Gerhard Wanner – författare

This book presents first-year calculus 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. 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, as well as researchers.

. . . 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.