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(More customer reviews)This book introduces differential forms to physicists. It is suitable for those with no advanced training in math other than multivarible calculus and linear algebra. No prior knowledge of topology is needed, although it doesn't hurt. The book starts with a good intro explaining the motivation for forms and when they might be useful over tensors and vectors. The exterior algebra is then presented in chapter 2, followed by a chapter on the exterior derivative. The rest of the book prestents a good deal of applications of forms including the statement and proof of the Newton-Leibniz-Ostrogradksy-Gauss-Green-Stokes Theorem, usually just called Stoke's Theorem. I'd recommend this book to any grad student in Theoretical physics that plans on doing research on physics in the 21st century.
Click Here to see more reviews about: Computational Methods for Modeling of Nonlinear Systems, Volume 11 (Mathematics in Science and Engineering)
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. - Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loevetransform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
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