They generally consist of a dry, factual account of the content of the book, its intended readership and the names of those who assisted in its preparation. There are, of course, exceptions, of which Den Hartog's preface to a text on mechanics is amongst the wittiest. Musing whimsically on the futility of prefaces in general, and on the inevitable demise of those who, like Heaviside, use them to settle old scores, Den Hartog's preface contains barely a single relevant fact.

Only in the final paragraph does he touch on more conventional matters with the observation that he has 'placed no deliberate errors in the book, but he has lived long enough to be quite familiar with his own imperfections'.

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## ISBN 13: 9780521534291

We, for our part, shall stay with a more conventional format. This work is more of a text than a monograph.

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Part A the larger part of the book is intended to serve as an introductory text for advanced undergraduate and post-graduate students in physics, applied mathematics and engineering. Part B, on the other hand, is more of a research monograph and we hope that it will serve as a useful reference for professional researchers in industry and academia. We have at all times attempted to use the appropriate level of mathematics required to expose the underlying phenomena. Too much mathematics can, in our opinion, obscure the interesting physics and needlessly frighten the student.

Conversely, a studious avoidance of mathematics inevitably limits the degree to which the phenomena can be adequately explained. It is our observation that physics graduates are often well versed in the use of Maxwell's equations, but have only a passing acquaintance with fluid mechanics. Engineering graduates often have the opposite background. Consequently, we have decided to develop, more or less from first principles, those aspects of electromagnetism and fluid mechanics xvn xviii Preface which are most relevant to our subject, and which are often treated inadequately in elementary courses.

The material in the text is heavily weighted towards incompressible flows and to engineering as distinct from astrophysical applications. There are two reasons for this. The first is that there already exist several excellent texts on astrophysical, geophysical and plasma MHD, whereas texts oriented towards engineering applications are somewhat thinner on the ground. Second, in recent years we have witnessed a rapid growth in the application of MHD to metallurgical processes. This has spurred a great deal of fruitful research, much of which has yet to find its way into textbooks or monographs.

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It seems timely to summarise elements of this research. We have not tried to be exhaustive in our coverage of the metallurgical MHD, but we hope to have captured the key advances. Civil Eng. Edinburgh Sect.

### 7 editions of this work

Copson , Partial differential equations , Dautray and J. Diaz and A. Weinstein , On the fundamental solutions of a singular Beltrami operator. Studies in mathematics and mechanics presented to Richard von Mises , pp. Fischer and J. Leblond , Solutions to conjugate Beltrami equations and approximation in generalized Hardy spaces , Advances in Pure and Applied Mathematics , vol. Fischer, J.

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Leblond, J. Partington, and E. Sincich , Bounded extremal problems in Hardy spaces for the conjugate Beltrami equation in simply-connected domains , Applied and Computational Harmonic Analysis , vol. Fischer, B. Marteau, and Y.

## Front Page: AMATH A: Applied Complex Analysis

Fokas and J. Lenells , Boundary-value problems for the stationary axisymmetric einstein equations: a rotating disc , Nonlinearity , vol. Garabedian , Partial Differential Equations , Gilbert , On generalized axiallly symmetric potentials , J. Reine Angew. Math , vol. Gilbert , Poisson's equation and generalized axiallly potential theory , Ann. Pura Appl , vol. Weinacht, R. Hall, and N. Anal , vol. Henrici , On the domain of regularity of generalized axiallly symmetric potentials , Proc. Amer , pp. Rau, H. Srivastava, H. Cohl, and J.

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Tohline , Developments in determining the gravitational potential using toroidal functions , Astron. Nachr , vol. Huber , Some results on generalized axially symmetric potentials , Proceedings of the conference on differential equations , pp. Savina , On splitting up singularities of fundamental solutions to elliptic equations in??? Segura and A. Gil , Evaluation of toroidal harmonics , Computer Physics Communications , vol. Ch and.

Shushkevich , Electrostatic problem for a torus and a disk , Zh. Fiz , vol. Ph, A. Van-milligen, and. Lopez-fraguas , Expansion of vacuum magnetic fields in toiroidal harmonics , Computer Physics Communications , vol. Vekua , New methods for solving elliptic equations , Virchenko and I. Fedotova , Generalized associated Legendre functions and their applications , Weinacht , Fundamental solutions for a class of singular equations , Contributions to Differential equations , vol.

Weinacht , A mean value theorem in generalized axially symmetric potential theory , Atti Accad. Lincei Rend.