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As computer-assisted modeling and analysis of physical processes have continued to grow and diversify, sensitivity and uncertainty analyses have become indispensable investigative scientific tools in their own right. While most techniques used for these analyses are well documented, there has yet to appear a systematic treatment of the method based on adjoint operators, which is applicable to a much wider variety of problems than methods traditionally used in control theory. This book fills that gap, focusing on the mathematical underpinnings of the Adjoint Sensitivity Analysis Procedure (ASAP) and the use of deterministically obtained sensitivities for subsequent uncertainty analysis.