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3190 results in Mathematical Methods

Page 39 of 160

Time-Domain Scattering
  • P. A. Martin
  • Published online:
    11 June 2021
    Print publication:
    24 June 2021
  • 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.

Deep Learning in Science
  • Pierre Baldi
  • Published online:
    17 April 2021
    Print publication:
    01 July 2021
  • This is the first rigorous, self-contained treatment of the theory of deep learning. Starting with the foundations of the theory and building it up, this is essential reading for any scientists, instructors, and students interested in artificial intelligence and deep learning. It provides guidance on how to think about scientific questions, and leads readers through the history of the field and its fundamental connections to neuroscience. The author discusses many applications to beautiful problems in the natural sciences, in physics, chemistry, and biomedicine. Examples include the search for exotic particles and dark matter in experimental physics, the prediction of molecular properties and reaction outcomes in chemistry, and the prediction of protein structures and the diagnostic analysis of biomedical images in the natural sciences. The text is accompanied by a full set of exercises at different difficulty levels and encourages out-of-the-box thinking.

  • 1 - Newton’s and Einstein’s Gravity

  • Thomas W. Baumgarte, Bowdoin College, Maine, Stuart L. Shapiro, University of Illinois, Urbana-Champaign
  • Book:
    Numerical Relativity: Starting from Scratch
    Published online:
    12 February 2021
    Print publication:
    08 April 2021, pp 1-42
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Page 39 of 160