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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.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
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| 001 | EBOOKCENTRAL_on1061148486 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
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| 008 | 181105s2018 enk o 001 0 eng d | ||
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| 020 | |a 9781527516168 |q (electronic bk.) | ||
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| 049 | |a UAMI | ||
| 100 | 1 | |a Apostol, Marian, |e author. | |
| 245 | 1 | 0 | |a Equations of mathematical physics / |c by Marian Apostol. |
| 264 | 1 | |a Newcastle upon Tyne, UK : |b Cambridge Scholars Publishing, |c 2018. | |
| 300 | |a 1 online resource (ix, 240 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 500 | |a Includes index. | ||
| 588 | 0 | |a Online resource; title from PDF title page (EBSCO, viewed November 5, 2018). | |
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 520 | |a 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 transforms, special functions, Laplace and Poisson, diffusion and vector equations. These basic tools are a set of methods and techniques, known as the equations of mathematical physics. At first sight, they look like a collection of disparate things. Many students in theoretical physics perceive them as st. | ||
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| 650 | 7 | |a SCIENCE |x Physics |x General. |2 bisacsh | |
| 650 | 7 | |a Mathematical physics |2 fast | |
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