ/∂rr=a = v(θ, ϕ) given -- 3.9.3 Exterior Problem, r ≥ a with ψ(a, θ, ϕ)= u(θ, ϕ) given 3.9.4 Exterior Problem, r ≥ a with ∂ψ/∂rr=a = v(θ, ϕ) given -- 3.9.5 Region Between Two Spheres, a ≤ r ≤ b with ψ(a, θ, ϕ)=u(θ, ϕ) and ψ(b, θ, ϕ)= v(θ, ϕ) given -- 3.9.6 Notes on Solving Other Boundary Conditions on Regions Between Two Spheres -- 3.10 Conducting Sphere in a Uniform External Electric Field -- 3.11 Flow of an Incompressible Fluid Around a Spherical Obstacle -- Problems -- Chapter 4 Bessel Functions and Applications -- 4.1 Introduction -- 4.2 Series Solutions of Bessel's Equation -- Bessel Functions -- 4.3 Neumann Functions -- 4.4 Small Argument and Asymptotic Expansions -- 4.5 Bessel Functions of Imaginary Argument -- 4.6 Laplace's Equation in Cylindrical Coordinates -- 4.7 Interior of a Cylinder of Finite Length -- 4.8 The Sturm-Liouville Eigenvalue Problem and Application of The Expansion Theorem -- 4.9 Interior of a Cylinder of Finite Length - Continued -- 4.10 Exterior of an Infinitely Long Cylinder -- 4.11 Cylinder in an External Field -- 4.12 Space between Two Infinite Planes -- 4.13 Fourier Bessel Transforms -- 4.14 Space between Two Infinite Planes - Continued -- Problems -- Chapter 5 Normal Mode Eigenvalue Problems -- 5.1 Introduction -- 5.2 Reduction of the Diffusion Equation and Wave Equation to an Eigenvalue Problem -- 5.3 The Vibrating String -- 5.4 The Vibrating Drumhead -- 5.5 Heat Conduction in a Cylinder of Finite Length -- 5.6 Particle in a Cylindrical Box (Quantum Mechanics) -- 5.7 Normal Modes of an Acoustic Resonant Cavity -- 5.8 Acoustic Wave Guide -- Problems -- Chapter 6 Spherical Bessel Functions and Applications -- 6.1 Introduction -- 6.2 Formulas for Spherical Bessel Functions in Terms of Elementary Functions -- 6.3 Eigenvalue Problem and Application of the Expansion Theorem -- 6.4 Expansion of Plane and Spherical Waves in Spherical Coordinates -- 6.5 The Emission of Spherical Waves 6.6 Scattering of Waves by a Sphere -- Problems -- Summary of Part I -- Section II Inhomogeneous Problems, Green's Functions, and Integral Equations -- Chapter 7 Dielectric and Magnetic Media -- 7.1 Introduction -- 7.2 Macroscopic Electrostatics in the Presence of Dielectrics -- 7.3 Boundary Value Problems in Dielectrics -- 7.3.1 Free Charge Distribution ρF Embedded in an Infinite Uniform Dielectric with a Constant Dielectric Constant ε -- 7.3.2 Point Charge in Front of a Semi-infinite Dielectric -- 7.3.3 Dielectric Sphere in a Uniform External Electric Field -- 7.4 Magnetostatics and the Multipole Expansion for the Vector Potential -- 7.5 Magnetic Media -- 7.6 Boundary Value Problems in Magnetic Media -- 7.6.1 Uniformly Magnetized Sphere, M Given -- 7.6.2 Magnetic Sphere in a Uniform External Magnetic Field -- 7.6.3 Long Straight Wire Carrying Current I Parallel to a Semi-infinite Slab of Material of Permeability μ -- Problems -- Chapter 8 Green's Functions: Part One -- 8.1 Introduction -- 8.2 Ordinary Differential Equations -- 8.3 General Theory, Various Boundary Conditions -- 8.4 The Bowed Stretched String -- 8.5 Expansion of Green's Function in Eigenfunctions -- 8.6 Poisson's Equation -- 8.7 Poisson's Equation for All Space -- 8.8 Electrostatics with Boundary Conditions on Surfaces at Finite Distances - The Image Method -- 8.9 Expansion of the Green's Function for the Interior of a Sphere in Series -- 8.10 The Helmholtz Equation - The Forced Drumhead -- 8.11 Eigenfunction Expansion of the Green's Function for the Helmholtz Equation -- Problems -- Chapter 9 Green's Functions: Part Two -- 9.1 Introduction -- 9.2 The Helmholtz Equation for Infinite Regions, Radiation, and the Wave Equation -- Sinusoidal Time Dependence -- 9.3 General Time Dependence -- 9.4 The Wave Equation 9.5 The Wave Equation for All Space, No Boundaries at Finite Distances -- 9.6 Field Due to a Point Source -- 9.6.1 Point Source Moving with Constant Velocity, v < -- c -- 9.6.2 Point Source Moving with Constant Velocity, v > -- c -- 9.7 The Diffusion Equation -- 9.8 The Diffusion Equation for All Space, No Boundaries at Finite Distances -- Problems -- Chapter 10 Integral Equations -- 10.1 Introduction -- 10.2 Quantum Theory of Scattering -- 10.3 Types of Integral Equations -- 10.3.1 First Kind -- 10.3.2 Second Kind -- 10.3.3 Volterra -- 10.3.4 Eigenvalue Problem -- 10.4 Integral Equations with Separable Kernels -- 10.5 Convolution Integral Equations -- 10.6 Iteration - Liouville-Neumann Series -- 10.7 Numerical Solution -- 10.8 Fredholm's Formulas -- 10.9 Conditions for Validity of Fredholm's Formulas -- 10.10 Hilbert-Schmidt Theory -- Problems -- Section III Complex Variable Techniques -- Chapter 11 Complex Variables -- Basic Theory -- 11.1 Introduction -- 11.2 Analytic Functions -- The Cauchy-Riemann Equations -- 11.3 Power Series -- 11.4 Multivalued Functions -- Cuts -- Riemann Sheets -- 11.5 Contour Integrals -- Cauchy's Theorem -- 11.6 Cauchy's Integral Formula -- 11.7 Taylor and Laurent Expansions -- 11.8 Analytic Continuation -- Problems -- Chapter 12 Evaluation of Integrals -- 12.1 Introduction -- 12.2 The Residue Theorem -- 12.3 Rational Functions (−∞, ∞) -- 12.4 Exponential Factors -- Jordan's Lemma -- 12.5 Integrals on the Range (0, ∞) -- 12.6 Angular Integrals -- 12.7 Transforming the Contour -- 12.8 Partial Fraction and Product Expansions -- Problems -- Chapter 13 Dispersion Relations -- 13.1 Introduction -- 13.2 Plemelj Formulas -- Dirac's Formula -- 13.3 Discontinuity Problem -- 13.4 Dispersion Relations -- Spectral Representations -- 13.5 Examples -- 13.6 Integral Equations with Cauchy Kernels -- Problems Chapter 14 Special Functions -- 14.1 Introduction -- 14.2 The Gamma Function -- 14.3 Asymptotic Expansions -- Stirling's Formula -- 14.4 The Hypergeometric Function -- 14.5 Legendre Functions -- 14.6 Bessel Functions -- 14.7 Asymptotic Expansions for Bessel Functions -- Problems -- Chapter 15 Integral Transforms in the Complex Plane -- 15.1 Introduction -- 15.2 The Calculation of Green's Functions by Fourier Transform Methods -- 15.2.1 The Helmholtz Equation -- 15.2.2 The Wave Equation -- 15.2.3 The Klein-Gordon Equation -- 15.3 One-Sided Fourier Transforms -- Laplace Transforms -- 15.4 Linear Differential Equations with Constant Coefficients -- 15.5 Integral Equations of Convolution Type -- 15.6 Mellin Transforms -- 15.7 Partial Differential Equations -- 15.8 The Wiener-Hopf Method -- 15.8.1 Potential Given on Semi-Infinite Plate -- 15.8.2 Diffraction by a Knife Edge -- Problems -- Bibliography -- Index Mathematical physics Mathematische Methode (DE-588)4155620-3 gnd Mathematische Physik (DE-588)4037952-8 gnd Physik (DE-588)4045956-1 gnd |
| subject_GND | (DE-588)4155620-3 (DE-588)4037952-8 (DE-588)4045956-1 |
| title | Mathematical methods for physics |
| title_auth | Mathematical methods for physics |
| title_exact_search | Mathematical methods for physics |
| title_exact_search_txtP | Mathematical methods for physics |
| title_full | Mathematical methods for physics H.W. Wyld ; edited by Gary Powell |
| title_fullStr | Mathematical methods for physics H.W. Wyld ; edited by Gary Powell |
| title_full_unstemmed | Mathematical methods for physics H.W. Wyld ; edited by Gary Powell |
| title_short | Mathematical methods for physics |
| title_sort | mathematical methods for physics |
| topic | Mathematical physics Mathematische Methode (DE-588)4155620-3 gnd Mathematische Physik (DE-588)4037952-8 gnd Physik (DE-588)4045956-1 gnd |
| topic_facet | Mathematical physics Mathematische Methode Mathematische Physik Physik |
| work_keys_str_mv | AT wyldhenrywilliamjr mathematicalmethodsforphysics AT powellgary mathematicalmethodsforphysics |