Kategoria BISAC: Mathematics >> Differential Equations - General

Eine spannende Abhandlung zu ausgewahlten Fragen der Mechanik quer durch die Jahrhunderte der Physik. Ohne groen mathematischen Ballast zeigt Acheson, wie hier die Infinitesimalrechnung - oder auch Calculus - den passenden Schlussel zum Verstandnis liefert. Das dynamische Verhalten der vorgestellten Systeme wird sowohl analytisch als auch mit Simulationen untersucht. Dazu werden QBasic-Programme verwendet, die so einfach sind, da sie jeder leicht zum Laufen bringen und seinen Fragestellungen entsprechend anpassen kann. Der Inhalt wird durch historische Darstellungen der Mechanik und durch...

In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and...

The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. All the results are included with detailed proofs, many of them simplified or rewritten on purpose for the book. The text is self-contained.

Pseudo-differential operators were initiated by Kohn, Nirenberg and Hormander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century.

The volume...