Special Functions Of Mathematical Physics And Chemistry Sneddon Pdf

Ian Naismith Sneddon (^∗December 8, 1919 in Renfrew, Scotland; †November 4, 2000 in Glasgow) was an applied mathematician whose main research interests were in the application of integral transforms to problems in the linear theory of elasticity, especially mixed boundary-value problems, an area in which he established a formidable international reputation. In addition to his research papers, he published an impressible number of influential books, most notably on integral transform methods.

Open image in new window Ian Naismith Sneddon

Early Life and Education

Ian Naismith Sneddon was born in Renfrew (near Glasgow, Scotland), on December 8, 1919. Shortly after he was born, his family moved to Partick in the West End of Glasgow where Ian's father worked as a slater and plasterer. Ian attended Thornwood Primary School and thereafter Hyndland Secondary School. He excelled at his studies, and his mathematical talent was recognized by the Principal Teacher of Mathematics, James Milroy, who provided Ian with much encouragement. At the early age of 15, he became Dux of the school (i.e., the top pupil), and at 16 in 1936, Ian enrolled at the University of Glasgow, where he studied both mathematics and physics (which was at that time referred to as natural philosophy). He graduated with a First Class Honours BSc in the combined subjects of mathematics and natural philosophy in 1940. He then moved to Cambridge University to continue his studies of mathematics and took Part II of the Mathematical Tripos, for which he was classified as a Wrangler, and in 1942 was qualified for a BA degree. At this point he was preparing to work in pure mathematics under the supervision of Professor G. H. Hardy, FRS, but war-related work called, and Ian was drafted to the Branch for Theoretical Research at the Armament Research Department at Fort Halstead in Kent, and this set the scene for a change in the direction of his interests.

Professional Life

It was in May 1944 that Ian moved to Fort Halstead, and he worked within the group superintended by the physicist N. F. Mott, FRS (later Sir Nevill and a Nobel Prize Laureate) in problems of solid mechanics. His work was closely associated with indentation problems and the fracture of steel used in tank armour plates, and this led to his solution of the problem of a "penny-shaped crack," in part based on methods applied in the Boussinesq problem. Ian rapidly became a leading international authority in the mathematical methods used for the solution of indentation and crack problems, developing expertise in the theory of integral transforms and mixed boundary value problems and applications within the context of linear elasticity.

After the war, in 1945, Mott returned to his position at Bristol University as Professor of Physics in the H.H. Wills Physical Laboratory and recruited Ian as a research fellow in theoretical physics. In the period until his departure from Bristol in 1946, Ian worked with Mott on the writing of the book Wave Mechanics and Its Applications (Mott and Sneddon, 1948), and this was published in 1948. In 1946 Ian was appointed as a lecturer in Department of Natural Philosophy at his alma mater, the University of Glasgow, where he undertook research in both theoretical nuclear physics and elasticity theory and embarked on a teaching career. He was awarded the degree of DSc by the University of Glasgow in 1948, his submitted work for which was awarded the university's Kelvin Medal.

During this period in Glasgow, Ian was working on a major book that focused on Fourier, Laplace, Mellin, and Hankel transforms and their applications and was almost completed when he was appointed, in 1950, to the first chair of mathematics at the University College of North Staffordshire in Keele (subsequently named Keele University). At the age of 30, he was the youngest professor of mathematics in the UK. His book, entitled Fourier Transforms (Sneddon, 1951), was published shortly after his arrival in Keele. It contained the dedication "To the University of Glasgow on the occasion of its fifth centenary 1451–1951."

At Keele Ian took on a heavy administrative responsibility and was involved in many university committees, but he managed to build up a small but strong group of mathematicians as well as to maintain his own research. This was in addition to the production of two undergraduate textbooks based on his teaching at both Glasgow and Keele: these widely used texts are entitled Special Functions of Mathematical Physics and Chemistry (Sneddon, 1956) and Elements of Partial Differential Equations (Sneddon, 1957).

After his 5 years at Keele, in 1956 Ian was invited to accept appointment as the newly established Simson Professor of Mathematics at the University of Glasgow, and he duly accepted and returned to Glasgow in 1957 where he remained until his retirement in 1985. In Glasgow Ian took on a heavy teaching load and introduced applied mathematics into the mathematics curriculum, which hitherto had been dominated by pure mathematics as applied aspects of the subject were taught within the Department of Natural Philosophy. He had a long and distinguished career in Glasgow and played a major role in the life of the university, contributing substantially to many university committees, as well as serving as Head of the Department of Mathematics, Dean of the Faculty of Science, and member of the University Court (the University's governing body). He was elected as a Fellow of the Royal Society of Edinburgh (FRSE) in 1958 and awarded the Makdougall-Brisbane Prize of the RSE in the same year. He also served as a member of the Council of the RSE, including a total of 6 years as vice president.

In addition to his commitment to the University of Glasgow and the Royal Society of Edinburgh, Ian travelled extensively outside Scotland. In particular, he spent many periods in the USA, including as a Visiting Professor at North Carolina, Duke and Indiana Universities, and the State University of New York. He also had strong connections with Poland and was recognized there as a Foreign Member of the Polish Academy of Science (1968) and as a Commander of the Order of Polonia Restituta (1969). He was awarded the Copernicus Medal of Polish Academy of Sciences (1973) and received an Honorary Doctorate from Warsaw University (1973), while in 1979 he became a Commander of the Polish Order of Merit and, in the same year, was awarded the Eringen Medal of the Society of Engineering Science in the USA.

Ian devoted much time to service at the national level. For example, he spent various periods as a member of the Scientific Advisory Council of the Ministry of Defence and was Chairman of the Mathematics Committee of the then Science Research Council (SRC, now EPSRC) and as a member of the Universities Science and Technology Board. In recognition of this work, he was awarded the honour of an OBE (Order of the British Empire) in 1969.

In the UK his academic distinction was recognized by the conferring on him of honorary doctorates at Heriot-Watt University (1982), the University of Hull (1983), and the University of Strathclyde (1994). The finest accolade he received was his election as a Fellow of the Royal Society (FRS) in 1983 just 2 years prior to his retirement from the University of Glasgow.

Scientific Contributions

Ian's main contributions were to the application of integral transform methods in problems of the mechanics of solids, particularly mixed boundary value problems, with a focus on the linear theories of elastostatics, elastodynamics, and thermoelasticty. These are exemplified by contact and surface loading problems and crack problems highlighted in the books Fourier Transforms (Sneddon, 1951); Mixed Boundary Value Problems in Potential Theory (Sneddon, 1966); Crack Problems in the Classical Theory of Elasticity (Sneddon and Lowengrub, 1969); The Use of Integral Transforms (Sneddon, 1972), listed in chronological order of publication; as well as The Linear Theory of Thermoelasticity (Sneddon, 1974), which was based on lectures given at the International Centre for Mechanical Sciences in Udine, Italy, and the set of notes The Use of Operators of Fractional Integration in Applied Mathematics (Sneddon, 1979), published by the Polish Academy of Sciences.

He also published An Introduction to the Mathematics of Medicine and Biology (Defares and Sneddon, 1960), presaging in 1960 what has become an important area of research in applied mathematics. In addition to his textbooks Special Functions of Mathematical Physics and Chemistry (Sneddon, 1956) and Elements of Partial Differential Equations (Sneddon, 1957) mentioned above, he published the textbook Fourier Series (Sneddon, 1961).

Ian Sneddon's books have been widely influential in both research and undergraduate teaching and in total have attracted well over 10,000 citations in Google Scholar. Ian's research output has been prodigious, and many of his research papers have been groundbreaking and are highly cited: particular mention should be made of the papers The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile (Sneddon, 1965), On certain integrals of Lipschitz–Hankel type involving products of Bessel functions (Eason et al., 1955), and The distribution of stress in the neighbourhood of a crack in an elastic solid (Sneddon, 1946), which, at the time of writing, have attracted, respectively, 3821, 2551, and 1454 citations, and these alone are indicative of his enormous influence.

Ian was an excellent advisor of PhD students, and 20 students graduated under his supervision, many of whom went on to become professors in various countries of the world, the most noted being A.J.M. Spencer, FRS, who was a professor at the University of Nottingham for many years.

Family and the Arts

In September 1943 Ian married Mary Campbell Macgregor, and Mary joined him in Cambridge until the move to Fort Halstead. Mary and Ian had three children, two sons and a daughter. In their home Ian and Mary offered warm and generous hospitality to many visitors, who remember such occasions with affection. Ian was renowned for the delightful fund of stories he recounted about famous mathematicians and scientists with whom he was acquainted.

Ian was an aficionado of the arts and in particular was heavily involved in the musical life of Scotland. He was a member of the Board of the Scottish National Orchestra, the Advisory Council of Scottish Opera, and was Chairman of the BBC Scottish Music Advisory Committee for several years. In addition, he was a member of the Board of the Citizens Theatre in Glasgow. Music also featured in his Polish connections during his many visits to Poland, and he was a strong supporter of the Scottish Polish Friendship Society.

Much more about Ian's life and work can be found in the excellent biographical memoir written by Professor Peter Chadwick, FRS (Chadwick, 2002) for the Royal Society. His entry in the MacTutor History of Mathematics (O'Connor and Robertson, 2003) is also a useful source of information, and, in particular, it contains links to obituaries in The Times and Scotsman newspapers and other links of interest.