Fourier analysis aims to decompose functions into a superposition of simple trigonometric functions, whose special features can be exploited to isolate specific components into manageable clusters before reassembling the pieces. This two-volume text presents a largely self-contained treatment, comprising not just the major theoretical aspects (Part I) but also exploring links to other areas of mathematics and applications to science and technology (Part II). Following the historical and co...

Das Buch umfasst die Analysis in einer Veränderlichen. Es behandelt den Stoff der Vorlesung Analysis 1, wie er gewöhnlich an Hochschulen im deutschsprachigen Raum gelehrt wird und ist sowohl als Lehrbuch als auch zum vertiefenden Selbststudium geeignet. Zahlreiche Beispiele und Übungsaufgaben werden bereitgestellt. Geschichtliche Hintergründe sind durchgehend zu finden. Darüber hinaus wird das wechselseitig fordernde Ineinandergreifen von Theorie und Anwendungen anhand vieler ausführlich b...

This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest.Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and nume...

Wolf's discovery demonstrating that a reporter gene is expressed in myocytes subsequent to injection of naked DNA, was exploited by immunologists and vaccinologists to develop a new generation of vaccines. This observation galvanized the research and in a short lapse of time, an oceanic volume of knowledge has been accumulated. The research carried out in a variety of animal models showed the efficacy of genetic immunization against viruses, bacteria, and some parasites by the ability to i...