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The Complex Variable Boundary Element Method (CVBEM) has an important role to play in a number of technical engineering situations and can be a tremendous help to scholars and practitioners preoccupied with solving problems in areas such as heat transport, structural mechanics and river hydraulics. As well as describing the extremely useful applications of this method, the authors explain the mathematical background to the CVBEM, which is vital to understanding the subject as a whole. Advances in the Complex Variable Boundary Element Method is the most comprehensive of books on this subject, bringing together ten years of work and boasting the latest news in CVBEM technology. It will be of particular interest to those concerned with solving technical engineering problems - scientists, graduate students, computer programmers and those working in industry may all find the book helpful. TOC:Overview of the CVBEM.- Advanced CVBEM Topics; Variable/High Order Basis Functions; Multiply Connected Domains/Regions; Two Dimensional Problems.- Applications of the CVBEM in Mathematics, Science and Engineering; Computer Interaction; Groundwater Containment Transport; Geothernal Models; Freezing Fronts; Numerical Errors - Domain Heat Transport Models; Ice Segregation; Slow-Moving Interface Problems; Parabolic Equations.- Topics of Numerical Analysis; Expansion Using Fractals; Matrix System; Logarithms.- Numerical Error Analysis; Partial Differential Equations; Error Analysis; Collocation Points; Locating / Relative Error.- Appendix A.- Appendix B.- Author Index.- Index.