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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

BooksJournals

    • Probabilities and Potential, A

      • 1st Edition
      • Volume 29
      • January 1, 1979
      • C. Dellacherie + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 8 5 8 9
      • eBook
        9 7 8 0 0 8 0 8 7 1 4 0 0

    • III: Scattering Theory

      • 1st Edition
      • Volume 3
      • April 28, 1979
      • Michael Reed + 1 more
      • English
      • Paperback
        9 7 8 0 1 2 3 9 5 8 2 7 3
      • Hardback
        9 7 8 0 1 2 5 8 5 0 0 3 2
      • eBook
        9 7 8 0 0 8 0 9 2 5 3 8 7
      Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself. As such, it is the most effective means, sometimes the only means, to study microscopic nature. To understand the importance of scattering theory, consider the variety of ways in which it arises. First, there are various phenomena in nature (like the blue of the sky) which are the result of scattering. In order to understand the phenomenon (and to identify it as the result of scattering) one must understand the underlying dynamics and its scattering theory. Second, one often wants to use the scattering of waves or particles whose dynamics on knows to determine the structure and position of small or inaccessible objects. For example, in x-ray crystallography (which led to the discovery of DNA), tomography, and the detection of underwater objects by sonar, the underlying dynamics is well understood. What one would like to construct are correspondences that link, via the dynamics, the position, shape, and internal structure of the object to the scattering data. Ideally, the correspondence should be an explicit formula which allows one to reconstruct, at least approximately, the object from the scattering data. The main test of any proposed particle dynamics is whether one can construct for the dynamics a scattering theory that predicts the observed experimental data. Scattering theory was not always so central the physics. Even thought the Coulomb cross section could have been computed by Newton, had he bothered to ask the right question, its calculation is generally attributed to Rutherford more than two hundred years later. Of course, Rutherford's calculation was in connection with the first experiment in nuclear physics.

    • Functional Analysis

      • 1st Edition
      • Volume 81
      • November 3, 1978
      • English
      • eBook
        9 7 8 0 0 8 0 8 7 3 9 7 8

    • The Finite Element Method for Elliptic Problems

      • 1st Edition
      • Volume 4
      • January 1, 1978
      • P.G. Ciarlet
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 7 1 7 9
      • eBook
        9 7 8 0 0 8 0 8 7 5 2 5 5
      The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author’s experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on “Additional Bibliography and Comments” should provide many suggestions for conducting seminars.

    • Algorithmic Aspects of Combinatorics

      • 1st Edition
      • January 1, 1978
      • B. Alspach + 2 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 4 9 6 3 6
      • eBook
        9 7 8 1 4 8 3 2 6 5 3 3 9

Related subjects

Mathematics and applied mathematics

Statistics and probability