Mathematics : Applied

Turbulence modelling is critically important for industries dealing with fluid flow and for applied mathematicians. This collection of lecture courses presented at a Newton Institute instructional conference on the title topic by leading researchers, has been edited or rewritten to provide a coherent account suitable for self-study. more...

Price: $144.00

The inaugural research program of the Institute for Mathematical Sciences at the National University of Singapore took place from July to December 2001 and was devoted to coding theory and cryptology. As part of the program, tutorials for graduate students and junior researchers were given by world-renowned scholars. These tutorials covered fundamental aspects of coding theory and cryptology and were designed to prepare for original research in these areas. The present volume collects the expanded lecture notes of these tutorials. more...

Price: $91.00

Complex Dynamics: Advanced System Dynamics in Complex Variables is a graduate-level monographic textbook. It is designed as a comprehensive introduction into methods and techniques of modern complex-valued nonlinear dynamics with its various physical and non-physical applications. This book is a complex-valued continuation of our previous two monographs, Geometrical Dynamics of Complex Systems and High-Dimensional Chaotic and Attractor Systems, Volumes 31 and 32 in the Springer book series Intelligent Systems, Control and Automation: Science and Engineering, where we had developed the most powerful mathematical machinery to deal with high-dimensional nonlinear, attractor and chaotic real-valued dynamics. The present monograph is devoted to understanding, prediction and control of both low- and high-dimensional, as well as both continuous- and discrete-time, nonlinear systems dynamics in complex variables. Its objective is to provide a serious reader with a serious scientific tool that will enable him/her to actually perform a competitive research in modern complex-valued nonlinear dynamics. This book has seven Chapters. The first, introductory Chapter explains ???in plain English??? the objective of the book and provides the preliminaries in complex numbers and variables; it also gives a soft introduction to quantum dynamics. The second Chapter develops low-dimensional dynamics in the complex plane, theoretical and computational, continuous- and discrete-time. The third Chapter presents a modern introduction to quantum dynamics, mainly following Dirac's notation. The fourth Chapter develops geometrical machinery of complex manifolds, essential for the further text. The fifthChapter develops high-dimensional complex continuous dynamics, which takes place on complex manifolds. The sixth Chapter develops the formalism of complex path integrals, which extends the continuous dynamics to the general high-dimensional dynamics, which can be both discrete and stochastic. more...

Price: $199.00

Complex variables provide powerful methods for attacking many difficult problems, and it is the aim of this book to provide a thorough grounding in these methods and their application. This new edition has been improved throughout and is ideal for use in undergraduate and introductory graduate courses in complex variables. more...

Price: $52.00

The book provides a survey of numerical methods for acoustics, namely the finite element method (FEM) and the boundary element method (BEM). In particular, the FEM is often used for interior problems whereas BEM is quite popular for exterior problems. This book shows that both methods can be effectively used for many other cases, FEM even for open domains and BEM for closed ones. Emphasis of the book is put on numerical aspects and on treatment of the exterior problem in acoustics, i.e. noise radiation. Numerical aspects cover the use of different types of elements, discussing the rule of using a fixed number of elements per wavelength and iterative solution techniques for the arising system of equations. Fast boundary element techniques and multi-domain BEM are discussed in this context too. Exterior problems in the context of finite elements will survey different techniques of treatment such as infinite elements, absorbing boundary conditions and perfectly matched layers. Further, the fields of frequency-range solutions by Lanczos via Pade approximation and modal solutions are covered. In the context of BEM, the so-called irregular frequencies are considered. This is followed by considering sound propagation above an impedance plane, formulation of spectral elements, a method for treatment of thin radiators and radiation modes. Both chapters conclude with sections on fluid-structure interaction, on inverse problems and on energy methods, respectively. Finally, the book discusses future challenges in the field of numerical methods in acoustics. more...

Price: $179.00