A selection of some important topics in complex analysis, intended as a sequel to the author's Classical complex analysis (see preceding entry). The five chapters are devoted to analytic continuation; conformal mappings, univalent functions, and nonconformal mappings; entire function; meromorphic fu

Selected Topics in Applied MathematicsBy Charles L. Byrne

Selected Topics in Approximation and Computation is a combination of expositions of basic classical methods of approximation leading to popular splines and new explicit tools of computation, including sinc methods, elliptic function methods, and positive operator approximation methods. It also provides an excellent summary of worst case analysis in Information Based Complexity. It relates optimal computational methods e=with the theory of s-numbers and m-widths.

This edited volume consists of twelve contributions related to the EU Marie Curie Transfer of Knowledge Project Cooperation of Estonian and Norwegian Scienti c Centres within Mathematics and its Applications, CENS-CMA (2005-2009), - der contract MTKD-CT-2004-013909, which ?nanced exchange visits to and from CENS, the Centre for Nonlinear Studies at the Institute of Cybernetics of Tallinn University of Technology in Estonia. Seven contributions describe research highlights of CENS members, two the work of members of CMA, the Centre of Mathematics for Applications,Univ- sity of Oslo, Norway, as the partner institution of CENS in the Marie Curie project, and three the ?eld of work of foreign research fellows, who visited CENS as part of theproject. Thestructureofthebookre?ectsthedistributionofthetopicsaddressed: Part I Waves in Solids Part II Mesoscopic Theory Part III Exploiting the Dissipation Inequality Part IV Waves in Fluids Part V Mathematical Methods The papers are written in a tutorial style, intended for non-specialist researchers and students, where the authors communicate their own experiences in tackling a problem that is currently of interest in the scienti?c community. The goal was to produce a book, which highlights the importance of applied mathematics and which can be used for educational purposes, such as material for a course or a seminar. To ensure the scienti?c quality of the contributions, each paper was carefully - viewed by two international experts. Special thanks go to all authors and referees, without whom making this book would not have been possible.

This book is ideal for engineering, physical science and applied mathematics students and professionals who want to enhance their mathematical knowledge. Advanced Topics in Applied Mathematics covers four essential applied mathematics topics: Green's functions, integral equations, Fourier transforms and Laplace transforms. Also included is a useful discussion of topics such as the Wiener–Hopf method, finite Hilbert transforms, the Cagniard–De Hoop method and the proper orthogonal decomposition. This book reflects Sudhakar Nair's long classroom experience and includes numerous examples of differential and integral equations from engineering and physics to illustrate the solution procedures. The text includes exercise sets at the end of each chapter and a solutions manual, which is available for instructors.

Most of the topics in applied mathematics dealt with in this handbook can be grouped rather loosely under the term analysis. They involve results and techniques which experience has shown to be of utility in a very broad variety of applications. Although care has been taken to collect certain basic results in convenient form, it is not the purpose of this handbook to duplicate the excellent collections of tables and formulas available in the National Bureau of Standards Handbook of Mathematical Functions (AMS Series 55, U.S. Government Printing Office) and in the references given therein. Rather, the emphasis in the present handbook is on technique, and we are indeed fortunate that a number of eminent applied mathe maticians have been willing to share with us their interpretations and experiences. To avoid the necessity of frequent and disruptive cross-referencing, it is expected that the reader will make full use of the index. Moreover, each chapter has been made as self-sufficient as is feasible. This procedure has resulted in occasional duplication, but as compensation for this the reader may appreciate the availability of different points of view concerning certain topics of current interest. As editor, I would like to express my appreciation to the contributing authors, to the reviewers, to the editorial staff of the publisher, and to the many secretaries and typists who have worked on the manuscript; without the partnership of all of these people, this handbook would not have been possible.