Lectures on selected topics in mathematical physics : elliptic functions and elliptic integrals /

This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may no...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Schwalm, W. (William) (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, [2015]
Colección:IOP (Series). Release 2.
IOP concise physics.
Temas:
Elliptic functions.
SCIENCE / Physics / Mathematical & Computational.
Mathematical Physics.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Preface
  • 1. Elliptic functions as trigonometry
  • 1.1. Definition of Jacobian elliptic functions and trigonometric identities
  • 1.2. Differential equations
  • 1.3. Anharmonic oscillator
  • 2. Differential equations satisfied by the Jacobi elliptic functions : pendula
  • 2.1. Oscillatory motion of a pendulum at large amplitude
  • 2.2. Motion traversing the whole circle
  • 2.3. The sine-Gordon equation : a series of pendula
  • 2.4. Series of pendula : 'super luminal' case
  • 3. General reduction of the DE in terms of Jacobi functions
  • 3.1. Linear fractional transformation and cross ratio
  • 3.2. Reduction of general quartic case
  • 3.3. Finding the coefficients of the linear fractional transformation
  • 4. Elliptic integrals
  • 4.1. Review of complex variables up through residues
  • 4.2. Branching and multi-valued functions in complex planes
  • 4.3. Elliptic integrals and elliptic functions in complex planes
  • 4.4. Example
  • 4.5. Reduction of the most general elliptic integral in terms of the three Legendre forms.

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