This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory from Newton, Leibniz, Euler, and Hamilton to limit cycles and strange attractors. In a second chapter a modern treatment of Runge-Kutta and extrapolation methods is given. Also included are continuous methods for dense output, parallel Runge-Kutta methods, special methods for Hamiltonian systems, second order differential equations and delay equations. The third chapter begins with the classical theory of multistep methods, and concludes with the theory of general linear methods. Many applications from physics, chemistry, biology, and astronomy together with computer programs and numerical comparisons are presented. This new edition has been rewritten, errors have been eliminated and new material has been included. The book will be immensely useful to graduate students and researchers in numerical analysis and scientific computing, and to scientists in the fields mentioned above.

The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). The book is divided into four chapters. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergence and asymptotic expansions. Stiff and differential-algebraic problems arise everywhere in scientific computations (e.g., in physics, chemistry, biology, control engineering, electrical network analysis, mechanical systems). Many applications as well as computer programs are presented.

First-year calculus presented roughly in the order in which it first was discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations, while the establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, and researchers alike.

In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapteroffers an introduction to projective geometry, which emerged in the19thcentury.

Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.
"

Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches. The second edition is substantially revised and enlarged, with many improvements in the presentation and additions concerning in particular non-canonical Hamiltonian systems, highly oscillatory mechanical systems, and the dynamics of multistep methods.

In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapteroffers an introduction to projective geometry, which emerged in the19thcentury.

Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.
"

This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.

This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a modern treatment of Runge-Kutta and extrapolation methods. Chapter three begins with the classical theory of multistep methods, and concludes with the theory of general linear methods. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs which help him/her learn to solve all kinds of ordinary differential equations. This new edition has been rewritten and new material has been included.

Das Buch adressiert die zwei Themen Erstellung ressourceneffizienter Software sowie den ressourceneffizienten Betrieb von Software. Für die Mehrheit aller Unternehmen in Deutschland sind bei der Entwicklung von Software die Dimensionen „in budget“, „in time“ und „in function“ wichtig. Die Dimension „in climate“ gewinnt vor dem Hintergrund der Klima- und der Energiekrise stark an Bedeutung. Dabei muss die Dimension „in climate“ nicht im Kontrast zu den anderen Dimensionen stehen. Bei näherer Betrachtung kann sie sogar die anderen Dimensionen ergänzen. In Bezug auf den Betrieb von IT-Systemen liegt aktuell der Fokus bei den deutschen Firmen auf Performance und Verfügbarkeit. Einbußen in diesen beiden Bereichen wird oftmals mit einem Mehr an Infrastruktur begegnet, welches höheren Ressourcenverbrauch bedeutet und damit ggf. höhere CO2-Emissionen impliziert. Dabei müssen Performance und Verfügbarkeit nicht im Widerspruch zu moderaten CO2-Emissionen stehen. Dieses Buch stellt zunächst die Ergebnisse einer Umfrage unter Entscheiderinnen und Entscheidern zum Thema Green-IT dar, mit Fragen zu einer nachhaltigen IT in Bezug auf die Entwicklung und den Betrieb von Software. Aufbauend auf der Umfrage werden konkrete Maßnahmen zur Reduktion von CO2 beim Entwurf und beim Bau von Software dargestellt sowie Möglichkeiten eines energieeffizienten Betriebs im eigenen Rechenzentrum und in der Cloud aufgezeigt. Neben einem ausführlichen Theorieteil bietet das Buch mehrere Best-Practice-Beispiele und eine illustrative Fallstudie.

This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. It presents a

theory of symplectic and symmetric methods, which include various specially designed integrators, as well as discusses their construction and practical merits. The long-time behavior of the numerical solutions is studied using a backward error analysis combined with KAM theory.

Diese Einfuhrung in die Analysis orientiert sich an der historischen Entwicklung: Die ersten zwei Kapitel schlagen den Bogen von historischen Berechnungsmethoden zu unendlichen Reihen, zur Differential- und Integralrechnung und zu Differentialgleichungen. Die Etablierung einer mathematisch stringenten Denkhaltung im 19. Jahrhundert fur ein und mehrere Variablen ist Thema der darauffolgenden Kapitel. Viele Beispiele, Berechnungen und Bilder machen den Band zu einem Lesevergnugen fur Studierende, fur Lehrer und fur Wissenschaftler.

The subject of this book is the solution of stiff differential equations and of differential-algebraic systems. This second edition contains new material including new numerical tests, recent progress in numerical differential-algebraic equations, and improved FORTRAN codes.

From the reviews:

"A superb book...Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text." --MATHEMATICS TODAY

Dieses Buch fuhrt Sie in die Programmierung verteilter Systeme in Java ein. Besonderer Wert wird auf die Realisierung serverseitiger Anwendungen im Rahmen der Java EE-Architektur gelegt. Schritt fur Schritt lernen Sie alle wichtigen Technologien und Bestandteile von Enterprise Java sowie deren Zusammenspiel kennen. Jedes Kapitel enthalt zahlreiche Beispiele und UEbungsaufgaben, sodass der Leser nach der Lekture des Buches in der Lage ist, komponentenbasierte Webanwendungen auf Basis der Java Enterprise-Architektur zu erstellen. Alle UEbungen inklusive Loesungen sowie die Abbildungen des Buches stehen online auf der Webseite des Verlags zur Verfugung.