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Partial differential equations in physics (engelsk)
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Summary: Partial differential equations in physics.
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Seneste udgave, e-bogFront Cover; Partial Differential Equations in Physics; Copyright Page; Foreword; Editor's Foreword; Table of Contents; Chapter 1. Fourier Series and Integrals; 1. Fourier Series; 2. Example of a Discontinuous Function.Gibbs' Phenomenon and Non-Uniform Convergence; 3. On the Convergence of Fourier Series; 4. Passage to the Fourier Integral; 5. Development by Spherical Harmonics; 6. Generalizations: Oscillating and Osculating Approximations.Anhar-monic Fourier Analysis. An Example of Non-Final Determination of Coefficients; Chapter 2. Introduction to Partial Differential Equations ; 7. How the Simplest Partial Differential Equations Arise8. Elliptic, Hyperbolic and Parabolic Type. Theory of Characteristics; 9. Differences Among Hyperbolic, Elliptic, and Parabolic Differential Equations. The Analytic Character of Their Solutions; 10. Green's Theorem and Green's Function for Linear, and, in Particular, for Elliptic Differential Equations; 11. Riemann's Integration of the Hyperbolic Differential Equation; 12. Green's Theorem in Heat Conduction . The Principal Solution of Heat Conduction; Chapter III. Boundray Value Problems in Heat Conduction ; 13. Heat Conductors Bounded on One Side14. The Problem of the Earth's Temperature; 15. The Problem of a Ring-Shaped Heat Conductor; 16. Linear Heat Conductors Bounded on Both Ends; 17. Reflection in the Plane and in Space; 18. Uniqueness of Solution for Arbitrarily Shaped Heat Conductors; Chapter IV. Cylinder and Sphere Problems; 19. Bessel and Hankel Functions; 20. Heat Equalization in a Cylinder; 21. More About Bessc.1 Functions; 22. Spherical Harmonics and Potential Theory; 23. Green's Function of Potential Theory for the Sphere. Sphere and Circle Problems for Other Differential Equations ; 24. More About Spherical HarmoniesAppendix I: Reflection on a Circular-Cylindrical or Spherical Mirror; Appendix II: Additions to the Riemann Problem of Sound Waves in Section 11; Chapter V. Eigenfunctions and Eigen Values; 25. Eigen Values and Eigcnfunctions of the Vibrating Membrane; 26. General Remarks Concerning the Boundary Value Problems of Acous- tics and of Heat Conduction; 27. Free and Forccd Oscillations . Crecn's Function for the Wave Equation; 28. Infinite Domains and Continuous Spectra of Eigen Values. The Con- dition of Radiation ; 29. The Eigen Value Spectrum of Wave Mechanics . Balmer's Term30. Green's Function for the Wave Mechanical Scattering Problem. The Rutherford Formula of Nuclear Physics; Appendix I: Normalization of the Eigenfunctions in the Infinite Domain; Appendix II: A New Method for the Solution of the Exterior Boundary Value Problem of the Wave Equation Presented for the Special Case of the Sphere; Appendix III: The Wave Mechanical Eigenfunctions of the Scattering Problem in Parabolic Coordinates; Appendix IV: Plane and Spherical Waves in Unlimited Space of an Arbitrary Number of Dimensions ; Chapter VI. Problems of Radio
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