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; and methods 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 particular branches, such as optimal filtering and information compression.

Fractional Calculus (Mathematics in Science and Engineering, Vol. 111) (Volume 111)

Science & Math

Keith B. Oldham

Jerome Spanier

Mathematics

Elsevier Science

The product of a collaboration between a mathematician and a chemist, this text is geared toward advanced undergraduates and graduate students. Not only does it explain the theory underlying the properties of the generalized operator, but it also illustrates the wide variety of fields to which these ideas may be applied. Rather than an exhaustive treatment, it represents an introduction that will appeal to a broad spectrum of students. Accordingly, the mathematics is kept as simple as possible. The first of the two-part treatment deals principally with the general properties of differintegral operators. The second half is mainly oriented toward the applications of these properties to mathematical and other problems. Topics include integer order, simple and complex functions, semiderivatives and semi-integrals, and transcendental functions. The text concludes with overviews of applications in the classical calculus and diffusion problems.

The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order (Dover Books on Mathematics)

Dover Publications

See the best price to sell, buy, or rent books by Jerome Spanier. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Jerome Spanier