Book contents
- Frontmatter
- Contents
- Preface
- Chapter 1 Introduction
- Chapter 2 Typical equations of mathematical physics. Boundary conditions
- Chapter 3 Cauchy problem for first-order partial differential equations
- Chapter 4 Classification of second-order partial differential equations with linear principal part. Elements of the theory of characteristics
- Chapter 5 Cauchy and mixed problems for the wave equation in ℝ1. Method of traveling waves
- Chapter 6 Cauchy and Goursat problems for a second-order linear hyperbolic equation with two independent variables. Riemann's method
- Chapter 7 Cauchy problem for a 2-dimensional wave equation. The Volterra–D'Adhemar solution
- Chapter 8 Cauchy problem for the wave equation in ℝ3. Methods of averaging and descent. Huygens's principle
- Chapter 9 Basic properties of harmonic functions
- Chapter 10 Green's functions
- Chapter 11 Sequences of harmonic functions. Perron's theorem. Schwarz alternating method
- Chapter 12 Outer boundary-value problems. Elements of potential theory
- Chapter 13 Cauchy problem for heat-conduction equation
- Chapter 14 Maximum principle for parabolic equations
- Chapter 15 Application of Green's formulas. Fundamental identity. Green's functions for Fourier equation
- Chapter 16 Heat potentials
- Chapter 17 Volterra integral equations and their application to solution of boundary-value problems in heat-conduction theory
- Chapter 18 Sequences of parabolic functions
- Chapter 19 Fourier method for bounded regions
- Chapter 20 Integral transform method in unbounded regions
- Chapter 21 Asymptotic expansions. Asymptotic solution of boundary-value problems
- Appendix 1 Elements of vector analysis
- Appendix 2 Elements of theory of Bessel functions
- Appendix 3 Fourier's method and Sturm–Liouville equations
- Appendix 4 Fourier integral
- Appendix 5 Examples of solution of nontrivial engineering and physical problems
- References
- Index
Index
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Chapter 1 Introduction
- Chapter 2 Typical equations of mathematical physics. Boundary conditions
- Chapter 3 Cauchy problem for first-order partial differential equations
- Chapter 4 Classification of second-order partial differential equations with linear principal part. Elements of the theory of characteristics
- Chapter 5 Cauchy and mixed problems for the wave equation in ℝ1. Method of traveling waves
- Chapter 6 Cauchy and Goursat problems for a second-order linear hyperbolic equation with two independent variables. Riemann's method
- Chapter 7 Cauchy problem for a 2-dimensional wave equation. The Volterra–D'Adhemar solution
- Chapter 8 Cauchy problem for the wave equation in ℝ3. Methods of averaging and descent. Huygens's principle
- Chapter 9 Basic properties of harmonic functions
- Chapter 10 Green's functions
- Chapter 11 Sequences of harmonic functions. Perron's theorem. Schwarz alternating method
- Chapter 12 Outer boundary-value problems. Elements of potential theory
- Chapter 13 Cauchy problem for heat-conduction equation
- Chapter 14 Maximum principle for parabolic equations
- Chapter 15 Application of Green's formulas. Fundamental identity. Green's functions for Fourier equation
- Chapter 16 Heat potentials
- Chapter 17 Volterra integral equations and their application to solution of boundary-value problems in heat-conduction theory
- Chapter 18 Sequences of parabolic functions
- Chapter 19 Fourier method for bounded regions
- Chapter 20 Integral transform method in unbounded regions
- Chapter 21 Asymptotic expansions. Asymptotic solution of boundary-value problems
- Appendix 1 Elements of vector analysis
- Appendix 2 Elements of theory of Bessel functions
- Appendix 3 Fourier's method and Sturm–Liouville equations
- Appendix 4 Fourier integral
- Appendix 5 Examples of solution of nontrivial engineering and physical problems
- References
- Index
Summary
- Type
- Chapter
- Information
- Partial Differential Equations in Classical Mathematical Physics , pp. 672 - 677Publisher: Cambridge University PressPrint publication year: 1994