USE OF INTEGRAL TRANSFORMS, by Ian N. Sneddon. 539 pages, diagrams, 6ax9)in. New York, McGraw-Hill, 1972. Price, $21.50.
The state prerequisite of a good knowledge of the methods of advanced calculus and solution of elementary differential equations seems adequate for most of the material in the book, although some of the applications, such as in quantum mechanics, may not be fully appreciated or understood by the reader with minimal prerequisite knowledge. A background in complex variables may be helpful. There are few misprints, but some of these, such as the author’s middle initial on the cover of the book, are indeed notable. In all, Professor Sneddon has written a book well suited for a first year undergraduate doing a science or engineering course that is explicitly concerned with the use and application of integral transforms. The book should also be a valuable addition to science, engineering and mathematics libraries. i, y
The author’s aim, “to provide an introduction to the use of integral transforms for students of applied mathematics, physics and engineering”, is admirably achieved in this very readable book. In Chap. 1, using various boundaryvalue problems as motivation, the author introduces the Fourier, Laplace, Mellin and Hankel transforms, which are the topics, respectively, of Chaps. 2-5. The more specialized Kontorovich-Levedev and Mehler-Fock transforms are treated in the next two chapters which also contain applications of the transforms to diverse areas: including statistics, quantum mechanics, elasticity, diffusion problems, potential problems in various regions, vibration problems and mixed boundary value problems. Chapters 8 and 9 contain finite versions of some of the transforms and a brief, though rigorous, introduction to generalized functions, respectively. There are two appendices: one on Bessel functions and one consisting of tables of transforms. While the author defines the different transforms on sufficiently wide classes of functions for many physical applications, the reader does not see any of the beautiful applications of generalized integral transforms. It seems that the author has tried to strike a medium between a much longer book with a rigorous treatment of generalized integral transforms, and a heuristic introduction to generalized integral transforms at the outset and formal use of the concepts throughout the text. While each reader may decide the relative merits of such an approach, the reviewer feels it is appropriate. As it is, the book seems to be of proper length. Furthermore, the pitfalls of an intuitive approach not followed by rigorous justification are avoided. Also, the interested reader is referred by the author to A. H. Zemanian’s books on generalized integral transforms.
d-S WILLIAM L. PERRY Department of Mathematics Texm A & M University College Station, Texas
EINSTEIN: THE LIFE AND TIMES, by Ronald W. Clark. 718 pages, illus., 6 x 9 in. New York and Cleveland, The World Publishing Co., 1971. Price, $15.00 hard cover. New York, Avon. Price, $1.95 paperback. To say that this is the best biography of Einstein we have is to give it insufficient praise : it is, in effect, the only adequate one. Of earlier biographies the only two of repute are those by Seelig and Frank. However, while Seelig’s biography contains a great deal of interesting (though largely undigested) documentary material on Einstein’s Swiss period it deals with almost everything else in one long but inadequate chapter; and Frank’s book was published before Einstein’s death and was the result of very little archive research. For the rest we have large
Book Reviews numbers of interesting but limited personal memoirs, more or less useless journalistic narratives and a series of wildly inaccurate hagiographies written during his lifetime. Rarely has a man with so mafry biographers been so badly served by them. Hence the publication of Clark’s EinsteirL is a major event in the history of Einstein scholarship. Clark is the first to have systematically surveyed the Einstein holdings in dozens of archives scattered throughout America, Europe and the Middle East. Inaddition he hs.s read most, though not all, of the published biographical literature on Einstein. This makes his biography the most accurate and comprehensive that we yet have. Not that it gives us the whole story. Legal problems have prevented the publication of Einstein’s correspondence with his first wife and Clark’s book contains few extracts from correspondence between close friends and members of Einstein’s family. Perhaps the letters are lost,, perhaps they rarely touch anything more than superficialities. Nonetheless, the few hints given by Clark (pp. 530-2) about Einstein’s relations with his second wife, Elsa, are est,raordinarily fascinating and suggest that much more is to be discovered about Einstein’s personal life. As far as his relations with his first wife are concerned Clark is compelled to speculate, helped by Einstein’s letters to his close friend and confidant, Michelangelo Besso (to whom he also confied the special theory of relativity while they worked together at the Berne Patents Office). The speculation suggests that peculiar psychological problems were at the root of the break-up of and the few brief the first marriage, remarks from Elsa which are quoted later suggest that she suffered from the same source. Certsinly Einstein was a man of very peculiar psychological make-up and our understanding of his charecter is certainly not complete. Perhaps Clark would have got nearer the truth had he read C. P. Snow’s essay on Einstein in Vurieties of Men, which seems to me one of the most percipient of all the pieces written on Einstein. Snow’s theory is that the monolithic unity of
Einstein’s personality, which infected everything from his attitude to physics to his choice of music, was the result of a conscious decision, taken sometime between the special and the general theories of relativity, to repress the more turbulent elements of his youth. This massive repression undoubtedly took its toll in his capacity for normal human relations later on. Clark gives little sense of the unity of Einstein’s life being more concerned to emphasize the tensions: Einstein the pacifist who urged the building of the atomic bomb; the anti-nationalist who was a Zionist ; an early pioneer of physical indeterminacy who became later its bitterest opponent. All this was true; but Einstein’s life was all of one piece much more than this suggests. The book’s major fault is its somewhat broken-backed structure. Einstein’s life is pursued more or less chronologically until 1919 but from then until the story reaches 1933 a thematic approach is adopted. There are reasons to support this sort of structure: in the period 1919-33 there were many different aspects to Einstein’s life: the effects of his fame, his involvement in politics, his conversion to Zionism and his travels. It might have seemed better to deal with each separately, but the attempt frankly is a failure. The aspects were interrelated: you cannot discuss Einstein’s travels separately from his espousal of Zionism as they were undertaken in many cases to further the Zionist cause. Nor can you properly understand his off-on relations with the League of Nations unless it is realized that for much of the time he was out of Europe. Clark’s attempts to hold the thing together by cross-references are inadequate and the story becomes hard to follow even for those with some knowledge of the events of Einstein’s life. For B few chapters near the middle the book takes on more the aspect of a collection of related essays. Science is fairly dealt with in the earlier sections of the book which cover the astoundingly productive years from 1901 to 1919. But thereafter it somewhat recedes in importance with only occasional references to the fact that Einstein was still searching for a unified field theory or
Journal of The Franklin Institute
Book Reviews still seekini to refute quantum indeterminacy. The unified field theory is badly treated: Clark thinks of it as a nonstarter from the beginning and there is no att,empt to differentiate the various theories Einstein produced in his last three decades, nor to outline the state of the game after Einstein’s death. It is not pointed out that Einstein’s motivation for working on the unified field theory was equally his motivation for working on general relativity: to produce a theory of great scope and great simplicity. Clark treats it as flatly paradoxical that the great scientific revolutionary should have become so conservative. Clark also overestimates the loneliness of Einstein’s rearguard action against indeterminacy; there is no mention of the fact that he was joined by de Broglie, SchrGdinger and BGhm. Nor is there any elucidation of the differing philosophical views which underlie the two different approaches to physics. Moreover, some work gets completely ignored; in particular there is no mention of the beautiful papers on the equations of motion written with Infeld in the 1930s. Of course. one cannot expect too much physics in a biography even of such a whole-hearted physicist as Einstein but these omissions are serious if one is to get a balanced view of Einstein’s scientific activity. The scientific exposition Clark gives is usually accurate though not impeccably so. There is a mistake in the formulation of the Einstein-Rosen-Podolsky paradox on p. 537 ; a considerable underestimation of the difficulty of the clock paradox (pp. 90-l) and a general uncertainty about the empirical status of the general theory of relativity. As science recedes in the last two-thirds of the book so politics increases in importance. Again Clark emphasizes the paradoxes at the expense of the continuity of Einstein’s humanitariansim. We certainly do not look to Einstein’s political writings to gain detailed knowledge of international affairs but this does not justify Clark’s repeated (and unsubstantiated) charges of Einstein’s political ignorance and naivet& Indeed, these charges seem to amount to no more than the fact that Einstein’s political intuitions differed
Vol.300,No. 1,July 1975
radically from those of the men in power. This counts against Einstein only if you hold that Cherwell, Weizmann and Roosevelt, indeed Moltke, Truman and Hitler, were unfailing oracles of political sagacity. What you get from Einstein’s political writings is a good deal of moral insight and a moving expression of what is best in the liberal tradition. And, who knows, perhaps even in our political barbarism moral insight counts for something. After all, the man was interviewed enough, he must have been saying things that were meaningful to someone. Clark is too often ready to bandy around charges of inconsistency. Political truths are not eternal. There is no inconsistency in opposing the German Empire during World War I and supporting the German Republic afterwards; in supporting conscientious objection in the ‘twenties and rearmament against Hitler in the ‘thirties. Nor is this woolly idealism: it indicates that Einstein had his feet firmly on the ground. He was one of the first to appreciate the significance of Hitler’s rise to power, and one of the first to recognize the dangers of atomic weapons. He was not only a clever man, he was a wise man, and little of this wisdom comes through in Clark’s account. Nonetheless, Clark gives us more new material on Einstein’s political work than we might have expected. One always supposed that Nathan and Norden had said the last word on this subject in Einstein on Peace (1960). They then claimed that it was “unlikely” that the discovery of new material would force a reinterpretation of Einstein’s views. Clark has indeed found a quantity of new material, particularly concerning Einstein’s work for the League of Nations’ Committee on Intellectual Co-operation and his work for the U.S. Government during World War II. In all this we have much to be grateful for. Clark also gives us a much more detailed account of Einstein’s contribution to the early Manhattan Project than we have previously had and comes to the very reasonable conclusion that Einstein’s contribution (in particular his famous letter to Roosevelt) was not a decisive factor in the American atomic bomb project, but it did help to prepare
Book Reviews the way in America for the British Maud Report which indicated in 1941 the feasibility of building the bomb. Einstein’s letter did ensure that the American government was aware of the possibility and had set up the National Defense Research Committee which could consider the Maud Report with some antecedent knowledge. However, Clark throws away this conclusion later on with comments like. 9“Einstein . . . had started” America’s nuclear effort (p. 578) and that Einstein; “had helped push the buttons that killed 120,000” (p. 617). These extreme statements are far from the truth. A minor complaint concerns the method of giving references which make it extremely frustrating to try to read the book through and to learn where all the information comes from at the same time. Indeed, not all quotations are referenced. This is regrettable in a book based on so much research and which is by far the most scholarly biography of Einstein. One feels a bit ashamed having criticized so much a book as good as Clark%. But it is already the standard biography of Einstein and is likely to remain so for many years. Its very preeminence makes one wish that it was just a little bit better. NICHOLAS GRIFFIN Research School of Social Science8 Australian National University Canberra, Australia
OPTIMIZATION AND STABILITY PROBLEMS IN CONTINUUMMECHANICS, edited by P. K. C. Wang. 94 pages, diagoams, 7 x 10 in. New York, Springer-Verlag, 1973. Price 5X.95. This book, Vol. 21 of the series Lecture Notes in Physic8, contains expan ded versions of five lectures presented at a symposium held in conjunction with the Western Applied Mechanics Conference at the University of Southern California, Los Angeles, 24 August, 1971. The first three lectures deal with optimization problems and the last two with stability problems. The first Lecture is “The Method of Dubovitskii-Milyutin in Mathematical Programming”, by H. Halkin. The method
involves convex approximations of sets and separated convex sets. It furnishes necessary conditions for certain classes of optimization problems. Extensions of the method are discussed and the relation to a necessary condition of Fritz John is given. In the second lecture, R. Shield gives a survey of “Optimum Design of Structures through Variational Principles”. Topics include minimum-volume design of structures of perfectly plastic materials required to carry given loads, uniform strength design with a constraint on the range of stresses, elastic design for given deflection and optimum layout of framed structures. New examples include design for minimizing the maximum deflection of a beam and optimum layout of frames for pure bending. The third lecture concerns “Optimization Problems in Hydrofoil Propulsion” and is authored by T. Y. Wu, A. T. Chwang and P. K. C. Wang. The problem considered is that an extracting ilow energy from a fluid medium by a flexible hydrofoil or airfoil. The flow is assumed to contain a wave component, such as gravity waves in water or wavy gusts in air. For a fixed thrust, the authors seek the profile which will minimize the required power. In some cases a net mechanical power can be extracted from the flow. The paper generalizes previous work by Wu. E. F. Infante describes recent results in the fourth lecture, “Stability Theory for General Dynamical Systems and Some Applications”. The concept of a dynamical system is defined and related to several classes of ordinary, partial and functional differential equations. A general stability theorem is then given, which involves a Liapunov functional, and the application of the theory is illustrated with three examples : oscillations in a transmission line, bifurcation of solutions to a partial differential equation arising in chemical reactor analyses and asymptotic stability in thermoelasticity. Finally, E. M. Barston discusses “Stability of Dissipative Systems with Applications to Fluids and Magnetofluids”. For a case of linear dissipative systems, conditions for exponential stability are listed.