Gerhard Wanner

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.

A concise and authoritative introduction to scanning electron microscopy in the biological sciences In A Practical Guide to Scanning Electron Microscopy distinguished electron microscopist Gerhard Wanner delivers a practical handbook for biological scientists working with microbial, plant, and animal cells and tissues, enabling them to successfully apply scanning electron microscopy (SEM) to their object of study. The book begins with an introduction to the principles of electron microscopy and the operation of electron microscopes before moving on to describe the preparation and mounting of specimens. It also explores the process of recoding images and their subsequent analysis, along with a wide range of advanced microscopy techniques, including cryo-SEM, FIB-SEM tomography, and stereo-SEM. Scanning Electron Microscopy in the Biosciences contains hundreds of carefully selected microscopic images, as well as hands-on, step-by-step guidance required to perform a successful TEM experiment. Readers will also find: Thorough introductions to optics, electron microscopy, electrons, and the components of electron microscopesIn-depth examinations of the preparation of biological specimens and specimen mounting for scanning electron microscopyA comparison of different SEM modes and their strengths and weaknessesAn introduction to novel techniques such as correlative light and electron microscopy (CLEM), array tomography, and cryo-scanning electron microscopy Perfect for cell biologists and microbiologists, A Practical Guide to Scanning Electron Microscopy in the Biosciences also belongs in the libraries of neurobiologists and biophysicists.

Dieses Buch führt 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 für Schritt lernen Sie alle wichtigen Technologien und Bestandteile von Enterprise Java sowie deren Zusammenspiel kennen.Jedes Kapitel enthält zahlreiche Beispiele und Übungsaufgaben, sodass der Leser nach der Lektüre des Buches in der Lage ist, komponentenbasierte Webanwendungen auf Basis der Java Enterprise-Architektur zu erstellen.Alle Übungen inklusive Lösungen sowie die Abbildungen des Buches stehen online auf der Webseite des Verlags zur Verfügung.

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 chapter offers an introduction to projective geometry, which emerged in the 19thcentury.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.

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 chapter offers an introduction to projective geometry, which emerged in the 19thcentury.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 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.

Diese Einführung in die Analysis orientiert sich in ihrem Aufbau an der zeitlichen Entwicklung der Themen. Die ersten zwei Kapitel schlagen den Bogen von historischen Berechnungsmethoden praktischer Problemen hin zu unendlichen Reihen, Differential- und Integralrechnung und zu Differentialgleichungen. Das Etablieren einer mathematisch stringenten Denkhaltung im 19. Jahrhundert für Analysis ein und mehrerer Variablen wird in den Kapiteln III und IV behandelt. Viele Beispiele, Berechnungen und Bilder ergänzen das Buch und machen es zu einem Lesevergnügen für Studierende, Lehrer und Forscher.

"Whatever regrets may be, we have done our best." (Sir Ernest Shack­ 0 leton, turning back on 9 January 1909 at 88 23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential algebraic equations. It contains three chapters: Chapter IV on one-step (Runge-Kutta) meth­ ods for stiff problems, Chapter V on multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretical nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered con­ secutively in each section and indicate, in addition, the section number. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.

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.

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.

. . . that departed from the traditional dry-as-dust mathematics textbook. (M. Kline, from the Preface to the paperback edition of Kline 1972) Also for this reason, I have taken the trouble to make a great number of drawings. (Brieskom & Knorrer, Plane algebraic curves, p. ii) . . . I should like to bring up again for emphasis . . . points, in which my exposition differs especially from the customary presentation in the text­ books: 1. Illustration of abstract considerations by means of figures. 2. Emphasis upon its relation to neighboring fields, such as calculus of dif­ ferences and interpolation . . . 3. Emphasis upon historical growth. It seems to me extremely important that precisely the prospective teacher should take account of all of these. (F. Klein 1908, Eng\. ed. p. 236) Traditionally, a rigorous first course in Analysis progresses (more or less) in the following order: limits, sets, '* continuous '* derivatives '* integration. mappings functions On the other hand, the historical development of these subjects occurred in reverse order: Archimedes Cantor 1875 Cauchy 1821 Newton 1665 . ;::: Kepler 1615 Dedekind . ;::: Weierstrass . ;::: Leibniz 1675 Fermat 1638 In this book, with the four chapters Chapter I. Introduction to Analysis of the Infinite Chapter II. Differential and Integral Calculus Chapter III. Foundations of Classical Analysis Chapter IV. Calculus in Several Variables, we attempt to restore the historical order, and begin in Chapter I with Cardano, Descartes, Newton, and Euler's famous Introductio.

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.

"Whatever regrets may be, we have done our best." (Sir Ernest Shack­ 0 leton, turning back on 9 January 1909 at 88 23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential algebraic equations. It contains three chapters: Chapter IV on one-step (Runge-Kutta) meth­ ods for stiff problems, Chapter V on multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretical nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered con­ secutively in each section and indicate, in addition, the section number. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.

. . . that departed from the traditional dry-as-dust mathematics textbook. (M. Kline, from the Preface to the paperback edition of Kline 1972) Also for this reason, I have taken the trouble to make a great number of drawings. (Brieskom & Knorrer, Plane algebraic curves, p. ii) . . . I should like to bring up again for emphasis . . . points, in which my exposition differs especially from the customary presentation in the text­ books: 1. Illustration of abstract considerations by means of figures. 2. Emphasis upon its relation to neighboring fields, such as calculus of dif­ ferences and interpolation . . . 3. Emphasis upon historical growth. It seems to me extremely important that precisely the prospective teacher should take account of all of these. (F. Klein 1908, Eng\. ed. p. 236) Traditionally, a rigorous first course in Analysis progresses (more or less) in the following order: limits, sets, '* continuous '* derivatives '* integration. mappings functions On the other hand, the historical development of these subjects occurred in reverse order: Archimedes Cantor 1875 Cauchy 1821 Newton 1665 . ;::: Kepler 1615 Dedekind . ;::: Weierstrass . ;::: Leibniz 1675 Fermat 1638 In this book, with the four chapters Chapter I. Introduction to Analysis of the Infinite Chapter II. Differential and Integral Calculus Chapter III. Foundations of Classical Analysis Chapter IV. Calculus in Several Variables, we attempt to restore the historical order, and begin in Chapter I with Cardano, Descartes, Newton, and Euler's famous Introductio.