Perturbation methods in applied mathematics

Perturbation methods in applied mathematics

390 on the problems of ventilating railway tunnels, on metro routes (pp. 264--268) and main line (pp. 268--273), is given. Problems arising from railw...

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390 on the problems of ventilating railway tunnels, on metro routes (pp. 264--268) and main line (pp. 268--273), is given. Problems arising from railway tunnel operation include passenger discomfort due to air pressure rise, and the removal of waste heat (heat gain). The importance of tunnel aerodynamics is indicated by the estimate that 13.5 MW would be needed to overcome drag for a single ferry train in the 1974 design Channel Tunnel, though this is reduced to 5.8 MW by providing cross passages at 250 m spacing (p. 272). The magnitude of the heat gain in long tunnels is considerable. The projected St. Gotthard Base tunnel is double-tracked, 48.67 km long. The heat input per day from 282 trains and tunnel plant is estimated at 25 MW supplemented by 10 MW from high temperature rocks. Bibliography (pp. 276--315). The accounts of the many techniques and materials reviewed throughout the two volumes are of necessity very brief, and the thorough bibliography, together with the source list provided with each chapter enables material to be gathered for more specialist study at a deeper level. The bibliography is divided into several sections: General books and reports (107 sources), publications of Institution of Civil Engineers, U.K. (203 sources); publications of the American Society of Civil Engineers (155 sources); British Tunnelling Society (23 sources); Construction Industry Research and Information Association (18 sources), Transport and Road Research Laboratory (57 sources), a list of 37 conferences on tunnelling, and 29 relevant to tunnelling; and papers in several journals and periodicals (112 sources). The bibliography is followed by a 6 page double-column index. Both volumes can be thoroughly recommended. The authors' and publishers' aims are met, and the books are models of how a broad subject, with its many techniques, materials and codes, can be reviewed and presented in a useful, educative manner. Photographs and figures are plentiful and of good quality. Broad reviews of technologies, relating and referencing the many sub-sections, are increasingly needed to unite into a single outline the body of specialist knowledge contained in the many research papers and reports. Prospective reviewers of other technologies could study these two volumes with profit, for they demonstrate how such an exercise can be successfully executed. M.C. DUFFY

Perturbation Methods in Applied Mathematics, by J. Kevorkian and J.D. Cole, Springer-Verlag, New York, 1981. ISBN 3-540-90507-3, x + 558 pages, 79 figs., hard cover DM 88.--/US$ 41.90. This text is a revised and updated version of the earlier text "Pertubation Methods in Applied Mathematics" by one of the present authors (J.D. Cole), including some new material on celestial mechanics, mathematical biology and other areas. A knowledge of the basics of ordinary and partial differen-


tial equations is assumed and some familiarity with perturbation techniques would be useful. The b o o k is aimed at the applied mathematician at the advanced undergraduate or graduate level and concentrates on singular perturbation problems. These problems are divided into t w o types: layer-type problems and cumulative-perturbation problems. The text is comprehensive and is written in five chapters. Chapter 1 is a short introduction and contains some background on asymptotic expansions, limit process expansions, matching and general asymptotic expansions. The following three chapters are more substantial. Chapter t w o deals with the application of limit process expansions to ordinary differential equations: this is achieved by considering a series of examples. In chapter three cumulative perturbation problems are tackled using the multiple-variable expansion procedures: again a series of examples is considered and in particular there is a large section devoted to satellite problems. Chapter four applies the methods discussed earlier to partial differential equations, again through a series of examples, including some taken from biology. Finally, chapter five considers in some detail examples taken from fluid mechanics. There is a considerable number of problems for the student to try, an essential feature of any text-book, b u t unfortunately answers are not supplied. In addition, there are many references to help the reader to take his studies further. Perhaps this b o o k is t o o comprehensive for the average undergraduate b u t it is essential reading for the graduate or research worker in this field and is a useful reference work for the bookshelf. H. CLARK

Energy Management Principles, by Craig B. Smith, Pergamon, New York, 1981. ISBN 0-08-028036-6, xx + 395 pages, 125 illustrations, hard cover approx. £24.70: paperback (ISBN 0-08-028811-1) US$29.50 This is a rather disappointing b o o k from the pen of a senior engineer of wide experience of energy management in the USA. With a dramatic cover, showing a silhouette of a process plant structure against a vivid yellow background, and approximately 400 pages the b o o k promises a lot b u t fails to deliver. Perhaps a major cause of the failure lies in the rather confused objectives of the author. In the Preface he claims to be writing for the "junior, senior or first year graduate engineer" b u t some 400 pages later the b o o k is for the "senior, graduate or practising engineer or architect". Furthermore, whilst the cover implies an interest in process plant energy management the b o o k is heavily biased towards the HVAC field and specifically USA practices. The structure of the b o o k and the presentation of the material is difficult to fault, although the insertion of appendices between chapters is rather an irritating feature. Indeed the appendices comprise nearly one seventh of