Plane Networks and Their Applications

This concise, fast-paced text introduces the concepts and applications behind plane networks. Currently, there is nothing in book form dealing with the topics covered in this work. The presentation unfolds in a systematic, user-friendly style and goes from the basics to cutting-edge research.Key features include:* presentation of the basics required: fundamental material from linear algebra and differential equations* examination of classical mathematical tools for analyzing discrete networks, followed by a well-developed theory, which is the continuous analogue of a discrete network* transition from the discrete to the continuous case, described via finite elements; Ch. 3 involves an analysis of linear operators, variational calculus, boundary value problems for PDEs, and Green's functions; Green's functions are the continuous analogue of the discrete error covariance functions, and form the basis for all types of error prediction* numerous examples and illustrations* techniques applied to leveling and other observation types of networks in one and two dimensions* several different applications of the continuous theory* practical problems, supported by MATLAB files, underscore the continuous theory; additional material can be downloaded from the author's website at www.kom.auc.dk/~borre/network* bibliography of recent results and indexPlane Networks and their Applications is aimed at applied mathematicians, mechanical engineers, geodesists and graduate students, and should be an excellent text for self-study, classroom, or reference