A course in the foundations of elementary analysis, this book provides an introduction to non-standard concepts and techniques. The text aims to be accessible to mathematicians, physicists, engineers and students in related disciplines.

Standard and Nonstandard Analysis: Fundamental Theory, Techniques, and Applications (Mathematics and Its Applications)

Science & Math

Hoskins, R. F.

Mathematics

Ellis Horwood, Ltd.

Generalised functions (Ellis Horwood series in mathematics and its applications)

Halsted Press

A topic of major importance to engineers and physicists, the theory of distributions remains a difficult subject for the non-mathematician. This version of the theory presents a more natural approach.

Introduction to the Theory of Distributions (Monographs and Surveys in Pure and Applied Mathematics)

Campos Ferreira, J

Sousa-Pinto, Jose

Chapman and Hall/CRC

Generalised Functions (Mathematics & Its Applications)

Prentice Hall Europe (a Pearson Education company)

Delta Functions: An Introduction to Generalised Functions

Horwood Pub Ltd

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.Explains and compares the various standard types of generalised functions that have been developed during the 20th CenturyContains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions

Theories of Generalised Functions: Distributions, Ultradistributions and Other Generalised Functions

Pinto, J S

Woodhead Publishing

This undergraduate text deals with basics of group theory and its application to the analysis of vibrational spectra, molecular orbital description of bonding, ligand field theory and other themes within inorganic chemistry. Concise and student- friendly, the book adopts a diagrammatic rather than a rigorous mathematic approach, providing support for lecture courses in chemical group theory offering students opportunities to test their understanding. Problem solving is stressed with numerous self-assessment questions and problem exercises, along with tutorial hints and solutions to selected problems. Part 1 covers the essentials of symmetry and group theory, including symmetry elements and operations, point groups and representations. Part 2 focuses on the application of group theory to vibrational spectroscop building step-wise to show how group theory guides the analysis of vibrational spectra. A brief overview of infrared and Raman spectroscopy techniques is followed by a complete worked example to reiterate key points from earlier sections. Part 3 describes the application of group theory to a molecular orbital approach to chemical bonding. After laying a foundation of the basic rules for forming molecular orbitals using H, and H as examples, the book addresses more complex problems by comparing angular and linear structures for water and planar and pyramidal structures for ammonia. A description of the application of group theory to the bonding in octahedral main group and transitional metal complexes then follows, including an analysis of the influencing crystal field splitting energies. The book concludes with a description of the bonding in ferrocene, bringing together all the ideas presented in earlier sections.

Literature & Fiction

Genre Fiction

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.Second edition has been updated, restructured and modernised to answer specific difficulties typically found by students encountering delta functions for the first timeAttention is focused on techniques, with a liberal selection of worked examples and exercisesReadily accessible to a broad audience of scientists, mathematicians and engineers and can be used as a working manual in its own right

Delta Functions: Introduction to Generalised Functions

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