There was a special year devoted to the topic of several complex variables at the Mittag-Leffler Institute in Stockholm, Sweden, and this volume contains the resulting survey papers and research papers. The work covers a broad spectrum of developments in this field. The contributors include H. Alexander; F. Almgren; E. Almar; M. Andersson; E. Bedford; J. Belanger; S. Bell; B. Berndtsson; U. Cegrell; C.H. Chang and H.P. Lee; J. Chaumat and A.M. Chollet; J. D'Angelo; J. P. Demailley; P. Dolbeault; A. Dor; F. Forstneric; B. Gaveau, M. Okada, and T. Okada; R. Greene and S. Krantz; A. Iordan; C. Laurent-Thiebaut and J. Leiterer; L. Lempert; I. Lieb and M. Range; L. Qi-King; P. Manne; A. Noell; M. Passare; J. Riihentaus; J. P. Rosay and W. Rudin; R. Saerens and W. Zame; A. Sergeev; N. Sibony; E.L. Stout; F. Treves; S. Webster; H. H. Wu; and A. Zeriahi.

The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.

Diskrete und kontinuierliche Methoden der mathematischen Optimierung werden in diesem Lehrbuch integriert behandelt. Nach einer Einfuhrung werden konvexe Mengen (mit einer Anwendung auf notwendige Optimalitatsbedingungen bei Ungleichungsrestriktionen) behandelt, gefolgt von einer genaueren Betrachtung des Spezialfalls von Polyedern und dessen Zusammenhang zum Linearen Programmieren. Eine ausfuhrliche Darstellung des Simplexverfahrens schliesst diesen Teil ab. Danach wird die Konvexitat von Funktionen (inklusive einiger Abschwachungen) untersucht und fur ein grundliches Studium von Optimalitatskriterien sowie der Lagrange-Dualitat verwendet. Schliesslich folgen noch ein Ausblick auf allgemeine Algorithmen sowie ein kurzer Anhang zur affinen Geometrie. In der Neuauflage ist Anordnung und Darstellung des behandelten Stoffs nochmals grundlich im Sinne der aktuellen BA-Studiengange Mathematik, Wirtschaftswissenschaften und Informatik uberarbeitet worden.

Die Bezeichnung Kontrolltheorie ist eine etwas ungliickliche neudeutsche Sprachschopfung, die auch von Fachleuten nur zogernd akzeptiert wird. In gangigen Nachschlagewerken wird man ihn vergeblich suchen; denkbar ware, daJ3 man in Zukunft eine kurze Eintragung folgender Art findet: Die K. befaJ3t sich mit mathematischen Modellen fUr die Prozesse der Steuerung und Selbst- regulierung, also mit den theoretischen Moglichkeiten der Beeinflussung von dynamischen Systemen. Diese mehr intuitive und vage Definition ist der Aus- gangspunkt fUr die einleitenden Betrachtungen im Kap. 1, welches den Leser iiber den Gegenstand dieses Buches ausfUhrlicher informiert. Die Vorganger der Kontrolltheorie hieJ3en im deutschen Sprachraum Rege- lungs-und Steuerungstheorie oder auch technische Kybernt: tik. Aus der Sicht des Mathematikers lebten sie von Anleihen bei verschiedenen mathematischen Diszi- plinen: Differentialgleichungen, Variationsrechnung, Funktionentheorie und Sto- chastik. Man brauchte daher - dies war die giingige Meinung - auch nur tiber die notigen Grundkenntnisse aus diesen Gebieten zu verfUgen, urn sich in der Rege- lungstheorie ohne fremde Hilfe zurechtfinden zu konnen. Diese Einschatzung mochte noch in den sechziger J ahren bis zu einem gewissen Grade zutreffen; heute liegen die Dinge anders. Die Kontrolltheorie ist eine angewandte Disziplin mit eigenem Profil und nicht mehr einfach eine Anhaufung mathematischer Hilfs- mittel. Urn mit ihrer spezifischen Problematik vertraut zu werden und einen Uber- blicJ

Fur viele Aufgabenstellungen bei der Automatisierung technischer Systeme sowie im Bereich der Naturwissenschaften und Wirtschaftswissenschaften benotigt man genaue mathematische Modelle fur das dynamische Verhalten von Systemen. Das Werk behandelt Methoden zur Ermittlung dynamischer Modelle aus gemessenen Signalen, die unter dem Begriff Systemidentifikation oder Prozessidentifikation zusammengefasst werden. "Band 2" beschreibt weitergehende Methoden und Anwendungen: - Maximum-Likelihood-Methode; - Rekursive Parameterschatzung; - Modellabgleich-Verfahren; - Mehrgrossen- und nichtlineare Systeme; - Anwendungen in Maschinenbau und Elektrotechnik, Energie- und Verfahrenstechnik. Beide Bande bilden eine Einheit und fuhren systematisch von den Grundlagen bis zu den Problemen des praktischen Einsatzes. Sie wenden sich daher sowohl an Studenten der Fachrichtungen Elektrotechnik, Maschinenbau, Informatik, Mathematik, Natur- und Wirtschaftswissenschaften als auch an die in der Praxis tatigen Ingenieure und Wissenschaftler."

Fur viele Aufgabenstellungen bei der Automatisierung technischer Systeme und im Bereich der Naturwissenschaften und Wirtschaftswissenschaften benotigt man genaue mathematische Modelle fur das dynamische Verhalten von Systemen. Das Werk behandelt Methoden zur Ermittlung dynamischer Modelle aus gemessenen Signalen, die unter dem Begriff Systemidentifikation oder Prozessidentifikation zusammengefasst werden. In "Band 1" werden die grundlegenden Methoden behandelt. Nach einer kurzen Einfuhrung in die benotigten Grundlagen linearer Systeme wird zunachst die Identifikation nichtparametrischer Modelle mit zeitkontinuierlichen Signalen mittels Fourieranalyse, Frequenzgangmessung und Korrelationsanalyse behandelt. Dann folgt eine Einfuhrung in die Parameterschatzung fur parametrische Modelle mit zeitdiskreten Signalen. Dabei steht die Methode der kleinsten Quadrate im Vordergrund, gefolgt von ihren Modifikationen, der Hilfsvariablenmethode und der stochastischen Approximation."

It is commonly believed that macroeconomic models are not useful for policy analysis because they do not take proper account of agents' expectations. Over the last decade, mainstream macroeconomic models in the UK and elsewhere have taken on board the Rational Expectations Revolution' by explicitly incorporating expectations of the future. In principle, one can perform the same technical exercises on a forward expectations model as on a conventional model -- and more Rational Expectations in Macroeconomic Models deals with the numerical methods necessary to carry out policy analysis and forecasting with these models. These methods are often passed on by word of mouth or confined to obscure journals. Rational Expectations in Macroeconomic Models brings them together with applications which are interesting in their own right. There is no comparable textbook in the literature. The specific subjects include: (i) solving for model consistent expectations; (ii) the choice of terminal condition and time horizon; (iii) experimental design: i.e., the effect of temporary vs permanent, anticipated vs. unanticipated shocks; deterministic vs. stochastic, dynamic vs. static simulation; (iv) the role of exchange rate; (v) optimal control and inflation-output tradeoffs. The models used are those of the Liverpool Research Group in Macroeconomics, the London Business School and the National Institute of Economic and Social Research.

Not many disciplines can c1aim the richness of creative ideas that make up the subject of analytical mechanics. This is not surprising since the beginnings of analyti cal mechanics mark also the beginnings of the theoretical treatment of other physical sciences, and contributors to analytical mechanics have been many, inc1uding the most brilliant mathematicians and theoreticians in the history of mankind. As the foundation for theoretical physics and the associated branches of the engineering sciences, an adequate command of analytical mechanics is an essential tool for any engineer, physicist, and mathematician active in dynamics. A fascinating dis cipline, analytical mechanics is not only indispensable for the solution of certain mechanics problems but also contributes so effectively towards a fundamental under standing of the subject of mechanics and its applications. In analytical mechanics the fundamental laws are expressed in terms of work done and energy exchanged. The extensive use of mathematics is a consequence of the fact that in analytical mechanics problems can be expressed by variational State ments, thus giving rise to the employment of variational methods. Further it can be shown that the independent variables may be either displacements or impulses, thus providing in principle the possibility of two complementary formulations, i.e. a dis placement formulation and an impulse formulation, for each problem. This duality is an important characteristic of mechanics problems and is given special emphasis in the present book."

This book presents the concepts and algorithms of advanced industrial process control and on-line optimization within the framework of a multilayer structure. It describes the interaction of three separate layers of process control: direct control, set-point control, and economic optimization. The book features illustrations of the methodologies and algorithms by worked examples and by results of simulations based on industrial process models.

This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variable, the topic is classical and rather well understood. In several variables, the necessary understanding of holomorphic functions via partial differential equations has a recent origin, and Professor Stein's book, which emphasizes the potential-theoretic aspects of the boundary value problem, should become the standard work in the field. Originally published in 1972. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Global analysis describes diverse yet interrelated research areas in analysis and algebraic geometry, particularly those in which Kunihiko Kodaira made his most outstanding contributions to mathematics. The eminent contributors to this volume, from Japan, the United States, and Europe, have prepared original research papers that illustrate the progress and direction of current research in complex variables and algebraic and differential geometry. The authors investigate, among other topics, complex manifolds, vector bundles, curved 4-dimensional space, and holomorphic mappings. Bibliographies facilitate further reading in the development of the various studies. Originally published in 1970. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This textbook on the calculus of variations leads the reader from the basics to modern aspects of the theory. One-dimensional problems and the classical issues such as Euler-Lagrange equations are treated, as are Noether's theorem, Hamilton-Jacobi theory, and in particular geodesic lines, thereby developing some important geometric and topological aspects. The basic ideas of optimal control theory are also given. The second part of the book deals with multiple integrals. After a review of Lebesgue integration, Banach and Hilbert space theory and Sobolev spaces (with complete and detailed proofs), there is a treatment of the direct methods and the fundamental lower semicontinuity theorems. Subsequent chapters introduce the basic concepts of the modern calculus of variations, namely relaxation, Gamma convergence, bifurcation theory and minimax methods based on the Palais-Smale condition. The prerequisites are knowledge of the basic results from calculus of one and several variables. After having studied this book, the reader will be well equipped to read research papers in the calculus of variations.

Global analysis describes diverse yet interrelated research areas in analysis and algebraic geometry, particularly those in which Kunihiko Kodaira made his most outstanding contributions to mathematics. The eminent contributors to this volume, from Japan, the United States, and Europe, have prepared original research papers that illustrate the progress and direction of current research in complex variables and algebraic and differential geometry. The authors investigate, among other topics, complex manifolds, vector bundles, curved 4-dimensional space, and holomorphic mappings. Bibliographies facilitate further reading in the development of the various studies. Originally published in 1970. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Ce livre est une initiation aux approches modernes de l'optimisation mathematique de formes. Il s'appuie sur les seules connaissances de premiere annee de Master de mathematiques, mais permet deja d'aborder les questions ouvertes dans ce domaine en pleine effervescence. On y developpe la methodologie ainsi que les outils d'analyse mathematique et de geometrie necessaires a l'etude des variations de domaines. On y trouve une etude systematique des questions geometriques associees a l'operateur de Laplace, de la capacite classique, de la derivation par rapport a une forme, ainsi qu'un FAQ sur les topologies usuelles sur les domaines et sur les proprietes geometriques des formes optimales avec ce qui se passe quand elles n'existent pas, le tout avec une importante bibliographie.

Ce cours est une introduction A la modA(c)lisation mathA(c)matique et A l'analyse numA(c)rique pour la chimie molA(c)culaire quantique, un champ peu connu des mathA(c)maticiens et pourtant riche en sujets d'investigation. Le point de vue choisi est celui du mathA(c)maticien appliquA(c). Le cours est construit de maniA]re auto-consistante. Seules des notions de base en analyse fonctionnelle sont requises pour l'aborder. Les outils mathA(c)matiques plus A(c)laborA(c)s sont introduits progressivement et les connaissances nA(c)cessaires en physique et en thA(c)orie spectrale sont regroupA(c)es dans des annexes. On prA(c)sente d'abord les modA]les les plus utilisA(c)s en pratique. Puis, on analyse ces modA]les d'un point de vue mathA(c)matique (questions d'existence de solutions, d'unicitA(c), ...). On introduit ensuite les diffA(c)rentes stratA(c)gies numA(c)riques employA(c)es pour la rA(c)solution pratique, et on fournit, quand ceci est possible, des A(c)lA(c)ments d'analyse numA(c)rique de ces mA(c)thodes. Les liens existants entre les modA]les de la chimie molA(c)culaire et des sujets connexes sont aussi explorA(c)s: modA(c)lisation de la phase liquide, physique de l'A(c)tat cristallin, biologie, simulation des matA(c)riaux, ... Le cours peut aussi intA(c)resser le chimiste ou le physicien curieux de comprendre les techniques mathA(c)matiques dont relA]vent les modA]les qu'il utilise, et de dA(c)couvrir comment de telles techniques peuvent amA(c)liorer significativement l'efficacitA(c) et la qualitA(c) des simulations numA(c)riques.

The book is an introduction to the mathematical modelling and the numerical analysis for computational quantum chemistry. The text isself-consistent: no particular familiarity with the subject nor the mathematical tools is required. Only a basic training in functional analysis is necessary. The models are introduced and discussed. They are analyzed mathematically. The numerical techniques are presented and, when possible, also analyzed. Topics closely related to molecular simulation are also addressed, such as solid state physics, liquid state physics, biology, and materials science. The book can
also be useful for students and researchers of those fields, curious about the mathematical techniques and the numerical strategies.

This hands-on guide is primarily intended to be used in undergraduate laboratories in the physical sciences and engineering. It assumes no prior knowledge of statistics. It introduces the necessary concepts where needed, with key points illustrated with worked examples and graphic illustrations. In contrast to traditional mathematical treatments it uses a combination of spreadsheet and calculus-based approaches, suitable as a quick and easy on-the-spot reference. The emphasis throughout is on practical strategies to be adopted in the laboratory.
Error analysis is introduced at a level accessible to school leavers, and carried through to research level. Error calculation and propagation is presented though a series of rules-of-thumb, look-up tables and approaches amenable to computer analysis. The general approach uses the chi-square statistic extensively. Particular attention is given to hypothesis testing and extraction of parameters and their uncertainties by fitting mathematical models to experimental data. Routines implemented by most contemporary data analysis packages are analysed and explained. The book finishes with a discussion of advanced fitting strategies and an introduction to Bayesian analysis.

Guicciardini presents a comprehensive survey of both the research and teaching of Newtonian calculus, the calculus of "fluxions", over the period between 1700 and 1810. Although Newton was one of the inventors of calculus, the developments in Britain remained separate from the rest of Europe for over a century. While it is usually maintained that after Newton there was a period of decline in British mathematics, the author's research demonstrates that the methods used by researchers of the period yielded considerable success in laying the foundations and investigating the applications of the calculus. Even when "decline" set in, in mid century, the foundations of the reform were being laid, which were to change the direction and nature of the mathematics community. The book considers the importance of Isaac Newton, Roger Cotes, Brook Taylor, James Stirling, Abraham de Moivre, Colin Maclaurin, Thomas Bayes, John Landen and Edward Waring. This will be a useful book for students and researchers in the history of science, philosophers of science and undergraduates studying the history of mathematics.

These lecture notes are devoted to the analysis of a nonlocal equation in the whole of Euclidean space. In studying this equation, all the necessary material is introduced in the most self-contained way possible, giving precise references to the literature when necessary. The results presented are original, but no particular prerequisite or knowledge of the previous literature is needed to read this text. The work is accessible to a wide audience and can also serve as introductory research material on the topic of nonlocal nonlinear equations.

This book deals with a class of mathematical problems which involve the minimization of the sum of a volume and a surface energy and have lately been refered to as 'free discontinuity problems'. Examples of such problems come from fracture mechanics, image analysis, or the theory of phase transitions. A systematic introduction to this field, this book is highly suitable for graduate students, bridging the gap between research level texts and elementary textbooks on measure theory and calculus of variation. The first half of the book contains a comprehensive and updated treatment of the theory of Functions of Bounded Variation and of the mathematical prerequisites of that theory, that is Abstract Measure Theory and Geometric Measure Theory.

This text discusses existence and necessary conditions, such as Potryagin's maximum principle, for optimal control problems described by ordinary and partial differential equations. These necessary conditions are obtained from KuhnTucker theorems for nonlinear programming problems in infinite dimensional spaces. The optimal control problems include control constraints, state constraints and target conditions. Evolution partial differential equations are studied using semigroup theory, abstract differential equations in linear spaces, integral equations and interpolation theory. Existence of optimal controls is established for arbitrary control sets by means of a general theory of relaxed controls. Applications include nonlinear systems described by partial differential equations of hyperbolic and parabolic type and results on convergence of suboptimal controls.

A paperback edition of this successful textbook for final year undergraduate mathematicians and control engineering students, this book contains exercises and many worked examples, with complete solutions and hints making it ideal not only as a class textbook but also for individual study. The intorduction to optimal control begins by considering the problem of minimizing a function of many variables, before moving on to the main subject: the optimal control of systems governed by ordinary differential equations.

Modelle von komplexen, dynamischen Systemen findet man heute nicht nur innerhalb der Nachrichten- und Regelungstechnik, sondern auch in den anderentechnischen Disziplinen, den Natur-, Sozial-, Wirtschafts- und Umweltwissenschaften. Seitdem gr- ere elektronische Rechnerkapazit{ten verf}gbar sind, erm-glicht die numerische Simulation die Systemanalyse anhand dieser Modelle. Dieses Lehrbuch f}hrt in die Simulationsmethode ein, nachdem der notwendige erste Schritt, die Modellbildung ausf}hrlich behandelt wurde. Ein umfangreiches Kapitel istder Identifikation gewidmet, bei der aufgrund vorhandener Me daten Struktur und Parameter von Modellen festgelegt werden. Als Beispiele zur Illustration dieser interdisziplin{ren Me- thoden werden zwar nat}rliche undtechnische Systeme verwen- det, der Lernstoff wird jedoch unabh{ngig von speziellen An- wendungen formuliert. Mathematikkenntnisse entsprechend dem Vordiplom in den Ingenieurwissenschaften werden zwar voraus- gesetzt, der Autor, selbst Ingenieur, bem}ht sich jedoch, auch die notwendig abstrakten Inhalte f}r Nicht-Mathematiker verst{ndlich darzustellen.

Dieser Band Numerische Mathematik hat Prinzipien des numerischen Rechnens, numerische lineare Algebra und Naherungsmethoden in der Analysis zum Inhalt. Der Begriff der Approximation zieht sich als roter Faden durch den gesamten Text. Die Betonung liegt dabei weniger auf der Bereitstellung moglichst vieler Algorithmen als vielmehr auf der Vermittlung mathematischer Uberlegungen, die zur Konstruktion von Verfahren fuhren. Jedoch werden auch der algorithmische Aspekt und entsprechende Effizienzbetrachtungen gebuhrend berucksichtigt. An vielen Stellen geht der dargebotene Stoff uber den Inhalt einer einschlagigen Vorlesung zur numerischen Mathematik hinaus, so dass man beim Gebrauch des Buches neben einer solchen Vorlesung eine Auswahl treffen wird. Dem Charakter der Reihe Grundwissen Mathematik entsprechend sind zahlreiche historische Anmerkungen eingeflochten. Besonderer Wert wird auf Querverbindungen und motivierende Erklarungen gelegt. Das Buch eignet sich zum Selbststudium und auch als Begleittext zu Vorlesungen. Diese 2. Auflage wurde uberarbeitet und erganzt. Zu den Erganzungen gehort eine Darstellung der Idee der schnellen Fouriertransformation.

0.1. Grauert, H.; Lieb, I.: Differential- und Integralrechnung I. Funktionen einer reel len Veranderlichen (Heidelberger Taschen- bucher 26). 4. Aufl. Springer, Berlin - Heidelberg - New York 1976. 0.2. Grauert, H.; Fischer, w.: Differential- und Integralrechnung II. Differentialrechnung in mehreren Veranderlichen. Differential- gleichungen (Heidelberger Taschenbucher 36). 3. Aufl. Ebenfalls 1978. 0.3. Grauert, H.; Lieb, I.: Differential- und Integralrechnunq III. Integrationstheorie. Kurven- und Flachenintegrale (Heidelberger Taschenbuch 43). 2. Aufl. Ebenfalls 1977. 0.4. Janich, K.: Analysis fur Physiker und Ingenieure. Springer, Berlin - Heidelberg - New York - Tokyo 1983. 0.5. Kuratowski, K.: Introduction to Calculus (Pure and Appl. Math. 17). Pergamon - Polish Scient. Publ., Oxford - London - New York- Paris - Warszawa 1961 (Ubersetzung aus dem Polnischen) . 0.6. Sikorski, R.: Advanced Calculus. Functions of Several Variables (Monogr. Mat. 51). Polish Scient. Publ., Warszawa 1969 (Ubersetzung aus dem Polnischen) - 0.7. Strubecker, K.: Einfuhrung in die hahere Mathematik mit beson- derer Berlicksichtigung ihrer Anwendungen auf Geometrie, Physik, Naturwissenschaften und Technik, Band I: Grundlagen. 2. Aufl. R. Oldenbourg, Munchen - \, lien 1966. 0.8. Strubecker, K.: Einfuhrung in die hohere Mathematik --., Band II: Differentialrechnung einer reellen Veranderlichen. Ebenfalls 1967. 0.9. Strubecker, K.: Einfuhrung in die hohere Mathematik -.-, Band III: Integralrechnung einer reellen Veranderlichen. Ebenfalls 1980. 0.10. Wa ter, W.: Analysis I (Grundwiss. Math. 3). Springer, Berlin- Heidelberg - New York - Tokyo 1984.