There is almost no field in Mathematics which does not use Mathe matical Analysis. Computer methods in Applied Mathematics, too, are often based on statements and procedures of Mathematical Analysis. An important part of Mathematical Analysis is Complex Analysis because it has many applications in various branches of Mathematics. Since the field of Complex Analysis and its applications is a focal point in the Vietnamese research programme, the Hanoi University of Technology organized an International Conference on Finite or Infinite Dimensional Complex Analysis and Applications which took place in Hanoi from August 8 - 12, 2001. This conference th was the 9 one in a series of conferences which take place alternately in China, Japan, Korea and Vietnam each year. The first one took place th at Pusan University in Korea in 1993. The preceding 8 conference was th held in Shandong in China in August 2000. The 9 conference of the was the first one which took place above mentioned series of conferences in Vietnam. Present trends in Complex Analysis reflected in the present volume are mainly concentrated in the following four research directions: 1 Value distribution theory (including meromorphic funtions, mero morphic mappings, as well as p-adic functions over fields of finite or zero characteristic) and its applications, 2 Holomorphic functions in several (finitely or infinitely many) com plex variables, 3 Clifford Analysis, i.e., complex methods in higher-dimensional real Euclidian spaces, 4 Generalized analytic functions."

An intensive development of the theory of generalized analytic functions started when methods of Complex Analysis were combined with methods of Functional Analysis, especially with the concept of distributional solutions to partial differential equations. The power of these interactions is far from being exhausted. In order to promote the further development of the theory of generalized analytic functions and applications of partial differential equations to Mechanics, the Technical University of Graz organized a conference whose Proceedings are contained in the present volume. The contributions on generalized analytic functions (Part One) deal not only with problems in the complex plane (boundary value and initial value problems), but also related problems in higher dimensions are investigated where both several complex variables and the technique of Clifford Analysis are used. Part Two of the Proceedings is devoted to applications to Mechanics. It contains contributions to a variety of general methods such as L p-methods, boundary elements and asymptotic methods, and hemivariational inequalities. A substantial number of the papers of Part Two, however, deals with problems in Ocean Acoustics. The papers of both parts of the Proceedings can be recommended to mathematicians, physicists, and engineers working in the fields mentioned above, as well as for further reading within graduate studies.

Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole. To set the groundwork and mitigate the difficulties newcomers often experience, An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis, such as metric spaces and the Green-Gauss Integral Formula. The approach leads to brief, clear proofs of basic statements - a distinct advantage for those mainly interested in applications. Alternate approaches, such as Fichera's proof of the Goursat Theorem and Estermann's proof of the Cauchy's Integral Theorem, are also presented for comparison. Discussions include holomorphic functions, the Weierstrass Convergence Theorem, analytic continuation, isolated singularities, homotopy, Residue theory, conformal mappings, special functions and boundary value problems. More than 200 examples and 150 exercises illustrate the subject matter and make this book an ideal text for university courses on complex analysis, while the comprehensive compilation of theories and succinct proofs make this an excellent volume for reference.