# Reviews of Douglas Jones's books

We present below information about fifteen of Douglas Jones's books. The information is varied, there are some short extracts from reviews, some extracts from the Preface, and some information given by the Publisher. Let us make one further comment. It is difficult to decide when a new edition of a book should be considered a separate book and when it should be considered as merely a slight update of a previous edition. We have not been entirely consistent in this below; for some books reviews of different editions appear under the original, while sometimes we have presented the new edition and a new book.

Electrical and Mechanical Oscillations: An Introduction (1961)

The Theory of Electromagnetism (1964)

Generalised Functions (1966)

Introductory Analysis (Volume 1, 1969; Volume 2, 1970) with D W Jordan

Methods in Electromagnetic Wave Propagation (1979, 2nd edition 1994)

Elementary Information Theory (1979)

The Theory of Generalised Functions (1982)

Differential Equations and Mathematical Biology (1983, 3rd edition 2010), with B D Sleeman

Magnetite Biomineralization and Magnetroreception in Organisms. A New Biomagnetism (1985) with Joseph L Kirschvink and Bruce J MacFadden

Acoustic and Electromagnetic Waves (1986)

Methods in electromagnetic wave propagation (Volume 1, 1987, Volume 2, 1987)

Methods in electromagnetic wave propagation (Second edition) (1994)

Assembly Programming and the 8086 Microprocessor (1988)

80 × 86 Assembly Programming (1991)

Introduction to Asymptotics: A Treatment Using Nonstandard Analysis (1997)

**Click on a link below to go to information on that book**Electrical and Mechanical Oscillations: An Introduction (1961)

The Theory of Electromagnetism (1964)

Generalised Functions (1966)

Introductory Analysis (Volume 1, 1969; Volume 2, 1970) with D W Jordan

Methods in Electromagnetic Wave Propagation (1979, 2nd edition 1994)

Elementary Information Theory (1979)

The Theory of Generalised Functions (1982)

Differential Equations and Mathematical Biology (1983, 3rd edition 2010), with B D Sleeman

Magnetite Biomineralization and Magnetroreception in Organisms. A New Biomagnetism (1985) with Joseph L Kirschvink and Bruce J MacFadden

Acoustic and Electromagnetic Waves (1986)

Methods in electromagnetic wave propagation (Volume 1, 1987, Volume 2, 1987)

Methods in electromagnetic wave propagation (Second edition) (1994)

Assembly Programming and the 8086 Microprocessor (1988)

80 × 86 Assembly Programming (1991)

Introduction to Asymptotics: A Treatment Using Nonstandard Analysis (1997)

**1. Electrical and Mechanical Oscillations: An Introduction (1961), by D S Jones.**

**1.1. Review by: D H Smith.**

*Science Progress*(1933-)

**49**(195) (1961), 553.

This book is an addition to the publishers' series, The Library of Mathematics. It deals only with oscillations of systems with one degree of freedom, since more complicated systems are discussed elsewhere in the series. The first two chapters cover equations of motion and the linear vibrations of undamped systems. Damped mechanical and electrical vibrations are then considered and the fifth chapter deals adequately with non-linear vibrations. A set of examples follows each chapter. The work is addressed chiefly to physicists and engineers, but it is unfortunate that many of the results are expressed in forms that will be largely unfamiliar to physicists and almost completely so to electrical engineers.

**2. The Theory of Electromagnetism (1964), by D S Jones.**

**2.1. From the Publisher:**

The Theory of the Electomagnetism covers the behaviour of electromagnetic fields and those parts of applied mathematics necessary to discover this behaviour. This book is composed of 11 chapters that emphasize the Maxwell's equations. The first chapter is concerned with the general properties of solutions of Maxwell's equations in matter, which has certain macroscopic properties. The succeeding chapters consider specific problems in electromagnetism, including the determination of the field produced by a variable charge, first in isolation and then in the surface distributions of an antenna. The next two chapters are concerned with the effects of surrounding the medium by a perfectly conducting boundary as in a cavity resonator and as in a waveguide. Other chapters are devoted to discussions on the effect of a plane interface where the properties of the medium change discontinuously; the propagation along cylindrical surfaces; the study of the waves scattered by objects both with and without edges. This book further reviews the harmonic waves and the difficulties involved in going from harmonic waves to those with a more general time dependence. The final chapter provides some information about the classical theory of electrons, magneto-hydrodynamics and waves in a plasma. This book will prove useful to physicists, and physics teachers and students.

**2.2. From the Preface:**

[The author aims] to provide a text which will take the student from a first

acquaintance with Maxwell's equations to within striking distance of modern research.

**2.3. Review by: V C A Ferraro.**

*The Mathematical Gazette*

**49**(369) (1965), 348-349.

In recent years several treatises on Electromagnetism have appeared; the volume under review is a worthy addition to the series. In some ways it is also the most comprehensive in so far as very detailed expositions are given of almost every aspect of electromagnetism, including the theory of scattering and diffraction of electromagnetic waves by various obstacles - a difficult subject which the author has made particularly his own. Because of the large number of specialised mathematical techniques which are needed in electromagnetism, the author has interspersed throughout the body of the book introductory sections on such topics as special functions of mathematical physics, the tensor calculus, eigenfunction theory, linear operators, asymptotic evaluation of integrals and partial differential equations. The general reader will undoubtedly welcome their inclusion. The aim of the book is best expressed in the author's own words, namely, 'to provide a text which will take the student from a first acquaintance with Maxwell's equation to within a striking distance of modern research'. In this the author has admirably succeeded. The book is a fount of information and as such will become one of the standard works of reference in the subject. The undergraduate will also find it useful for his specialised reading and it will be invaluable to research workers in this field.

**2.4. Review by: Ivar Stakgold.**

*SIAM Review*

**8**(3) (1966), 399-400.

Research scientists and students alike will be in D S Jones' debt for his authoritative treatise on electromagnetic theory. This excellent book will surely rank among the major contributions in the field for many years to come. The chapters on radiation, wave guides, refraction, and diffraction are especially impressive in the depth and elegance of the treatment. Other topics such as magnetohydrodynamics, plasma physics, and the theory of electrons are discussed, but only at an introductory level. If I were to choose the highlight of the work it would be the two chapters on the theory of diffraction. Here we find the first comprehensive and modern exposition of this topic from the applied mathematician's point of view. The various high-frequency approximations which have been developed in recent years are carefully examined and compared. Another outstanding feature is the treatment of edge conditions and scattering from objects with edges.

**2.5. Review by: W E Williams.**

*Mathematical Reviews*MR0161555

**(28 #4759).**

The author states in his Preface that the book is intended to take the reader from Maxwell's equations to the frontiers of research, and the reviewer feels that this has been achieved to a very great extent and in a remarkably clear fashion. The scope of each chapter is extremely wide, research sources are given in some detail and particular attention paid to experimental work where relevant, and the exposition throughout is extremely clear. The only drawback is one which must inevitably arise with a project of this magnitude, namely, that most of the research work of the last two or three years is not discussed at all. The author states in his Preface that the book is intended to take the reader from Maxwell's equations to the frontiers of research, and the reviewer feels that this has been achieved to a very great extent and in a remarkably clear fashion. The scope of each chapter is extremely wide, research sources are given in some detail and particular attention paid to experimental work where relevant, and the exposition throughout is extremely clear. The only drawback is one which must inevitably arise with a project of this magnitude, namely, that most of the research work of the last two or three years is not discussed at all. ... This book is one which can be regarded as a valuable contribution to the literature on electromagnetic theory and one which will prove extremely valuable to both the research student and the experienced research worker. The author is to be complimented for both attempting such an ambitious project and for completing the task in such an admirable fashion.

**3. Generalised Functions (1966), by D S Jones.**

**3.1. Review by: Philip Heywood.**

*The Mathematical Gazette*

**53**(384) (1969), 211-212.

This book gives a comprehensive account of generalised functions and their application in mathematics. ... Professor Jones has made the least possible demands on his readers' knowledge of analysis. He has carefully separated the sections on functions over R_n from the easier material which is sufficient for many applications, and he has included a large number of worked examples and well chosen exercises. All the results and almost all the proofs can be understood by a reader with an elementary knowledge of convergence and integration. Only rarely is there an appeal to more advanced mathematics, as for example when the Hahn-Banach theorem is used ... [The book] can be confidently recommended to anyone who wishes to get to grips with the theory of generalised functions.

**3.2. Review by: A H Zemanian.**

*Mathematical Reviews*

**MR0217534**

**(36 #623).**

This book is the most thorough exposition to date of the Temple-Lighthill approach to generalized functions. It extends Lighthill's results [M J Lighthill,

*Introduction to Fourier analysis and generalized functions*, Cambridge Univ. Press, New York, 1958] in many directions and presents a variety of applications to other subjects in pure and applied mathematics. There are also many examples and problems, some of which illustrate the text and others which extend the theory. The treatment is careful, and the book is quite suitable for use by students who have taken advanced calculus.

**4. Introductory Analysis (Volume 1, 1969; Volume 2, 1970), by D S Jones and D W Jordan.**

**4.1. From the Preface:**

Volumes 1 and 2 of this book together present the coordinate geometry and analysis needed by students of the sciences in the early stages of a university or college course, and by those taking a pre-specialization course for mathematicians. The work is based on lecture courses given at the University of Keele: one to an unselected group of first-year students having eventual specialisms ranging from mathematics to the social sciences but not yet committed to a principal field of study, and another to those already specializing in the physical sciences. These groups had studied calculus at school, but the present book does not assume previous experience of the subjects covered. Our intention is to stress those mathematical ideas most central in scientific applications, and to emphasize the applicable nature of the subject by providing, as far as possible, physical, graphical or numerical illustration of all principal results. It is important to convey the relation between mathematical and physical language, as, for example, with the ideas of density and 'infinite distance', but examples requiring a detailed understanding of scientific topics have been avoided. On the other hand, much attention is given to simple numerical processes, which provide excellent illustrations of the uses of analysis in a field of general importance. A high standard of mathematical argument is used, mitigated by a leisurely exposition; proofs are generally given in full, but when a proper proof would be too difficult the corresponding result is stated and discussed without proof. Theoretical results are very fully illustrated by textual description and by many worked examples. Some sections are in small print. Their omission does not put the reader at a disadvantage in understanding what follows, but they can be read through with profit even in a first course.

**4.2. Review by: W L Ferrar.**

*The Mathematical Gazette*

**55**(391) (1971), 85.

These are two volumes of a series, edited by Professor Jones, entitled 'Introductory Mathematics for Scientists and Engineers'. They set a high standard. The avowed intention of the authors is to stress those mathematical ideas most central in scientific applications, to give much attention to numerical processes where these provide good illustrations of the uses of analysis, and to mitigate a high standard of mathematical argument by a leisurely exposition. They begin at the very beginning of coordinate geometry and move on slowly, steadily, even remorselessly until Volume 1 has provided, in the space of some five hundred pages, as firm and solid a foundation in real analysis as any scientist could possibly need. The book covers limits, functions, continuity, derivatives, maxima and minima, mean value theorem, sequences, series and (from both aspects) integrals. ... There is so much careful and leisurely explanation in Volume 1 and such a completeness of treatment that the book is necessarily long, even a touch formidable for its intended audience; it is, by any standards, an excellent presentation, well written and well printed. Volume 2 deals with selected topics, following the same general lines of a high standard of mathematical argument tempered by leisurely exposition. Some of the chapters can be studied independently of the rest. ... The authors, perhaps a little optimistically, consider that the two volumes together present the coordinate geometry and analysis needed by students of the sciences in the early stages of a university or college course. I think that a course for scientists which contained all of it would be over-loaded. With all the topics treated so extensively and so thoroughly, undergraduate scientists will not often master much of it in their first two years, but will begin to "know about" some of it, master the parts they find that they need, and possibly return to the rest later, assured of a sound source of detailed knowledge. All science libraries, in college or university, should ensure that these books are available to their students.

**5. Methods in Electromagnetic Wave Propagation (1979, 2nd edition 1994), by D S Jones.**

**5.1. Extract from the book:**

The concept of an antenna as a piece of wire or portion of dielectric which radiates electromagnetic energy is simple enough in principle, but the derivation of quantitative results of value for design purposes is fraught with difficulties. Even when the isolated antenna can be described as a straightforward boundary-value problem, it can rarely be solved with any ease. In fact the antenna, to be of any use as an element of a communication system, must be coupled with a transmission line or waveguide, and coupling forms an important but complicated part of any real system. For these reasons a substantial amount of analysis has been devoted to antennas, not always with success. The advent of large computers has made it possible to generate numerical answers to problems which had hitherto defied solution. It must be confessed, however, that the mathematical detail has often obscured the physical principles involved leaving the engineer up in the air when both analysis and computer fail. For example, to keep computer requirements reasonable, some type of symmetry is often assumed but the symmetry is usually lost as soon as a transmission line is connected. While it is our purpose to enumerate some of the analytical and numerical techniques that have been tried, it is hoped not to lose sight completely of physical principles which may be helpful.

**5.2. Review by: Peter W Barber.**

*American Scientist*

**68**(4) (1980), 461-462.

A modern-day practitioner of applied electromagnetic theory must be as conversant with numerical techniques as with Maxwell's equations. For example, to find the electromagnetic field scattered by a solid conducting object of arbitrary shape, it is necessary to solve numerically an integral equation for the unknown surface current. Should the integral equation be written in terms of the electric or the magnetic field? What methods are available for solving integral equations and what are their limitations? These are the types of problems addressed in this book. The volume presents a comprehensive treatment of the application of functional analysis and numerical techniques to the solution of electromagnetics problems. Fundamentals of numerical analysis, including interpolation, linear equations, and matrices are introduced, and practical problems such as stability and ill-conditioned systems are considered. ... Those interested in obtaining a state of-the-art knowledge of the application of numerical methods to the solution of electromagnetics problems will find the book useful. It is comprehensive (400 recent papers and reports are referenced) and well written. The basic concepts are covered in such detail that this would be an excellent book on which to base a graduate course in applied electromagnetic theory (the author has included numerous exercises).

**5.3. Review by: G P Bava.**

*Mathematical Reviews*

**MR0571011**

**(81k:78001).**

Starting from the requirement of a general background in mathematics and electromagnetic theory, the book develops analytical and numerical techniques useful for the solution of a wide class of problems in electromagnetic wave propagation. ... Approximately 400 problems can be found throughout the book. Most of them are rather interesting (and perhaps not easy to solve) and are undoubtedly useful in increasing the reader's experience.

**5.4. Review by: Larry Carin.**

*American Scientist*

**84**(4) (1996), 407-409.

Most recent texts dealing with electromagnetic fields are generally of an applied nature, utilizing the minimum mathematical rigour necessary to describe a given concept. ... Douglas Jones's new edition of 'Methods in Electromagnetic Wave Propagation' is unusual in its mathematical rigor and emphasis on general concepts rather than on a large number of practical examples. For these reasons, this new text is most appropriate for advanced graduate students or professional researchers working in this area. ... this book has features that make it an important contribution to the general electromagnetic literature. ... In summary, Jones has contributed a useful text that explores electromagnetic scattering and propagation with a level of mathematical rigor uncommon in most such texts. Because of this level of sophistication, it is most appropriate for advanced practitioners of electromagnetics. The unique quality of the presentation should make it a valuable addition to the libraries of active researchers.

**6. Elementary Information Theory (1979), by D S Jones.**

**6.1. Review by: F J Beutler.**

*Mathematical Reviews*

**MR0541146**

**(80j:94001).**

This modest volume is a self-contained textbook suitable for students with only a calculus background; thus, some results are demonstrated, while the proofs of others are only sketched or even omitted. Coverage includes probability, entropy and information, source coding, channel capacity and coding, error-correcting codes, and continuous channels. There are many useful problems at the end of each chapter, but no bibliographical references whatsoever.

**7. The Theory of Generalised Functions (1982), by D S Jones.**

**7.1. From the Publisher:**

Starting from an elementary level Professor Jones discusses generalised functions and their applications. He aims to supply the simplest introduction for those who wish to learn to use generalised functions and there is liberal provision of exercises with which to gain experience. The study of more advanced topics such as partial differential equations, Laplace transforms and ultra-distributions should also make it a valuable source for researchers. The demands placed upon the reader's analytical background are the minimum required to approach this topic. Therefore, by selecting chapters it is possible to construct a short introductory course for students, a final-year option for honours undergraduates or a comprehensive postgraduate course.

**7.2. From Jones's Obituary by: B D Sleeman and I D Abrahams.**

*Biogr. Mems Fell. R. Soc.*

**61**(2015), 203-224.

... it is fitting to note the following remark of Lighthill relating to the theory of generalized functions made at a conference in 1992 at Dundee University to mark Douglas's 70th birthday; it concerned Douglas's book

*The theory of generalised functions*(21): I have moreover been overjoyed that my tiny 80-page

*Introduction to Fourier analysis and generalised functions*[Lighthill 1958], which concentrates on functions of just one variable, has proved to be a suitable appetite-whetting 'starter', as it were, leading up to Douglas's superbly concocted 'main dish' in 540 pages which extends all the results in a comprehensive fashion and includes the corresponding properties of functions of many variables.

**7.3. Review by: Harris S Shultz.**

*Mathematical Reviews*

**MR0665103**

**(83k:46035).**

The major changes from the first edition [

*Generalised functions*, McGraw-Hill, New York, 1966] are outlined as follows. A new definition of x^{-m}, for positive integers m, is given. In contrast to the first edition, this generalized function is given as a limit of a sequence of generalized functions. Accordingly, there is a revised approach to delta functions on a hypersurface and to hyperbolic and ultrahyperbolic distances and their Fourier transforms. Totally new to the text is the treatment of ultradistributions, which provide for the Fourier transform of any weak function (that is, distribution).

**8. Differential Equations and Mathematical Biology (1983, 3rd edition 2010), by D S Jones and B D Sleeman.**

**8.1. From the Publisher:**

This textbook shows how first-order ordinary differential equations (ODEs) are used to model the growth of a population, the administration of drugs, and the mechanism by which living cells divide. The authors present linear ODEs with constant coefficients, extend the theory to systems of equations, model biological phenomena, and offer solutions to first-order autonomous systems of nonlinear differential equations using the Poincaré phase plane. They also analyse the heartbeat, nerve impulse transmission, chemical reactions, and predator-prey problems. After covering partial differential equations and evolutionary equations, the book discusses diffusion processes, the theory of bifurcation, and chaotic behaviour. It concludes with problems of tumour growth and the spread of infectious diseases.

**8.2. Review by: Hal L Smith.**

*SIAM Review*

**46**(1) (2004), 183-184.

Mathematical biology is enjoying a lot of attention these days and the inevitable consequence is a steady stream of introductory texts. ... The book under review has a somewhat broader aim. To understand the authors' intentions, a quote from the preface is illuminating: "In recent years, mathematics has made a considerable impact as a tool with which to model and understand biological phenomena. In return biology has confronted the mathematician with a variety of challenging problems which have stimulated developments in the theory of non-linear differential equations. This book is the outcome of the need to introduce undergraduates of mathematics, the physical and biological sciences to some of these developments. It is primarily directed to university students who are interested in modelling and the application of mathematics to biological and physical situations." The authors suggest that the book may serve a multipurpose role: (1) as a text for a first ODE course, or (2) as a course in biological modelling for students of math and the physical sciences, or (3) as a course in differential equations models of biology for life sciences students. ... Despite the authors' contention that the book could be used as a course on modelling in biology, it is really more accurate to say that applications to biology are presented. ... A strength of the present book is its concise coverage of a broad range of topics in differential equations that are useful in the analysis of mathematical models in biology and the application of some of these topics to a diverse collection of such models. It is truly remarkable how much material is squeezed into this slim book's 400 pages.

**8.3. Review by: Robert E O'Malley, Jr.**

*SIAM Review*

**52**(3) (2010), 586-587.

While they were colleagues in Dundee, the distinguished applied analysts Douglas Jones and Brian Sleeman published a book in 1983 with Allen & Unwin with the same title as this one. The outline of the new book is nearly the same, except that a chapter on "Catastrophe Theory and Biological Phenomena" has been replaced by successful new chapters on "Bifurcation and Chaos" and "Numerical Bifurcation Analysis," while more computational approaches and the use of MATLAB have been added throughout. Much progress by these authors and others over the past quarter century in modelling biological and other scientific phenomena make this differential equations textbook more valuable and better motivated than ever. The intended audience is broad and, in contrast with many texts on modelling in biology, the differential equations cover age is quite sophisticated. ... Overall, this book should convince math majors how demanding math modelling needs to be and biologists that taking an other course in differential equations will be worthwhile. The co-authors deserve congratulations as well as course adoptions.

**8.4. Review by: Jian Hong Wu.**

*Mathematical Reviews*

**MR1967145**

**(2004g:92003).**

The title precisely reflects the contents of the book, a valuable addition to the growing literature in mathematical biology from a deterministic modelling approach. This book is a suitable textbook for multiple purposes: for applied qualitative theory of differential equations and for mathematical biology, and at multiple levels: for senior undergraduate students majoring in applied mathematics, for graduate students in applied mathematics, and for students in theoretical ecology interested in mathematical modelling. ... Overall, topics are carefully chosen and well balanced. I would like to see a chapter on delay differential equations with applications, but this may be just a personal preference. The book is written by experts in the research fields of dynamical systems and population biology. As such, it presents a clear picture of how applied dynamical systems and theoretical biology interact and stimulate each other - a fascinating positive feedback whose strength is anticipated to be enhanced by outstanding texts like the work under review.

**9. Magnetite Biomineralization and Magnetroreception in Organisms. A New Biomagnetism (1985), by Joseph L Kirschvink, Douglas S Jones and Bruce J MacFadden.**

**9.1. From the Publisher:**

The mystery of how migrating animals find their way over unfamiliar terrain has intrigued people for centuries, and has been the focus of productive research in the biological sciences for several decades. Whether or not the earth's magnetic field had anything to do with their navigational abilities has surfaced and been dismissed several times, beginning at least in the mid to late 1800s. This topic generally remained out of the mainstream of scientific research for two reasons: (1) The apparent irreproducibility of many of the behavioural experiments which were supposed to demonstrate the existence of the magnetic sense; and (2) Perceived theoretical difficulties which were encountered when biophysicists tried to understand how such a sensory system might operate. However, during the mid to late 1960s as the science of ethology (animal behaviour) grew, it became clear from studies on bees and birds that the geomagnetic field is used under a variety of conditions. As more and more organisms were found to have similar abilities, the problem shifted back to the question as to the basis of this perception. Of the various schemes for transducing the geomagnetic field to the nervous system which have been proposed, the hypothesis of magnetite-based magnetoreception discussed at length in this volume has perhaps the best potential for explaining a wide range of these effects, even though this link is as yet clear only in the case of magnetotactic bacteria.

**9.2. Review by: Irwin R Isquith.**

*BioScience*

**38**(1) (1988), 58.

The editors of this volume not only had the task of bringing together an extremely diverse group of specialists, but also of giving credibility to a subject that in the past has been looked upon with some suspicion. They succeeded very well in both endeavours. The volume is a comprehensive compilation of works by 52 contributors, representing geological, physical, and biological disciplines. Such a broad approach will prove to be invaluable to researchers in many disciplines, especially biology. ... The editors confront head on the major disagreements that exist in the study of biomagnetism as they have strictly defined it. ... These disagreements, however, do not detract from the book; indeed, they enrich it, because it becomes obvious that there is considerable research currently taking place.

**9.3. Review by: Robert C Beason.**

*The Quarterly Review of Biology*

**61**(3) (1986), 429-430.

This volume admirably accomplishes the stated objectives of its editors - to bring together the literature on the biological aspects of magnetite, which has been scattered in a variety of biological and geological journals.

**10. Acoustic and Electromagnetic Waves (1986), by D S Jones.**

**10.1. From the Publisher:**

This work aims to provide a unified treatment of view acoustics and electromagnetism in order to underline their common and disparate features and the way in which cross-fertilization occurs. It is assumed that the reader has taken a first course in which the governing equations are derived. Although it is expected that enough electricity and magnetism will have been covered for Maxwell's equations to have been met or in fluid mechanics that the equation of sound waves will have been encountered, nevertheless the book is so designed that developments in either without acquaintance with the other can be followed. Topics discussed in the text include field representations, radiation from fixed and moving sources, guiding of waves by tubes, refraction and reflection, scattering by objects and problems in the time domain.

**10.2. Review by: A D Rawlins.**

*The Mathematical Gazette*(2)

**71**(455) (1987), 84-85.

The author makes the point that the mathematical investigations of (vector) electromagnetism and (scalar) acoustic waves often run along similar paths, and therefore a book which traces the common strands would be helpful to workers in both areas. His objective with this book is that the reader will be able to cope with up-to-date research work in both fields. As far as electromagnetism is concerned the author assumes the reader has reached the stage of Maxwell's equations via the customary course on static electricity, magnetostatics, and current electricity. The book follows logically on these courses in that its viewpoint is macroscopic. No attempt is made to relate the macroscopic laws to any theory, such as wave mechanics, of microscopic structure. Similarly, fluid motion is regarded as a macroscopic phenomenon whose governing equations are assumed to be familiar to the reader though a brief derivation of the equations needed to describe the propagation of sound is given. ... This is a stimulating and well produced book. There must be very few techniques of applied mathematics dealing with waves which are not explained here and illustrated by good concrete examples. It is likely to be an almost indispensable work of reference for anybody attempting research in acoustic or electromagnetic wave phenomena. The high degree of thoroughness, which is the hallmark of this author's previous well known treatise on electromagnetism, makes this outstandingly excellent book a welcome addition to the literature of applied mathematics.

**10.3. Review by: John A DeSanto.**

*Mathematical Reviews*MR0943347

**(89h:76032).**

This is an advanced textbook which emphasizes both the interrelationship between acoustic and electromagnetic waves and the practical solution of boundary value problems of current research interest in both areas. The emphasis is on the use of sophisticated classical analytical techniques for problem definition, and the development of approximate analytical methods for their solution. The aim of the book is to bring the reader to the level of contemporary research in many areas. ... The book is exceptionally well written and well edited. It could serve as a text for an advanced course on wave theory with an applied mathematics flavor. The interplay between acoustic and electromagnetic techniques serves to clarify both disciplines, and the many well-chosen problems will develop the reader's skills in both disciplines.

**11. Methods in electromagnetic wave propagation (Volume 1, 1987, Volume 2, 1987), by D S Jones.**

**11.1. From the Publisher:**

The aim of these two volumes is to develop a framework of theory and numerical analysis that can be applied to solving numerous problems associated with the propagation of electromagnetic waves. Volume I is devoted to the theoretical background and the topic of guided waves, and Volume II concentrates on radiating waves, produced both by transmitters and by scattering from irradiated targets. The book is aimed at postgraduates and researchers in electrical engineering, applied mathematics, and physics.

**11.2. Review by: Sergej M Zverev.**

*Mathematical Reviews*MR0911478

**(89a:78001a).**

*Mathematical Reviews*MR0911479

**(89a:78001b).**

This book is a carefully written introduction to the whole field of the problems and methods of electromagnetics including their numerical analysis. Influenced by the author's earlier books [

*The theory of electromagnetism*, Macmillan, New York, 1964;

*Acoustic and electromagnetic waves*, Oxford Univ. Press, New York, 1985], it is directed to the computational aspects of noncanonical problems ...

**12. Methods in electromagnetic wave propagation (Second edition) (1994), by D S Jones.**

**12.1. From the text:**

Modern methods of tackling problems associated with electromagnetic waves involve a judicious mixture of analysis and computation. The analysis occurs in the mathematical formulation and in establishing that it has the requisite properties. Conversion to a form suitable for the computer entails numerical analysis, whose justification may also rest on a considerable body of analysis. Therefore, the aim of this volume is to develop a suitable framework of theory and numerical analysis with applications to various aspects of the propagation of electromagnetic waves. The explanation is couched in as comprehensible a language as possible and it assumes a starting-point as early as is commensurate with the size of the text. Numerous exercises have been inserted at convenient points and some of these are open-ended so that any instructor has plenty of freedom in determining the mode of treatment. This new edition considers the analytical progress which has been made recently, and the wider availability of powerful computers. The conjugate gradient method and CGFFT are given extensive treatment. The coverage of finite methods has been expanded and conforming finite elements particularly appropriate to electromagnetic applications are described. The discussion of integral equations has been completely revised and new topics have been added, including Sobolev spaces, vector optimization, absorbing boundary conditions, and surface radiation conditions.

**13. Assembly Programming and the 8086 Microprocessor (1988), by D S Jones.**

**13.1. From the Preface:**

The Intel 8086 microprocessor is one of the most popular and appears in several versions of the IBM Personal Computer, many PC-compatibles and the IBM PS/2 Model 30. This book is written for those PC users who are already competent in one high level language (such as BASIC or PASCAL), but who need more flexibility and speed than such languages can provide. It begins by explaining the fundamentals of assembly programming and then describes the essential details of the 8086 chip. The book progresses by means of illustrative programs and subroutines to sophisticated topics such as floating-point arithmetic and operation system calls. Also contained are a large number of exercises.

**14. 80 × 86 Assembly Programming (1991), by D S Jones.**

**14.1. From the Preface:**

Many personal computers are based on one of the 86 series of Intel microprocessors, namely the 8086, 80286, 80386, and the 80486, in order of increasing power. Programming the computer in the relevant assembly language allows the user to take full advantage of the speed and power of the microprocessor. This book is written for PC users who already have some familiarity with a high-level language such as Basic, C, or Pascal, and who want the extra facilities and efficiency of assembly language. The book starts at an elementary level with the basics of assembly programming and the properties of the microprocessor in its simplest mode of operation, the real address mode. Instructions for this mode of the 8086 and 80286 are progressively introduced through illustrative programs and subroutines. Further topics discussed are operating system calls and the 80286 protected mode. A separate chapter deals with the additional instructions of the 80386 and its modes of operation. Expanded and extended memory are also covered. The 80x87 coprocessors are treated for the benefit of readers who have one either as a part of the 80486 or as a complement to their 80x86. Numerous exercises are provided throughout the text. These enable readers to test their understanding and to gain experience in assembly programming.

**15. Introduction to Asymptotics: A Treatment Using Nonstandard Analysis (1997), by D S Jones.**

**15.1. From the Publisher:**

Many branches of science and engineering involve applications of mathematical analysis. An important part of applied analysis is asymptotic approximation which is, therefore, an active area of research with new methods and publications being found constantly. This book gives an introduction to the subject sufficient for scientists and engineers to grasp the fundamental techniques, both those which have been known for some time and those which have been discovered more recently. The asymptotic approximation of both integrals and differential equations is discussed and the discussion includes hyperasymptotics as well as uniform asymptotics. There are many numerical examples to illustrate the relation between theory and practice. Exercises in the chapters enable the book to be used as a text for an introductory course.

**15.2. Review by: Adri B Olde Daalhuis.**

*SIAM Review*

**40**(3) (1998), 733-735.

Asymptotics is an old topic in applied analysis, dating back to the time of Laplace. Although it is an old subject, new methods, new applications, and new problems continue to appear in the literature. Consequently, every so many years one needs new books, and some of them should be introductory books that give a short introduction to the field and also to the new "hot topics." ... As an introductory book to asymptotics, with chapters on uniform asymptotics and exponential asymptotics, this book clearly fills a gap. The use of nonstandard analysis should not be a reason to avoid the book. Moreover, it has a friendly size and contains many convincing numerical examples and interesting exercises. Hence, I recommend the book to everyone who works in asymptotics.

**15.3. Review by: L G Chambers.**

*The Mathematical Gazette*

**83**(497) (1999), 369.

The object of this book is to indicate the use of some new ideas in the treatment of asymptotic approximations and their applications. ... This is an interesting book and shows how a new idea can be used to tackle an old subject. In the course of the text there are a number of worked examples. The usefulness of Maple and Mathematica in the treatment of these becomes apparent. There are also a number of exercises at the end of each chapter. It would have been interesting to see an example of some simple problem being worked by both 'standard' and 'non-standard' processes, so that the reader may compare the two methods. ... The treatment is clear and the book can be warmly recommended.

**15.4. Review by: W A J Luxemburg.**

*Mathematical Reviews*MR1464943

**(98i:41046).**

Asymptotic methods play a very important role in applied mathematics. In this small book the author presents an introduction to asymptotics intended more for the user than for analysts. A novelty of the treatment, however, is the use of Robinson's theory of infinitesimals of nonstandard analysis. Its use is in a sense more semantic than theoretical. The usual O(1) statements are replaced by the cyrillic character denoting the first letter of the word "infinitesimal'' and which is prominently displayed on the cover of the book. For the reader who is not familiar with nonstandard analysis the author has added an appendix entitled: An introduction to nonstandard analysis. It gives the reader a concise but very readable explanation of what Robinson's theory of infinitesimals is all about. ... A very attractive feature of the book is the numerous examples illustrating the methods. A fine collection of exercises enriches each chapter, challenging the reader to check his progress in understanding the methods.

Last Updated January 2019