Cargando…
Equations of mathematical physics /
The differential equations of mathematical physics have a twofold character: their physical content and their mathematical solutions. This book discusses the basic tools of theoretical physicists, applied mathematicians, and engineers, providing detailed insights into linear algebra, Fourier transfo...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Newcastle upon Tyne, UK :
Cambridge Scholars Publishing,
2018.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; Contents; 1 Preface; 2 Introductory Elements; 2.1 Linear Algebra; 2.1.1 Vectors; 2.1.2 Matrices; 2.1.3 Quadratic forms. Diagonalization; 2.1.4 Bessel inequality; 2.2 Integral Equations; 2.2.1 Fredholm equations; 2.2.2 Degenerate kernels; 2.2.3 Volterra equation; 2.3 Calculus of Variations; 2.3.1 Extrema points; 2.3.2 Variational problems; 2.4 Fourier Transform; 2.4.1 Delta function; 2.4.2 Fourier transform; 2.4.3 Fourier series; 2.4.4 Periodic functions; 2.4.5 Particular orthogonal circular functions; 2.5 Cauchy Integral; 2.5.1 Cauchy integral
- 2.5.2 Integrals. Laplace and Mellin transforms2.6 Series Expansions; 2.6.1 Taylor series; 2.6.2 Laurent series; 2.6.3 A series of Darboux; 2.6.4 Bernoulli numbers and polynomials; 2.6.5 Euler-Maclaurin formula; 2.6.6 Expansion in rational fractions. Infinite products; 2.6.7 Asymptotic series; 2.6.8 Steepest descent; 2.6.9 Numerical series and series of functions; 2.7 Curvilinear Coordinates; 2.7.1 Laplacian; 2.7.2 Divergence and curl; 2.8 Coulomb Potential; 2.8.1 Basic equation; 2.8.2 Fourier transform; 2.8.3 2+1 dimensions; 2.9 Bessel Functions; 2.9.1 Definition; 2.9.2 m − th order
- 2.9.3 Completeness, orthogonality and addition theorem2.9.4 Other Bessel functions; 2.9.5 A few recurrence relations; 2.9.6 Bessel functions of half-integer order; 2.10 Legendre Polynomials; 2.10.1 Definition; 2.10.2 Generating function and recurrence relations; 2.10.3 Legendre's equation; 2.11 Spherical Harmonics; 2.11.1 Associated Legendre functions; 2.11.2 Spherical harmonics; 2.11.3 Poisson's integral; 2.11.4 Laplace equation; 2.11.5 Spherical Bessel functions; 2.12 Spherical Waves; 2.12.1 Wave equation; 2.12.2 2+1 dimensions; 2.12.3 Spherical wave at infinity, Hankel function
- 2.12.4 Two dimensions, cylindrical waves2.12.5 Helmholtz equation, addition theorem; 2.13 Physical Equations; 2.13.1 Physical equations; 2.13.2 Laplace equation; 2.13.3 Associated Legendre functions; 2.13.4 Bessel functions; 2.13.5 Wave equation; 2.13.6 Heat equation; 2.14 Poisson Equation; 2.14.1 Generalized Poisson equation; 2.14.2 Planar geometry; 2.14.3 Cylindrical geometry; 2.14.4 Spherical geometry; 2.15 Transcendental Functions; 2.15.1 Differential equations. Hermite polynomials; 2.15.2 Airy function; 2.15.3 Hypergeometric function
- 2.15.4 Laguerre polynomials and other orthogonal polynomials2.15.5 Gamma function; 2.15.6 Zeta function; 2.15.7 Mathieu functions; 2.15.8 Elliptic functions; 3 Differential Equations. Generalities; 4 The Equation of the Harmonic Oscillator; 4.1 Homogeneous equation (free equation); 4.2 Inhomogeneous equation. Fundamental solution; 4.3 Green function; 4.4 Another representation of the solution. The Green theorem; 4.5 Image sources; 4.6 Generalized equation; 4.7 Another Green function; 4.8 Damped harmonic oscillator; 4.9 Resonance; 5 Laplace and Poisson Equations; 5.1 Green functions