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6965 results in Mathematical modeling and methods

Page 346 of 349

Mathematical Modelling of Natural Phenomena
  • Mathematical Modelling of Natural Phenomena (MMNP) is an international research journal, which publishes top-level original and review papers, short communications and proceedings on mathematical modelling in biology, medicine, chemistry, physics, and other areas. The journal is essentially functioning on the basis of topical issues representing active areas of research. Each topical issue has its own editorial board. The authors are invited to submit papers to the announced issues or to suggest new issues.The journal publishes research articles and reviews within the whole field of mathematical modelling, and it will continue to provide information on the latest trends and developments in this ever-expanding subject.

ESAIM: Mathematical Modelling and Numerical Analysis
  • The journal publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study - e.g. structure, well-posedness, solution properties - of a mathematical formulation of a problem (or class of problems). Numerical Analysis comprises the formulation and study - e.g. stability, convergence, computational complexity - of a numerical approximation or solution approach to a mathematically formulated problem (or class of problems).Papers submitted to ESAIM: M2AN should satisfy two additional criteria. First, papers should focus on mathematical models or numerical methods germane to current research topics and applications. Second, papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance. Applications may be drawn from the broad range of physical, life, and social sciences, and the many engineering disciplines.

The ANZIAM Journal

ESAIM: Control, Optimisation and Calculus of Variations
  • ESAIM: COCV publishes rapidly and efficiently papers and surveys in the areas of control, optimisation and calculus of variations. Articles may be theoretical,computational, or both, and they will cover contemporary subjects with impact on forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines.

  • 1 - Introduction

  • M. J. Lighthill
  • Book:
    An Introduction to Fourier Analysis and Generalised Functions
    Published online:
    05 March 2012
    Print publication:
    01 January 1958, pp 1-14

  • Summary

    Scope and purpose of the book

    This book grew out of an undergraduate course in the University of Manchester, in which the author attempted to expound the most useful facts about Fourier series and integrals. It seemed to him on planning the course that a satisfactory account must make use of functions like the delta function of Dirac which are outside the usual scope of function theory. Now, Laurent Schwartz in his Théorie des distributions* has evolved a rigorous theory of these, while Professor Temple has given a version of the theory (Generalised functions) which appears to be more readily intelligible to students. With some slight further simplifications the author found that the theory of generalised functions was accessible to undergraduates in their final year, and that it greatly curtails the labour of understanding Fourier transforms, as well as making available a technique for their asymptotic estimation which seems superior to previous techniques. This is an approach in which the theory of Fourier series appears as a special case, the Fourier transform of a periodic function being a ‘row of delta functions’.

    The book which grew out of the course therefore covers not only the principal results concerning Fourier transforms and Fourier series, but also serves as an introduction to the theory of generalised functions, whose general properties as well as those useful in Fourier analysis are derived, simply but without any departure from rigorous standards of mathematical proof.

Page 346 of 349