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Transform methods with applications to engineering and operations research
Book reviews computer program required is not detailed in the book, it has to be acquired separately (at a cost). The 470 page book is very well put together. It adopts a hierarchical structure taking the student through levels of increasing sophistication with numerous case studies and exercises but includes easily accessed reference material. Its explanations are clear and careful, even painstaking, and its references (alphabetic by author) quite extensive. In summary, a well written book but one which should be regarded as an input manual to a consultant's computer package.
B.W. HOLLOCKS British Steel Corporation Sheffield, U.K.
EGINHARD J. MUTH, Transform Methods with
Applications to Engineering and Operations Research, Prentice-Hall, Englewood Cliffs, N J, 1977, xi + 372 pages, $ 29.65. The book provides a thorough elementary introduction to transform methods. After an introductory chapter on the theory of complex numbers, the author defines the Laplace transform. A number of results about these transforms and techniques for obtaining transforms are treated. The next chapter on the inverse Laplace transform is almost completely devoted to the method of partial fraction decomposi. tion. Then in Chapter 5 a number of applications to the theory of ordinary differential equations, with examples from mechanical and electrical engineering and economics are given. This chapter contains also applications to integral equations and probab~ty theory. In the remaining part of the book a similar treatment of the z.transform is given. The book has a limited scope. Only Laplace and z-transforms are treated and that only at an elementary level. The treatment is very careful and transparent. There are many examples and exercises. Therefore, the book will be very useful in elementary cGur,~¢$.
M.L.J. HAUTUS Eindhoven University o f Technology, Eindhoven The Netherlands
385
HAROLD EXTON, Hypergeometric Integrals. Wiley, New York, 1973, S 15.00. The hypergeometric function began_ life as a power series which had as special cases many of the common (elementary and not so elementary) functions ,f mathematics and mathematical physics. Naturally, this was extended to the concept of the generalized hypergeometric function which was then investigated on its own account and also for its applications. This book is in two parts. Seven chapters comprise the first part and these give the general theory of integrals and transforms of hypergeometric functions together with examples of their uses in statistics and in mathematical physics. The second part consists of about one hundi'ed pages of tables of formulae and fifty pages of computer programs (in FORTRAN) for the evaluation of integrals. This book wiLl probably be useful in a variety of sciences. HoweveL the ootential user should always be on the lookout for misprints, for in a casual run through the book a few minor ones were noticed. (Even the Bateman project with its large number of helpers could not avoid them and corrections appeared regularly in Mathematics of Computation for many years.) Contents. Part One. Chapter 1. Hypergeometric functions of one or more variables. Integrals of Euler type. 3. Definite integrals and repeated integrals. 4. Contour Integrals. 5. lnf'mite Integrals. 6. Multiple Integrals. 7. Applications. Pa~ Two. A. Tables of Hypergeometric Integrals. B. Computer Programs. Selected Bibliography. .
D. KERSHAW University o f Lancaster Lancaster, U.K.
B.W. HOLLOCKS British Steel Corporation Sheffield, U.K.
EGINHARD J. MUTH, Transform Methods with
Applications to Engineering and Operations Research, Prentice-Hall, Englewood Cliffs, N J, 1977, xi + 372 pages, $ 29.65. The book provides a thorough elementary introduction to transform methods. After an introductory chapter on the theory of complex numbers, the author defines the Laplace transform. A number of results about these transforms and techniques for obtaining transforms are treated. The next chapter on the inverse Laplace transform is almost completely devoted to the method of partial fraction decomposi. tion. Then in Chapter 5 a number of applications to the theory of ordinary differential equations, with examples from mechanical and electrical engineering and economics are given. This chapter contains also applications to integral equations and probab~ty theory. In the remaining part of the book a similar treatment of the z.transform is given. The book has a limited scope. Only Laplace and z-transforms are treated and that only at an elementary level. The treatment is very careful and transparent. There are many examples and exercises. Therefore, the book will be very useful in elementary cGur,~¢$.
M.L.J. HAUTUS Eindhoven University o f Technology, Eindhoven The Netherlands
385
HAROLD EXTON, Hypergeometric Integrals. Wiley, New York, 1973, S 15.00. The hypergeometric function began_ life as a power series which had as special cases many of the common (elementary and not so elementary) functions ,f mathematics and mathematical physics. Naturally, this was extended to the concept of the generalized hypergeometric function which was then investigated on its own account and also for its applications. This book is in two parts. Seven chapters comprise the first part and these give the general theory of integrals and transforms of hypergeometric functions together with examples of their uses in statistics and in mathematical physics. The second part consists of about one hundi'ed pages of tables of formulae and fifty pages of computer programs (in FORTRAN) for the evaluation of integrals. This book wiLl probably be useful in a variety of sciences. HoweveL the ootential user should always be on the lookout for misprints, for in a casual run through the book a few minor ones were noticed. (Even the Bateman project with its large number of helpers could not avoid them and corrections appeared regularly in Mathematics of Computation for many years.) Contents. Part One. Chapter 1. Hypergeometric functions of one or more variables. Integrals of Euler type. 3. Definite integrals and repeated integrals. 4. Contour Integrals. 5. lnf'mite Integrals. 6. Multiple Integrals. 7. Applications. Pa~ Two. A. Tables of Hypergeometric Integrals. B. Computer Programs. Selected Bibliography. .
D. KERSHAW University o f Lancaster Lancaster, U.K.