Essential mathematics for the physical sciences. Volume I, Homogeneous boundary value problems, Fourier methods, and special functions /

Physics is expressed in the language of mathematics; it is deeply ingrained in how physics is taught and how it's practiced. A study of the mathematics used in science is thus a sound intellectual investment for training as scientists and engineers. This first volume of two is centered on metho...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Borden, Brett, 1954- (Autor), Luscombe, James (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, [2017]
Colección:IOP (Series). Release 4.
IOP concise physics.
Temas:
Mathematical physics.
Mathematical Physics.
SCIENCE / Physics / Mathematical & Computational.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Partial differential equations
  • 2. Separation of variables
  • 2.1. Helmholtz equation
  • 2.2. Helmholtz equation in rectangular coordinates
  • 2.3. Helmholtz equation in cylindrical coordinates
  • 2.4. Helmholtz equation in spherical coordinates
  • 2.5. Roadmap : where we are headed
  • 3. Power-series solutions of ODEs
  • 3.1. Analytic functions and the Frobenius method
  • 3.2. Ordinary points
  • 3.3. Regular singular points
  • 3.4. Wronskian method for obtaining a second solution
  • 3.5. Bessel and Neumann functions
  • 3.6. Legendre polynomials
  • 4. Sturm-Liouville theory
  • 4.1. Differential equations as operators
  • 4.2. Sturm-Liouville systems
  • 4.3. The SL eigenvalue problem, L[y] = -[lambda]wy
  • 4.4. Dirac delta function
  • 4.5. Completeness
  • 4.6. Hilbert space : a brief introduction
  • 5. Fourier series and integrals
  • 5.1. Fourier series
  • 5.2. Complex form of Fourier series
  • 5.3. General intervals
  • 5.4. Parseval's theorem
  • 5.5. Back to the delta function
  • 5.6. Fourier transform
  • 5.7. Convolution integral
  • 6. Spherical harmonics and friends
  • 6.1. Properties of the Legendre polynomials, Pl(x)
  • 6.2. Associated Legendre functions, Pl m(x)
  • 6.3. Spherical harmonic functions, Yl m([theta], [phi])
  • 6.4. Addition theorem for Yl m([theta], [phi])
  • 6.5. Laplace equation in spherical coordinates
  • 7. Bessel functions and friends
  • 7.1. Small-argument and asymptotic forms
  • 7.2. Properties of the Bessel functions, Jn(x)
  • 7.3. Orthogonality
  • 7.4. Bessel series
  • 7.5. Fourier-Bessel transform
  • 7.6. Spherical Bessel functions
  • 7.7. Expansion of plane waves in spherical coordinates
  • Appendices
  • A. Topics in linear algebra
  • B. Vector calculus
  • C. Power series
  • D. Gamma function, [Gamma](x).

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