The book's combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs.
The book's combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Preface 1. Introduction 2. Typical equations of mathematical physics. Boundary conditions 3. Cauchy problem for first-order partial differential equations 4. Classification of second-order partial differential equations with linear principal part. Elements of the theory of characteristics 5. Cauchy and mixed problems for the wave equation in R1. Method of travelling waves 6. Cauchy and Goursat problems for a second-order linear hyperbolic equation with two independent variables. Riemann's method 7. Cauchy problem for a 2-dimensional wave equation. The Volterra-D'Adhemar solution 8. Cauchy problem for the wave equation in R3. Methods of averaging and descent. Huygens's principle 9. Basic properties of harmonic functions 10. Green's functions 11. Sequences of harmonic functions. Perron's theorem. Schwarz alternating method 12. Outer boundary-value problems. Elements of potential theory 13. Cauchy problem for heat-conduction equation 14. Maximum principle for parabolic equations 15. Application of Green's formulas. Fundamental identity. Green's functions for Fourier equation 16. Heat potentials 17. Volterra integral equations and their application to solution of boundary-value problems in heat-conduction theory 18. Sequences of parabolic functions 19. Fourier method for bounded regions 20. Integral transform method in unbounded regions 21. Asymptotic expansions. Asymptotic solution of boundary-value problems Appendix I. Elements of vector analysis Appendix II. Elements of theory of Bessel functions Appendix III. Fourier's method and Sturm-Liouville equations Appendix IV. Fourier integral Appendix V. Examples of solution of nontrivial engineering and physical problems References Index.
Preface 1. Introduction 2. Typical equations of mathematical physics. Boundary conditions 3. Cauchy problem for first-order partial differential equations 4. Classification of second-order partial differential equations with linear principal part. Elements of the theory of characteristics 5. Cauchy and mixed problems for the wave equation in R1. Method of travelling waves 6. Cauchy and Goursat problems for a second-order linear hyperbolic equation with two independent variables. Riemann's method 7. Cauchy problem for a 2-dimensional wave equation. The Volterra-D'Adhemar solution 8. Cauchy problem for the wave equation in R3. Methods of averaging and descent. Huygens's principle 9. Basic properties of harmonic functions 10. Green's functions 11. Sequences of harmonic functions. Perron's theorem. Schwarz alternating method 12. Outer boundary-value problems. Elements of potential theory 13. Cauchy problem for heat-conduction equation 14. Maximum principle for parabolic equations 15. Application of Green's formulas. Fundamental identity. Green's functions for Fourier equation 16. Heat potentials 17. Volterra integral equations and their application to solution of boundary-value problems in heat-conduction theory 18. Sequences of parabolic functions 19. Fourier method for bounded regions 20. Integral transform method in unbounded regions 21. Asymptotic expansions. Asymptotic solution of boundary-value problems Appendix I. Elements of vector analysis Appendix II. Elements of theory of Bessel functions Appendix III. Fourier's method and Sturm-Liouville equations Appendix IV. Fourier integral Appendix V. Examples of solution of nontrivial engineering and physical problems References Index.
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