Matematik for ingeniører

Gaining expertise in marine floating systems typically requires access to multiple resources to obtain the knowledge required, but this book fills the long-felt need for a single cohesive source that brings together the mathematical methods and dynamic analysis techniques required for a meaningful analysis, primarily, of large and small bodies in oceans. You will be introduced to fundamentals such as vector calculus, Fourier analysis, and ordinary and partial differential equations. Then you'll be taken through dimensional analysis of marine systems, viscous and inviscid flow around structures surface waves, and floating bodies in waves. Real-life applications are discussed and end of chapter problems help ensure full understanding. Students and practicing engineers will find this an invaluable resource for developing problem solving and design skills in a challenging ocean environment through the use of engineering mathematics.

Designing a wind turbine is an interdisciplinary process that requires an understanding of challenges for all parties involved. The authors deliver an effective and economic way to organize such a design by respecting all the challenges involved. The book provides such insight by utilizing specific examples of existing modern designs. Detailed descriptions and explanations are given for those components of the wind turbine that are normally developed by the so-called original equipment manufacturers (OEM) of a particular type. The OEM needs to have full knowledge of the complete system that consists of all parts being rotor blades, nacelle, drive train, tower, and foundation including the dynamic properties and the response to the controller action. This full knowledge is called system competence. For a wind turbine the drive train is the most important system. It consists of many components like shafts, bearings, gearbox, and generator for a wind turbine with a gear box; in systems without a gearbox a large generator has to be integrated into the drive train.

Economic development, social sustainability, and environmental protection play a major role in terms of efforts for innovation, digitalization, business, and global development.  Today, nations all over the world attempt to accomplish the United Nations Sustainable Development Goals and to ensure sustainable patterns. Combining empirical and theoretical information, this book demonstrates advanced initiatives and concrete examples from universities, research institutes, and companies, regarding cross-cutting issues in sustainable development of a wide range of fields. The major focus in the book is the promotion of quality of life, by means of a more sustainable food production, and improved food security. Additionally, the importance of digital technologies, business policy, social aspects, and corporate governance in ensuring sustainable regional development is studied.This book is a truly interdisciplinary publication, useful to scholars, social movements, practitioners, and members of governmental agencies and private companies.

This new edition covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve a problem. This was a major theme of the first edition of this book and the fourth edition expands and further illustrates this relationship. As in the earlier editions, the material in this fourth edition is organized into three separate parts. Part I is a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. It is possible to go directly into Parts II and III omitting Part I, and, in fact, the book has been used in this way in many universities.New to this edition is a chapter devoted to Conic Linear Programming, a powerful generalization of Linear Programming. Indeed, many conic structures are possible and useful in a variety of applications. It must be recognized, however, that conic linear programming is an advanced topic, requiring special study. Another important topic is an accelerated steepest descent method that exhibits superior convergence properties, and for this reason, has become quite popular. The proof of the convergence property for both standard and accelerated steepest descent methods are presented in Chapter 8. As in previous editions, end-of-chapter exercises appear for all chapters.From the reviews of the Third Edition:"e;... this very well-written book is a classic textbook in Optimization. It should be present in the bookcase of each student, researcher, and specialist from the host of disciplines from which practical optimization applications are drawn."e; (Jean-Jacques Strodiot, Zentralblatt MATH, Vol. 1207, 2011)

This volume collects the edited and reviewed contribution presented in the 9th iTi Conference that took place virtually, covering fundamental and applied aspects in turbulence. In the spirit of the iTi conference, the volume is produced after the conference so that the authors had the opportunity to incorporate comments and discussions raised during the meeting.In the present book, the contributions have been structured according to the topics:I ExperimentsII Simulations and ModellingIII Data Processing and ScalingIV TheoryV Miscellaneous topics

While linear control is a well-established subject, analysis and design of nonlinear control systems remains a challenging topic due to some of the fundamental difficulties caused by nonlinearity. This book provides a unified computational approach to analysis and design of nonlinear systems.

Die meisten Nichtmathematiker werden Torricelli durch das nach ihm benannte Ausflussgesetz kennen, wonach die Geschwindigkeit eines aus einem Gefäss austretenden Wasserstrahls proportional zur Quadratwurzel aus der Füllhöhe ist, ebenso wie durch seinen Nachweis des Luftdrucks mithilfe seines Vakuumexperiments. Viel bedeutender aber sind seine Leistungen auf dem Gebiet der Mathematik als virtuoser Vertreter von Cavalieris umstrittener Indivisiblenmethode, wobei er seine Ergebnisse aber stets mit Beweisen nach der allgemein anerkannten ¿Art der Alten¿ absicherte. Auf diese Weise gelang ihm die Quadratur der Parabeln und Hyperbeln höherer Ordnung, der Zykloide, der logarithmischen Spirale (ebenso wie deren Rektifikation) und die Bestimmung der Schwerpunkte zahlreicher ebener und räumlicher Figuren.

This book, following the three published volumes of the book, provides the main purpose to collect research papers and review papers to provide an overview of the main issues, results, and open questions in the cutting-edge research on the fields of modeling, optimization, and dynamics and their applications to biology, economy, energy, industry, physics, psychology and finance. Assuming the scientific relevance of the presenting innovative applications as well as merging issues in these areas, the purpose of this book is to collect papers of the world experts in mathematics, economics, and other applied sciences that is seminal to the future research developments. The majority of the papers presented in this book is authored by the participants in The Joint Meeting 6th International Conference on Dynamics, Games, and Science - DGSVI - JOLATE and in the 21st ICABR Conference.  The scientific scope of the conferences is focused on the fields of modeling, optimization, and dynamics and their applications to biology, economy, energy, industry, physics, psychology, and finance. Assuming the scientific relevance of the presenting innovative applications as well as merging issues in these areas, the purpose of the conference is to bring together some of the world experts in mathematics, economics, and other applied sciences that reinforce ongoing projects and establish future works and collaborations.

Leicht verständlich und praxisorientiert behandelt das vorliegende Buch die wesentlichsten Gebiete der Linearen Optimierung, einem Kernbereich des Operations Research. Es wendet sich an Studierende betriebswirtschaftlicher und technischer Disziplinen. Aber auch Praktiker*innen aus kleinen und mittelständischen Unternehmen werden in hohem Maße davon profitieren. Da kaum mathematische Kenntnisse vorausgesetzt werden, fällt es gerade ihnen leicht, sich selbstständig in die Lineare Programmierung einzuarbeiten, die erhebliche Kostensenkungen und Zeiteinsparungen ermöglicht. Auch Studierende der Mathematik und der Informatik werden durch das Buch angesprochen, da sie sehr schnell einen Überblick über die Lineare Programmierung gewinnen können.Kurz und prägnant, dabei vollständig und mathematisch exakt, werden die Methoden hergeleitet, rezeptartig zusammengefasst, durch zahlreiche Beispiele und Übungsaufgaben ergänzt und mit zwei Fallstudien aus der betriebswirtschaftlichen und technischen Praxis angereichert. Nicht zu vergessen die softwaretechnische Umsetzung der Linearen Programme mittels Excel-Solver bzw. der Programmiersprache Python. Dieses Buch ist ein Muss für alle, die in die Thematik der Linearen Optimierung einsteigen möchten.Für die 3. Auflage ist das Werk vollständig durchgesehen und an einigen Stellen ergänzt sowie erweitert worden. Die C-Programme wurden durch Python-Programme ersetzt. In das Kapitel "Lineare Optimierung" wurden die Big-M-Methode, die Dreiphasen-Methode und das Revidierte Simplex-Verfahren neu aufgenommen. Ein Kapitel "Lineare Optimierung in der Spieltheorie" wurde hinzugefügt.

This book focuses on iterative solvers and preconditioners for mixed finite element methods. It provides an overview of some of the state-of-the-art solvers for discrete systems with constraints such as those which arise from mixed formulations.Starting by recalling the basic theory of mixed finite element methods, the book goes on to discuss the augmented Lagrangian method and gives a summary of the standard iterative methods, describing their usage for mixed methods. Here, preconditioners are built from an approximate factorisation of the mixed system.A first set of applications is considered for incompressible elasticity problems and flow problems, including non-linear models.An account of the mixed formulation for Dirichlet's boundary conditions is then given before turning to contact problems, where contact between incompressible bodies leads to problems with two constraints.This book is aimed at graduate students and researchers in the field of numerical methods and scientific computing.

This book presents computationally efficient MPC solutions. The classical model predictive control (MPC) approach to control dynamical systems described by the Wiener model uses an inverse static block to cancel the influence of process nonlinearity. Unfortunately, the model's structure is limited, and it gives poor control quality in the case of an imperfect model and disturbances. An alternative is to use the computationally demanding MPC scheme with on-line nonlinear optimisation repeated at each sampling instant.A linear approximation of the Wiener model or the predicted trajectory is found on-line. As a result, quadratic optimisation tasks are obtained. Furthermore, parameterisation using Laguerre functions is possible to reduce the number of decision variables. Simulation results for ten benchmark processes show that the discussed MPC algorithms lead to excellent control quality. For a neutralisation reactor and a fuel cell, essential advantages ofneural Wiener models are demonstrated.

This book gathers contributions on analytical, numerical, and application aspects of time-delay systems, under the paradigm of control theory, and discusses recent advances in these different contexts, also highlighting the interdisciplinary connections. The book will serve as a useful tool for graduate students and researchers in the fields of dynamical systems, automatic control, numerical methods, and functional analysis.

This book creates the emergence of disruptive technologies that have led to a significant change in the role of mathematics and statistics for problem solving, with the use of sophisticated software and hardware in solving complex systems and process. In the era of digital technology, mathematics and statistics need to be highly relevant to be able to cater for the needs of IR4.0 such as big data analytics, simulation, autonomous system, and cloud computing. Motivated by this development, a total of 26 chapters are contributed by respectable experts for this book. The main scope of the book is to conduct a new system of modeling and simulations on solving differential equations, nonlinear equations, energy, epidemiology, and risk assessment. This book is of interest for postgraduate students, researchers as well as other scientists who are working in numerical modeling and simulations based on efficient mathematical and statistical techniques.

Dieses kompakte Lehrbuch konzentriert sich anders als übrige Werke auf ein bestimmtes Gebiet der Ingenieurmathematikt. Damit sollen insbesondere Studierende durch überschaubare Inhalte nicht überfordert werden. Mit diesem Band zur Vervollständigung der Linearen Algebra sollen die Grundlagen aus Band 2 erweitert werden. Mit Beispielen aus den Ingenieur- und Naturwissenschaften werde die Bezüge zur Anwendung aufgezeigt. Der behandelte Stoff wird mit Beispielrechnungen vertieft. Jedes Kapitel wird mit verschiedenen Übungen zur Einarbeitung versehen. Dabei sind diese einerseits als Kurzaufgaben zum Verständnis gestaltet und andererseits in einer klassischen Form aufbereitet. Die Übungsaufgaben sind eingeteilt nach Schwierigkeitsgrad, was die Bearbeitungshürde herabsetzt und vielen Anforderungsniveaus gerecht wird. Das Buch wird schließlich mit Musterklausuren in drei Anforderungsumfängen abgerundet.