Matematik for ingeniører

This book focuses on fault diagnosis for linear discrete time-varying (LDTV) systems and its applications in modern engineering processes, with more weighting placed on the development of theory and methodologies. A comprehensive and systematic study on fault diagnosis for LDTV systems is provided, covering Hinfinity-optimization-based fault diagnosis, Hinfinity-filtering-based fault diagnosis, parity space-based fault diagnosis, Krein space technique-aided fault detection and fault estimation, and their typical applications in linear/nonlinear processes such as satellite attitude control systems and INS/GPS systems. This book benefits researchers, engineers, and graduate students in the fields of control engineering, electrical and electronic engineering, instrumentation science, and optoelectronic engineering.

The book is devoted to the solution of the problem of determining the presence of corona discharge on electrical equipment with acoustic radiation. It is shown that corona discharge leads not only to irreversible losses of electrical energy, but also interferes with the transmission of high-frequency signals, deteriorates insulating elements, can become a source of conditions for the occurrence of a destructive arc discharge and is one of the factors of changing the continuity of the electrical system as a whole. The book describes the processes in a corona discharge that lead to the occurrence of acoustic waves. The authors analyzed acoustic radiation from a corona discharge reproduced in laboratory conditions. The received acoustic signals were processed by Fourier transform. Thus, the features of the spectral function, which belong specifically to the corona discharge in electrical networks with industrial frequency current, were determined. Based on the inverse Fourier transform, a simplified model of the acoustic radiation of the corona discharge was constructed. The authors proposed a method for detecting the presence of a corona discharge based on the spectral characteristics of acoustic radiation. Techniques were developed to determine the presence of a corona discharge for the creation of stationary and mobile devices. The advantages of the method of detecting the presence of corona discharge by the acoustic spectrum are shown. The method makes it possible to determine the presence of a corona discharge remotely, even out of direct sight, regardless of the time of day and regardless of the season. The book states that determining the presence of a corona discharge is not enough, it is still necessary to determine its location. The method of finding the coordinates of the corona discharge as a source of sound was described. Methods of searching for corona discharge coordinates with a fixed scanning device and a moving scanning device are proposed. A UAV is proposed as a mobile platform for the scanning system. The influence of the Doppler effect on acoustic measurements when the UAV speed changes was taken into account. The authors have shown that the use of coronal discharge detection with UAVs will not only enable the prevention of coronal discharge, but also increase the frequency of surface inspections. This will allow timely measures to be taken to improve the reliability of the power system operation. The book is intended for the researchers, postgraduate students and students specialized in theory and calculations of electrical systems.

This book is the first academic monograph on the Five-Hundred-Meter Aperture Spherical Radio Telescope (FAST, or Chinäs ¿sky eye¿), which discusses the research on cable-driven and rigid parallel robots in detail. Taking the final scale model of the FAST feed support system as the object, it introduces the theoretical and engineering research on optimal design, accuracy improvement, and control of the cable-driven and rigid parallel robots, striving to clearly illustrate the core technology of the FAST feed support system, as well as the theoretical methodology and engineering technology of cable-driven and rigid parallel mechanisms. The theoretical innovation and technological breakthroughs of the cable-driven and rigid parallel robots directly support the implementation of the feed support system, which is one of the three major innovations of the FAST. This book is geared toward the high-performance development trend of robotics and follows the complete development process of the design, control, and engineering practice of the FAST feed support system. It systematically elaborates the core theories and technologies, such as dynamic modeling, precision analysis, dimension synthesis, vibration suppression control, and inertia matching of cable-driven and rigid parallel robots. This book elaborates on theoretical research and engineering practice, which have significant inspiration and reference effects. It guides readers to gain engineering experience and practical knowledge. The intended readership includes researchers, postgraduate students, undergraduate students, technology enthusiasts, etc.

Dieses Buch ist Teil eines 6-bändigen Werks. Es befasst sich mit der Anwendung von Differentialgleichungen in diversen Bereichen der Physik und dem Ingenieurwesen. Dabei wird die Bilanzgleichung ins Zentrum der Betrachtung gerückt. Die Lesenden lernen Schritt für Schritt, wie ein konkret gestelltes Problem mit Hilfe sinnvoller Voraussetzungen und Idealisierungen modelliert, als Bilanz formuliert und formalisiert und die entstandene Differentialgleichung bzw. das entstandene Differentialgleichungssystem exakt oder numerisch gelöst wird. Dieses didaktische Konzept wird durchgehend sorgfältig und konsequent für jedes Teilgebiet angewandt und ermöglicht auf diese Weise den Studierenden die Bilanz als etwas Grundlegendes zur Beschreibung eines physikalischen Sachverhalts zu begreifen. Sämtliche theoretisch gewonnenen Ergebnisse werden in Worten festgehalten, teilweise mit Hilfe von Computersimulationen dargestellt und von vielen, konkreten, vollständig gelösten Beispielen begleitet.

Dieses Buch ist Teil eines 6-bändigen Werks. Es ist als Wegweiser für den Einstieg in die Modellierung von Populationen und deren Interaktion gedacht. Die Lesenden erfahren in nachvollziehbaren Schritten, wie ein Ökosystem unter sinnvollen Annahmen und Idealisierungen mit Hilfe von Differentialgleichungen modelliert werden kann und wie die bestehenden Modelle bei einem Eingriff des Menschen oder aufgrund der Berücksichtigung von Phänomenen wie etwa intra- und interspezifische Konkurrenz oder Begrenzung des Nahrungsangebots usw. angepasst werden müssen. Die dabei entstandene Differentialgleichung bzw. das entstandene Differentialgleichungssystem wird exakt oder numerisch gelöst, die Ergebnisse in Worten und mit Hilfe von Computersimulationen festgehalten und von vielen, konkreten, vollständig gelösten Beispielen begleitet.

Dieser Band befasst sich mit den Anwendung von Differentialgleichungen in der klassischen Statik: Saiten, Balken und Platten. Die Theorie wird einleitend behandelt und anschließend die verschiedenen Anwendungen und Beispiele im Detail erklärt und diskutiert. Neu: Der methodisch-didaktische Ansatz wurde für ein besseres Verständnis neu strukturiert und die Übungen und Lösungen in den Text intergriert.

This proceedings volume convenes selected, peer-reviewed contributions presented at the POMS 2021 - International Conference on Production and Operations Management, which was virtually held in Lima, Peru, December 2-4, 2021. This book presents results in the field of Operations Management of key relevance to practitioners, instructors, and students. Topics focus on Operations Management, Logistics and Supply Chain Management, and Industrial and Production Engineering and Management, where mathematics and its applications play a role. In this work, readers will find a colorful collection of real-world case studies, accompanied by operations research-based managerial models. They touch on myriad topics, ranging from Artificial Intelligence and Data Analytics in Operations, Defense, Tourism, and other emerging issues in Operations Management to Healthcare Operations Management and Humanitarian Operations and Crisis Management.The POMS Lima 2021 International Conference has been organized by the Latin America & Caribbean Chapter of the Production and Operations Management Society, the most renowned professional and academic organization representing the interests of production and operations management professionals and academicians around the world. Since 2018, POMS International Conferences have been organized by POMS-LA, the first venue being in Rio de Janeiro, Brazil. Venue 2021 event was hosted by the Pontifical Catholic University of Peru and Pacific University, two Peruvian Latin-American leading academic institutions from Peru.

This book explores how AI is transforming digital marketing and what it means for businesses of all sizes and looks at how AI is being used to personalize content, improve targeting, and optimize campaigns. This book also examines some of the ethical considerations that come with using AI in marketing.

This book emphasizes simple and concise coverage of the fundamental aspects of measuring systems. It is designed to provide the reader with essential knowledge regarding signals, signal analysis, signal conditioning circuits, and data acquisition systems. The prerequisites are a basic knowledge of multivariable calculus, introductory physics, and a familiarity with basic electrical circuits and components. Delivers topics and techniques that are fundamental to the understanding of the measurement process. These include standards, dynamic characteristics of measuring devices, statistical analysis of data, uncertainty analysis, signal conditioning devices, transistors,and logic circuits, analog to digital converters. To aid in the understanding of the subject matter and related applications, the book chapters are complemented with examples and problems. Careful attention was paid to the details of figures and illustration to help enforce the learning objectives of this book.

The book addresses a relevant field of digital processing and measurement of signals in distribution networks. The importance of the covered topic is evidenced by extensive foreign and domestic professional literature, in the form of publications in leading international journals, and numerous professional and scientific books. For the past two decades, the author has published a number of papers both in international journals and at leading world conferences, further verifying the results he has achieved in this field. It should be noted that he is also the holder of several national patents, which were created precisely as a result of working on the problems of processing complex signals of voltage and current. Readers of this book will be the students of master and doctoral studies both in the country and abroad and experts in the field of signal processing. It is a valuable source for future authors of professional and scientific papers, as a basis on which to start when developing completely new techniques for processing complex signals not only in the power system, but also in other fields of engineering and everyday life.

Complex variable theory is attractive for engineers as it offers elegant approaches for certain types of differential equations in engineering including heat transfer, solid mechanics, and fluid mechanics. However, a gap exists between books written by mathematicians and books written by engineers in their specific fields. Naturally, mathematicians tend to emphasize rigorousness and consistency while less emphasizing applications. On the other hand, books written by engineers often jump directly to the specific topics assuming that the readers already have sufficient background of complex variables and the pathway from theory to the application is not clearly elucidated. This book closes the gap in the literature. providing a smooth transition from basic theory to the application is accomplished. Although it is not possible to cover all the topics in engineering exhaustively, the readers can at least find the logic of how and why complex variables are effective for some of the engineering problems. Another motivation for writing this book is to demonstrate that the readers can take advantage of a computer algebra system, Mathematica, to facilitate tedious algebra and visualize complex functions so that they can focus on principles instead of spending endless hours on algebra by hand. Unlike numerical tools such as MATLAB and FORTRAN, Mathematica can expand, differentiate, and integrate complex-valued functions symbolically. Mathematica can be used as a stand-alone symbolic calculator or a programming tool using the Wolfram Language. If Mathematica is not available locally, Wolfram Cloud Basic can be used online as a free service to execute Mathematica statements.

In this book, we introduce the parametrized, deformed and general activation function of neural networks. The parametrized activation function kills much less neurons than the original one. The asymmetry of the brain is best expressed by deformed activation functions. Along with a great variety of activation functions, general activation functions are also engaged. Thus, in this book, all presented is original work by the author given at a very general level to cover a maximum number of different kinds of neural networks: giving ordinary, fractional, fuzzy and stochastic approximations. It presents here univariate, fractional and multivariate approximations. Iterated sequential multi-layer approximations are also studied. The functions under approximation and neural networks are Banach space valued.

This book comprises select proceedings of the 1st International Conference on Heat Transfer and Fluid Dynamics (AHTFD 22). It covers latest research trends and development in diverse areas like, aerodynamics, complex fluid phenomenon, turbulence, flow control, thermal management, green buildings, micro-scale transport phenomena in biological systems, renewable energy, power generation, combustion and related applications in heat transfer and fluid dynamics, among others. The book is a valuable resource for researchers and professionals working in the various areas of mechanical engineering.

This book investigates in detail production scheduling technology in different kinds of shop environment to achieve sustainability manufacturing. Studies on shop scheduling have attracted engineers and scientists from various disciplines, such as electrical, mechanical, automation, computer, and industrial engineering. Pursuing a holistic approach, the book establishes a fundamental framework for this topic, while emphasizing the importance of intelligent optimization and the significant influence of production scheduling in the manufacturing systems. The book is intended for undergraduate and graduate students who are interested in intelligent optimization technology, shop scheduling, and green manufacturing systems or other scheduling applications.

This book, dedicated to Professor Georgi M. Dimirovski on his anniversary, contains new research directions, challenges, and many relevant applications related to many aspects within the broadly perceived areas of systems and control, including signal analysis and intelligent systems. The project comprises two volumes with papers written by well known and very active researchers and practitioners. The first volume is focused on more foundational aspects related to general issues in systems science and mathematical systems, various problems in control and automation, and the use of computational and artificial intelligence in the context of systems modeling and control. The second volume is concerned with a presentation of relevant applications, notably in robotics, computer networks, telecommunication, fault detection/diagnosis, as well as in biology and medicine, and economic, financial, and social systems too. 

This contributed volume investigates several mathematical techniques for the modeling and simulation of viral pandemics, with a special focus on COVID-19.  Modeling a pandemic requires an interdisciplinary approach with other fields such as epidemiology, virology, immunology, and biology in general.  Spatial dynamics and interactions are also important features to be considered, and a multiscale framework is needed at the level of individuals and the level of virus particles and the immune system.  Chapters in this volume address these items, as well as offer perspectives for the future.

The 2nd edition of this book provides novel topics and studyies in boundaries of networks and Big Data Systems.The central theme of this book is the extent to which the structure of the free dynamical boundaries of a system controls the evolution of the system as a whole. Applying three orthogonal types of thinking - mathematical, constructivist and morphological, it illustrates these concepts using applications to selected problems from the social and life sciences, as well as economics. In a broader context, it introduces and reviews some modern mathematical approaches to the science of complex systems. Standard modeling approaches (based on non-linear differential equations, dynamic systems, graph theory, cellular automata, stochastic processes, or information theory) are suitable for studying local problems. However they cannot simultaneously take into account all the different facets and phenomena of a complex system, and new approaches are required to solve the challenging problem of correlations between phenomena at different levels and hierarchies, their self-organization and memory-evolutive aspects, the growth of additional structures and are ultimately required to explain why and how such complex systems can display both robustness and flexibility. This graduate-level text addresses a broader interdisciplinary audience, keeping the mathematical level essentially uniform throughout the book, and involving only basic elements from calculus, algebra, geometry and systems theory.  

This book provides qualitative and quantitative methods to analyze and better understand phenomena that change in space and time. An innovative approach is to incorporate ideas and methods from dynamical systems and equivariant bifurcation theory to model, analyze and predict the behavior of mathematical models. In addition, real-life data is incorporated in the derivation of certain models. For instance, the model for a fluxgate magnetometer includes experiments in support of the model.The book is intended for interdisciplinary scientists in STEM fields, who might be interested in learning the skills to derive a mathematical representation for explaining the evolution of a real system. Overall, the book could be adapted in undergraduate- and postgraduate-level courses, with students from various STEM fields, including: mathematics, physics, engineering and biology.

Das Buch vermittelt Lösungsverfahren für partielle Riccati-Differenzialgleichungen (DGL). Diese DGL appliziert man zur mathematischen Beschreibung der Funktion von Faraday-Effekt-Stromsensoren. Ausgehend vom allgemeinen Lösungsverhalten erfolgt die Definition des individuellen sowie kollektiven Lösungsverhaltens einer beliebigen Gleichung. Reiner Thiele erklärt den Unterschied zwischen Individual- und Partiallösungen. Außerdem kreiert er Simulationsdiagramme und zeigt, dass es sich bei der Hardware um Regelkreise handelt.

This book contains select papers presented at the 3rd International Conference on Engineering Mathematics and Computing (ICEMC 2020), held at the Haldia Institute of Technology, Purba Midnapur, West Bengal, India, from 5-7 February 2020. The book discusses new developments and advances in the areas of neural networks, connectionist systems, genetic algorithms, evolutionary computation, artificial intelligence, cellular automata, self-organizing systems, soft computing, fuzzy systems, hybrid intelligent systems, etc. The book, containing 19 chapters, is useful to the researchers, scholars, and practising engineers as well as graduate students of engineering and applied sciences.

Maschinelles Lernen und künstliche Intelligenz sind omnipräsente Begriffe zur Verbesserung von technischen Prozessen. Die praktische Umsetzung an realen Problemen gestaltet sich aber oft schwierig und komplex. Dieses Lehrbuch erklärt Lernverfahren anhand von analytischen Konzepten im Zusammenspiel mit vollständigen Programmierbeispielen in Python und bezieht sich auf dabei stets auf reale technische Anwendungsszenarien. Es zeigt den Einsatz physikalisch-informierter Lernstrategien, die Einbeziehung von Unsicherheit in die Modellierung und den Aufbau von erklärbarer, vertrauenswürdiger künstlicher Intelligenz mit Hilfe spezialisierter Datenbanken.Dieses Lehrbuch richtet sich somit sowohl an Studierende der Ingenieurswissenschaften, Naturwissenschaft, Medizin und Betriebswirtschaft als auch an Anwender aus der Industrie (vor allem Data Scientists), Entwickler*innen von Expertendatenbanken und Softwareentwickler*innen.

Die Aufgabensammlung enthalt Aufgaben mit vollstandig durchgerechneten Losungen zu den Themen Analysis und lineare Algebra, wie sie im Kompendium Hohere Mathematik"e; dargestellt sind. Das Spektrum reicht von Aufgaben zur reinen Rechentechnik bis hin zu Anwendungsaufgaben, bei denen zunachst eine geeignete Modellierung gesucht ist, um dann die entsprechenden Techniken anwenden zu konnen. Ferner enthalt der Band speziell ausgewiesene Aufgaben, wie sie in Klausuren an Fachhochschulen oder Berufsakademien vorkommen konnen.

The work titled "Measuring Software Reengineering: A Framework Based on Metric Sets" explores software reengineering, focusing on improving existing systems' performance and maintainability. It proposes a novel approach that employs metrics to guide the reengineering process and enhance software quality. The study recommends practical software measurement practices for evaluating the feasibility of enhancing system maintainability. Three case studies demonstrate the approach's effectiveness, transforming software with issues into more organized, efficient, and maintainable versions. The Rainfall model, incorporating metrics, serves as a structured method for reengineering, addressing different scenarios. The study emphasizes empirical validation, comparing the metric-based approach with traditional methods in real-world projects. Overall, it underscores metrics' potential in managing risks, optimizing reengineering efforts, and providing a systematic approach to software evolution and improvement.

This volume contains select papers presented during the 4th  National Conference on Multidisciplinary Analysis and Optimization. It discusses new developments at the core of optimization methods and their application in multiple applications. The papers showcase fundamental problems and applications which include domains such as aerospace, automotive and industrial sectors. The variety of topics and diversity of insights presented in the general field of optimization and its use in design for different applications will be of interest to researchers in academia or industry.

This monograph is devoted to Eulerian models for fluid-structure interaction by applying the original point of view of level set methods.In the last 15 years, Eulerian models have become popular tools for studying fluid-structure interaction problems. One major advantage compared to more conventional methods such as ALE methods is that they allow the use of a single grid and a single discretization method for the different media. Level set methods in addition provide a general framework to follow the fluid-solid interfaces, to represent the elastic stresses of solids, and to model the contact forces between solids.This book offers a combination of mathematical modeling, aspects of numerical analysis, elementary codes and numerical illustrations, providing the reader with insights into the applications and performance of these models.Assuming background at the level of a Master's degree, Level Set Methods for Fluid-Structure Interaction provides researchers in the fields of numerical analysis of PDEs, theoretical and computational mechanics with a basic reference on the topic. Its pedagogical style and organization make it particularly suitable for graduate students and young researchers.

This book is intended for a wide range of researchers both from academia and industry interested in contributing to industries in an interdisciplinary way. The primary industries, including agriculture, fishery, and power industries, are the most fundamental infrastructure of the human societies. Traditionally, primary industries have been managed in the small family/community base, but with increase in population and development of society, the size of primary industry has grown. The efficiency, quality, and stability of these industries affect the societies significantly, so that they have become one of the major areas that mathematics could contribute to substantially. Also, primary industries are affected by the environment, where mathematical studies play an essential role. The conference was hosted by the research community in New Zealand, where such collaborative activities in mathematics between the industry and academia have been successfully established from an early stage. This enabled the conference to bring together a range of research topics- from pioneering works to cutting-edge results, from agriculture to geothermal energy and nuclear fusion, and from mathematical modeling and analysis to data analysis.