Wyniki wyszukiwania:

Classical mechanics is one of those special occurrences in science where interdisciplinary contributions have come together in a perfect blend, providing a most elegant and penetrating example of "modeling" in science. Following Lagrangrian principles, the author employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst behind new concepts and discoveries, such as the d'Alembert principle, complex systems dynamics, and Hamiltonian mechanics. Today, these same dynamics are now being focused to address other interdisciplinary areas of research in...

The second edition of this classic textbook presents a rigorous and self-contained introduction to real analysis with the goal of providing a solid foundation for future coursework and research in applied mathematics. Written in a clear and concise style, it covers all of the necessary subjects as well as those often absent from standard introductory texts. Each chapter features a Problems and Complements section that includes additional material that briefly expands on certain topics within the chapter and numerous exercises for practicing the key concepts.

The first eight chapters...

This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful selection of topics and engaging tone, readers will also learn how PDEs connect to cutting-edge research and the modeling of physical phenomena. The scope of the Third Edition greatly expands on that of the previous editions by including five new chapters covering additional PDE topics relevant for current areas of active research. This includes coverage of linear parabolic equations with measurable coefficients, parabolic DeGiorgi classes,...

Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete.

It seemed therefore timely to...

Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete.

It seemed therefore timely to...