Martin Time-Domain Scattering

Erscheinungsjahr 2021
ISBN: 978-1-108-88074-9
Verlag: Cambridge University Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 180

Reihe: Encyclopedia of Mathematics and its Applications

The wave equation, a classical partial differential equation, has been studied and applied since the eighteenth century. Solving it in the presence of an obstacle, the scatterer, can be achieved using a variety of techniques and has a multitude of applications. This book explains clearly the fundamental ideas of time-domain scattering, including in-depth discussions of separation of variables and integral equations. The author covers both theoretical and computational aspects, and describes applications coming from acoustics (sound waves), elastodynamics (waves in solids), electromagnetics (Maxwell's equations) and hydrodynamics (water waves). The detailed bibliography of papers and books from the last 100 years cement the position of this work as an essential reference on the topic for applied mathematicians, physicists and engineers.

Autoren/Hrsg.

Martin, P. A.

Fachgebiete

• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Naturwissenschaften Physik Mechanik Akustik, Schwingungsanalyse
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Akustik, Tontechnik
• Geisteswissenschaften Musikwissenschaft Musikwissenschaft Allgemein Musikalische Akustik, Tontechnik, Musikaufnahme
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

1. Acoustics and the Wave Equation; 2. Wavefunctions; 3. Characteristics and Discontinuities; 4. Initial-boundary Value Problems; 5. Use of Laplace Transforms; 6. Problems with Spherical Symmetry; 7. Scattering by a Sphere; 8. Scattering Frequencies and the Singularity Expansion Method; 9. Integral Representations; 10. Integral Equations; References; Citation Index; Index.

Über Autor(innen)

Martin, P. A.
P. A. Martin is Professor in the Department of Applied Mathematics and Statistics at Colorado School of Mines. He was the Editor-in-Chief of the SIAM Journal on Applied Mathematics and is the author of Multiple Scattering (Cambridge, 2006).