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The use of actual observations to infer the properties of a model is an inverse problem, which are often difficult as they may not have a unique solution. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, including many heuristic arguments. Prompted by recent developments in...

Reviews and extends the theory of Lie groups, develops differential geometry, proposing compact definitions of torsion and of curvature, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics.

Uses a unifying illustration: two simple theories are studied with some detail, the theory of heat conduction and the theory of linear elastic media.

Shows that the resulting equations derived in this manner differ quantitatively and qualitatively from those usually presented.

Reviews and extends the theory of Lie groups, develops differential geometry, proposing compact definitions of torsion and of curvature, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics.

Uses a unifying illustration: two simple theories are studied with some detail, the theory of heat conduction and the theory of linear elastic media.

Shows that the resulting equations derived in this manner differ quantitatively and qualitatively from those usually presented.