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Differential geometry. Global analysis --- Differential equations --- Numerical solutions --- Differential equations - Numerical solutions --- Systeme dynamique --- Vibration

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Symmetry is the key to solving differential equations. There are many well-known techniques for obtaining exact solutions, but most of them are special cases of a few powerful symmetry methods. Furthermore, these methods can be applied to differential equations of an unfamiliar type; they do not rely on special 'tricks'. Instead, a given differential equation is forced to reveal its symmetries, which are then used to construct exact solutions. This book is a straightforward introduction to the subject, and is aimed at applied mathematicians, physicists, and engineers. The presentation is informal, using many worked examples to illustrate the main symmetry methods. It is written at a level suitable for postgraduates and advanced undergraduates, and is designed to enable the reader to master the main techniques quickly and easily. The book contains methods that have not previously appeared in a text. These include methods for obtaining discrete symmetries and integrating factors.

Differential equations --- Symmetry. --- Mathematical physics. --- Numerical solutions. --- Differential equations - Numerical solutions. --- Mathematical physics

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Ordinary differential equations --- Numerical solutions of differential equations --- Differential equations --- Numerical solutions --- Numerical solutions. --- Differential equations - Numerical solutions

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Ordinary differential equations --- Numerical solutions of differential equations --- Differential equations --- Numerical solutions --- Numerical solutions. --- Differential equations - Numerical solutions

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"The treatment of inverse theory in this book is divided into four parts. Chapters 1 and 2 provide a general background, explaining what inverse problems are and what constitutes their solution as well as reviewing some of the basic concepts from linear algebra and probability theory that will be applied throughout the text. Chapters 3-7 discuss the solution of the canonical inverse problem : the linear problem with Gaussian statistics. This is the best understood of all inverse problems; and it is here that the fundamental notions of uncertainty, uniqueness, and resolution can be most clearly developed. Chapters 8-11 extend the discussion to problems that are non-Gaussian, nonlinear and continuous. Chapters 12-13 provide examples of the use of inverse theory and a discussion of the steps that must be taken to solve inverse problems on a computer"-- Provided by publisher

Geophysics - Measurement. --- Geophysics -- Measurement. --- Inverse problems (Differential equations) - Numerical solutions. --- Inverse problems (Differential equations) -- Numerical solutions. --- Oceanography - Measurement. --- Oceanography -- Measurement. --- Geophysics --- Oceanography --- Inverse problems (Differential equations) --- Physics --- Physical Sciences & Mathematics --- Cosmic Physics --- Measurement --- Numerical solutions --- Measurement. --- Numerical solutions. --- Oceanography, Physical --- Oceanology --- Physical oceanography --- Thalassography --- Geological physics --- Terrestrial physics --- Earth sciences --- Marine sciences --- Ocean --- Numerical analysis --- Geophysics - Measurement --- Oceanography - Measurement --- Inverse problems (Differential equations) - Numerical solutions