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"Frontiers in Applied MathematicsInverse problems arise in a number of important practical applications, ranging from biomedical imaging to seismic prospecting. This book provides the reader with a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems. It also addresses specialized topics like image reconstruction, parameter identification, total variation methods, nonnegativity constraints, and regularization parameter selection methods.Because inverse problems typically involve the estimation of certain quantities based on indirect measurements, the estimation process is often ill-posed. Regularization methods, which have been developed to deal with this ill-posedness, are carefully explained in the early chapters of Computational Methods for Inverse Problems. The book also integrates mathematical and statistical theory with applications and practical computational methods, including topics like maximum likelihood estimation and Bayesian estimation.Several web-based resources are available to make this monograph interactive, including a collection of MATLAB m-files used to generate many of the examples and figures. These resources enable readers to conduct their own computational experiments in order to gain insight. They also provide templates for the implementation of regularization methods and numerical solution techniques for other inverse problems. Moreover, they include some realistic test problems to be used to further develop and test various numerical methods."

"Here is a clearly written introduction to three central areas of inverse problems: inverse problems in electromagnetic scattering theory, inverse spectral theory, and inverse problems in quantum scattering theory. Inverse problems, one of the most attractive parts of applied mathematics, attempt to obtain information about structures by nondestructive measurements. Based on a series of lectures presented by three of the authors, all experts in the field, the book provides a quick and easy way for readers to become familiar with the area through a survey of recent developments in inverse spectral and inverse scattering problems."

"This book presents current research trends in the field of underwater acoustic wave direct and inverse problems. Until very recently, little has been published concerning model-based inversions of the boundaries and material constants of finite-sized targets located either in the water column or the sediments. This text is the first to investigate inverse problems in an ocean environment with a heavy emphasis placed on the description and resolution of the forward scattering problem.Marine Acoustics: Direct and Inverse Problems emphasizes computation of Green's Functions with new material added for elastic and poro-elastic seabeds. This timely publication addresses many areas of practical interest in connection with underwater acoustical imaging including ecological survey and clean up, protection of open water harbors, offshore petroleum and gas enterprises, as well as environmental and military uses. The ocean-seabed system is an acoustic waveguide and this is the only book that treats inverse problems in a waveguide. The propagation of acoustic waves in this system is treated for various types of seabeds and the direct and inverse problems are considered in realistic ocean environments. The inverse problem is to determine the shape of an impenetrable or penetrable object, or to determine the coefficients describing the seabed. This is done by acoustically illuminating the seabed and investigating the scattered field."

"This book offers a concise introduction to the analysis of electrical transients aimed at students who have completed introductory circuits and freshman calculus courses. While it is written under the assumption that these students are encountering transient electrical circuits for the first time, the mathematical and physical theory is not ‘watered-down.’ That is, the analysis of both lumped and continuous (transmission line) parameter circuits is performed with the use of differential equations (both ordinary and partial) in the time domain, and the Laplace transform. The transform is fully developed in the book for readers who are not assumed to have seen it before. The use of singular time functions (unit step and impulse) is addressed and illustrated through detailed examples.The appearance of paradoxical circuit situations, often ignored in many textbooks (because they are, perhaps, considered ‘difficult’ to explain) is fully embraced as an opportunity to challenge students. In addition, historical commentary is included throughout the book, to combat the misconception that the material in engineering textbooks was found engraved on Biblical stones, rather than painstakingly discovered by people of genius who often went down many wrong paths before finding the right one. MATLAB® is used throughout the book, with simple codes to quickly and easily generate transient response curves."