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Books in Real functions

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Delta Functions

  • 2nd Edition
  • March 31, 2009
  • R F Hoskins
  • English
  • eBook
    9 7 8 - 0 - 8 5 7 0 9 - 9 3 5 - 8
Delta Functions has now been updated, restructured and modernised into a second edition, to answer specific difficulties typically found by students encountering delta functions for the first time. In particular, the treatment of the Laplace transform has been revised with this in mind. The chapter on Schwartz distributions has been considerably extended and the book is supplemented by a fuller review of Nonstandard Analysis and a survey of alternative infinitesimal treatments of generalised functions. Dealing with a difficult subject in a simple and straightforward way, the text is readily accessible to a broad audience of scientists, mathematicians and engineers. It can be used as a working manual in its own right, and serves as a preparation for the study of more advanced treatises. Little more than a standard background in calculus is assumed, and attention is focused on techniques, with a liberal selection of worked examples and exercises.

Regression Analysis

  • 2nd Edition
  • March 27, 2006
  • Rudolf J. Freund + 2 more
  • English
  • Hardback
    9 7 8 - 0 - 1 2 - 0 8 8 5 9 7 - 8
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 2 2 9 7 - 5
Regression Analysis provides complete coverage of the classical methods of statistical analysis. It is designed to give students an understanding of the purpose of statistical analyses, to allow the student to determine, at least to some degree, the correct type of statistical analyses to be performed in a given situation, and have some appreciation of what constitutes good experimental design.

Mathematical Inequalities

  • 1st Edition
  • Volume 67
  • May 4, 2005
  • B. G. Pachpatte
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 4 5 9 3 9 - 4
The book addresses many important new developments in the field. All the topics covered are of great interest to the readers because such inequalities have become a major tool in the analysis of various branches of mathematics.

Theories of Generalised Functions

  • 1st Edition
  • January 1, 2005
  • R F Hoskins + 1 more
  • English
  • Paperback
    9 7 8 - 1 - 8 9 8 5 6 3 - 9 8 - 3
  • eBook
    9 7 8 - 0 - 8 5 7 0 9 - 9 4 8 - 8
Explaining and comparing the various standard types of generalised functions which have been developed during the 20th Century, this text also contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions. The book could readily be used as a main text on generalised functions for mathematical undergraduates in final year analysis courses, as it presupposes little more than a general mathematical background. It also makes a valuable reference text for non-specific applied mathematics students, such as physicists or electrical engineers, needing to gain expertise in the application of generalised functions to physical problems, without any prior acquaintance of the specialised subject matter. An ideal companion book to Delta Functions, also by Professor Hoskins.

Nonmeasurable Sets and Functions

  • 1st Edition
  • Volume 195
  • May 29, 2004
  • Alexander Kharazishvili
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 4 7 9 7 6 - 7
The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics:1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces;2. The theory of non-real-valued-measurable cardinals;3. The theory of invariant (quasi-invariant)extensions of invariant (quasi-invariant) measures.These topics are under consideration in the book. The role of nonmeasurable sets (functions) in point set theory and real analysis is underlined and various classes of such sets (functions) are investigated . Among them there are: Vitali sets, Bernstein sets, Sierpinski sets, nontrivial solutions of the Cauchy functional equation, absolutely nonmeasurable sets in uncountable groups, absolutely nonmeasurable additive functions, thick uniform subsets of the plane, small nonmeasurable sets, absolutely negligible sets, etc. The importance of properties of nonmeasurable sets for various aspects of the measure extension problem is shown. It is also demonstrated that there are close relationships between the existence of nonmeasurable sets and some deep questions of axiomatic set theory, infinite combinatorics, set-theoretical topology, general theory of commutative groups. Many open attractive problems are formulated concerning nonmeasurable sets and functions.