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The present volume is dedicated to celebrate the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Most articles published in this book, which consists of 32 articles in total, written by highly distinguished researchers, are in one way or another related to the scientific works of Herbert Amann. The contributions cover a wide range of nonlinear elliptic and parabolic equations with applications to natural sciences and engineering. Special topics are fluid dynamics, reaction-diffusion systems, bifurcation theory, maximal regularity, evolution equations, and the theory of function spaces.

Differential equations, Partial. --- Differential equations, Elliptic. --- Differential equations, Parabolic. --- Bifurcation theory. --- Fluid mechanics. --- Hydromechanics --- Continuum mechanics --- Differential equations, Nonlinear --- Stability --- Parabolic differential equations --- Parabolic partial differential equations --- Differential equations, Partial --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Partial differential equations --- Numerical solutions --- Global analysis (Mathematics). --- Differential equations, partial. --- Potential theory (Mathematics). --- Numerical analysis. --- Mathematical optimization. --- Analysis. --- Partial Differential Equations. --- Potential Theory. --- Numerical Analysis. --- Calculus of Variations and Optimal Control; Optimization. --- Fluid- and Aerodynamics. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mechanics --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Calculus of variations. --- Fluids. --- Hydraulics --- Physics --- Hydrostatics --- Permeability --- Isoperimetrical problems --- Variations, Calculus of --- 517.1 Mathematical analysis

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This third volume concludes our introduction to analysis, wherein we ?nish laying the groundwork needed for further study of the subject. As with the ?rst two, this volume contains more material than can treated in a single course. It is therefore important in preparing lectures to choose a suitable subset of its content; the remainder can be treated in seminars or left to independent study. For a quick overview of this content, consult the table of contents and the chapter introductions. Thisbookisalsosuitableasbackgroundforothercoursesorforselfstudy. We hope that its numerous glimpses into more advanced analysis will arouse curiosity and so invite students to further explore the beauty and scope of this branch of mathematics. In writing this volume, we counted on the invaluable help of friends, c- leagues, sta?, and students. Special thanks go to Georg Prokert, Pavol Quittner, Olivier Steiger, and Christoph Walker, who worked through the entire text cr- ically and so helped us remove errors and make substantial improvements. Our thanks also goes out to Carlheinz Kneisel and Bea Wollenmann, who likewise read the majority of the manuscript and pointed out various inconsistencies. Without the inestimable e?ortofour “typesetting perfectionist”, this volume could not have reached its present form: her tirelessness and patience with T X E and other software brought not only the end product, but also numerous previous versions,to a high degree of perfection. For this contribution, she has our greatest thanks.

Electronic books. -- local. --- Mathematical analysis. --- Mathematics. --- Mathematical analysis --- Applied Mathematics --- Engineering & Applied Sciences --- Math --- 517.1 Mathematical analysis --- Analysis (Mathematics). --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Measure theory. --- Analysis. --- Measure and Integration. --- Global Analysis and Analysis on Manifolds. --- Science --- Global analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Geometry, Differential --- Topology --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra)

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Mathematical analysis --- analyse (wiskunde)

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Differential geometry. Global analysis --- Mathematical analysis --- Mathematical physics --- differentiaalvergelijkingen --- analyse (wiskunde) --- differentiaal geometrie

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Der zweite Band dieser Einführung in die Analysis behandelt die Integrationstheorie von Funktionen einer Variablen, die mehrdimensionale Differentialrechnung und die Theorie der Kurven und Kurvenintegrale. Der im ersten Band begonnene moderne und klare Aufbau wird konsequent fortgesetzt. Dadurch wird ein tragfähiges Fundament geschaffen, das es erlaubt, interessante Anwendungen zu behandeln, die zum Teil weit über den in der üblichen Lehrbuchliteratur behandelten Stoff hinausgehen. Dies betrifft beispielsweise die Behandlung von Nemytskiioperatoren, welche eine transparente Einführung in die Variationsrechnung und Herleitung der Euler-Lagrangeschen Gleichungen ermöglicht. Ein weiteres Beispiel stellt die Darstellung der lokalen Theorie der Untermannigfaltigkeiten des Rn dar. Als Anwendungen der Theorie der Kurvenintegrale werden die Cauchyschen Integralsätze und die Theorie der holomorphen Funktionen bis einschließlich der Homologieversion des Residuensatzes entwickelt. Neben der Berechnung wichtiger bestimmter Integrale der Mathematik und der Physik, werden funktionentheoretische Eigenschaften der Gamma- und der Riemannschen Zetafunktionen besprochen. Zahlreiche Übungsaufgaben von unterschiedlichem Schwierigkeitsgrad und viele informative Abbildungen runden dieses Lehrbuch ab.

Mathematical analysis. --- Analysis (Mathematics). --- Analysis.