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6997 results in Mathematical modeling and methods

Page 348 of 350

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.

  • PREFACE

    • By E.A.M., Queens' College Cambridge
  • E. A. Maxwell
  • Book:
    An Analytical Calculus
    Published online:
    05 March 2012
    Print publication:
    01 January 1957, pp xi-xii

  • Summary

    I would express my gratitude to my pupils T. H. Gossling, G. H. Mitchell, D. W. G. Moore and A. Robinson for help with the examples and for suggestions for improvements to the text—an example of the real inversion of normal functions.

    As the fourth volume brings this work to its completion, I record my very deep indebtedness to Dr Sheila M. Edmonds, of Newnham College, Cambridge, who read the whole manuscript most searchingly. Those who know her personally will realize how much trouble she has taken; others would believe it impossible. I am most grateful to her.

    I am very happy to say how much I appreciate the cheerful and inspiring help given by the staff of the Cambridge University Press over a number of years.

Page 348 of 350