An Introduction to the Mathematical Theory of Inverse Problems

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Focusing on inverse problems, this graduate-level textbook serves as a comprehensive guide for various applications in geophysical exploration, system identification, and more. It delves into the challenges of ill-posed problems and explores regularization methods through analytical and numerical examples. The text covers three specific nonlinear inverse problems in depth, examining their direct counterparts concerning existence and uniqueness. Additionally, it offers theoretical insights and practical numerical procedures, enriched with exercises and illustrations to support mathematics and engineering coursework.