Matematik for ingeniører

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.

Das Aufgabenbuch zur Technischen Mechanik 2 (Elastostatik, Hydrostatik) enthalt die wichtigsten Formeln und etwa 150 vollstandig geloste Aufgaben. Weil der Weg zum erfolgreichen Studium der Technischen Mechanik uber das selbstandige Losen von Aufgaben fuhrt, legen die Autoren besonderen Wert darauf, dass Leser befahigt werden Losungswege zu finden und Grundgleichungen zu erstellen. In dem Band werden folgende Themen behandelt: Spannung und Verzerrung, Zug und Druck, Biegung, Torsion, der Arbeitsbegriff in der Elastostatik, Stabilitat, Hydrostatik.

In diesem Sammelband geht es darum, neue Algorithmen aus den Bereichen der Künstlichen Intelligenz (KI) und des Künstlichen Lebens (KL) und deren praktische Anwendung zu zeigen. Der wesentliche Aspekt des Bandes ist, dass in den Beiträgen exemplarisch gezeigt wird, dass und wie diese neuen Algorithmen auf praktische Probleme in sehr verschiedenen Bereichen erfolgreich eingesetzt werden können: Von der Modellierung betrieblicher Abläufe und des Managements bis zur Entscheidungsunterstützung bei der Wahl der Start- und Landebahn eines Flughafens, von der Analyse von Sensordaten bis zur Überwachung, Auswahl und Optimierung technischer Systeme sowie Alternativen für die Bildverarbeitung.

This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful selection of topics and engaging tone, readers will also learn how PDEs connect to cutting-edge research and the modeling of physical phenomena. The scope of the Third Edition greatly expands on that of the previous editions by including five new chapters covering additional PDE topics relevant for current areas of active research. This includes coverage of linear parabolic equations with measurable coefficients, parabolic DeGiorgi classes, Navier-Stokes equations, and more. The ¿Problems and Complements¿ sections have also been updated to feature new exercises, examples, and hints toward solutions, making this a timely resource for students.Partial Differential Equations: Third Edition is ideal for graduate students interested in exploring the theory of PDEs and how they connect to contemporary research. It can also serve as a useful tool for more experienced readers who are looking for a comprehensive reference.

This book aims to strengthen programming skills and foster creative thinking by presenting and solving 90 challenging problems. The book is intended for individuals with elementary, intermediate, and advanced Python programming skills who aspire to take their abilities to the next level. Additionally, the book is valuable for individuals interested in enhancing their creative thinking and logical reasoning skills. It is a self-instructional book meant to provide readers with the ability to solve challenging problems independently. The presented challenges are lucidly and succinctly expressed, facilitating readers to follow along and comprehend the problem-solving process. The challenges cover various fields, making it suitable for a wide range of individuals. The book is divided into eight chapters, beginning with an introduction in chapter one. The second chapter presents essential Python basics for programming challenging problems, while the subsequent chapters focuson specific types of challenges. These include math-based challenges in chapter three, number-based challenges in chapter four, string-based challenges in chapter five, game-based challenges in chapter six, count-based challenges in chapter seven, and miscellaneous challenges in chapter eight. Each chapter comprises a set of challenges with examples, hints, algorithms, and Python code solutions. The target audience of the book includes computer science and engineering students, teachers, software developers, and participants in programming competitions.

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.

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.

Dieses 6-bändige Werk 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 und von vielen, konkreten, vollständig gelösten Beispielen begleitet.

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.

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.

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.

Ein kompakter und praxisorientierter Einstieg, mit dem Studierende bereits fruh im Studium sehr gut zurechtkommen. Die verschiedenen Phasen einer Datenbankentwicklung werden mit ihren Vorgehensweisen, Konzepten und moglichen Problemquellen vorgestellt. Gerade die Anforderungsanalyse und die Moglichkeit zur Erstellung machtiger SQL-Anfragen werden als besonders praxisrelevante Aspekte betont. Studierende sind nach der Lekture in der Lage, in Praxisprojekten erfolgreich mitzuarbeiten und das Buch deckt eine Einfuhrungsvorlesung vollstandig ab. In der dritten Auflage wurden automatisierbare Testmoglichkeiten erganzt. Neben vielen kleinen Beispielen zur Verdeutlichung einzelner Aspekte wird ein durchgehendes Beispiel genutzt. Alle Kapitel schlieen mit Wiederholungsfragen und Ubungsaufgaben, deren Losungen online zum Download zur Verfugung stehen.

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.

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.

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 provides engineers and researchers knowledge to help them in system reliability analysis using machine learning, artificial intelligence, big data, genetic algorithm, information theory, multi-criteria decision making, and other techniques. It will also be useful to students learning reliability engineering.The book brings readers up to date with how system reliability relates to the latest techniques of AI, big data, genetic algorithm, information theory, and multi-criteria decision making and points toward future developments in the subject.