Matematik for ingeniører

Teknisk Matematik – Erhvervsakademierne er en specialudgave af Teknisk Matematik.Den er lavet til at dække undervisningen på erhvervsakademierne.Den er et dynamisk og letlæseligt materiale,hvor teori kobles med praktiske eksempler og opgaver.Bogen indeholder de første 8 kapitler af Teknisk Matematik.

This book investigates in detail the mathematical methods and computation methods in efficient solution of some open nonlinear seepage flow problems involved in engineering problems. Developed engineering technologies and some relevant practical field applications are also provided. The introduced open nonlinear problems include nonlinear quadratic pressure gradient term problem, compressible gas seepage flow problem and low-velocity non-Darcy seepage flow problem. Studies on these nonlinear seepage flow problems have attracted engineers and scientists from various disciplines, such as geo-energy engineering, civil and environmental engineering, fluid mechanics, applied mathematics and computation. In particular, the book systematically establishes a fundamental theory for a strongly nonlinear problem of low-velocity non-Darcy seepage flow from a new perspective of moving boundary, while emphasizing the usage of mathematical linearization transformation methods and computational methods into the analytical and numerical solution of the strongly nonlinear partial differential equations. Sufficient knowledge of mathematics is always introduced ahead of model solution to assist readers. And the procedure of strict formula deduction in the model solution process is provided in detail. High-solution figures and tables from model solution are rich in the book. Therefore, it is very helpful for the readers to master the nonlinear model solution methods and engineering technologies. The book is intended for upper undergraduate students and graduate students who are interested in engineering technology, fluid mechanics and applied mathematics, researchers and engineers working on geo-energy science and engineering and field applications.

This book comprises select peer-reviewed articles submitted for the proceedings of the International Conference on Mathematics and Computing (ICMC 2022), held by the School of Advanced Sciences, Vellore Institute of Technology, Vellore, India, in association with Ramanujan Mathematical Society, India, Cryptology Research Society of India and Society for Electronic Transactions and Security, India, from 6-8 January 2022. With an aim to identify the existing challenges in the areas of mathematics and computing, the book emphasizes the importance of establishing new methods and algorithms to address these challenges. The book includes topics on diverse applications of cryptology, network security, cyber security, block chain, IoT, mobile network, data analytics, applied algebra, mathematical analysis, mathematical modelling, fluid dynamics, fractional calculus, multi-optimization, integral equations, dynamical systems, numerical analysis and scientific computing. Divided into five major parts-applied algebra and analysis, fractional calculus and integral equations, mathematical modelling and fluid dynamics, numerical analysis, and computer science and applications-the book is a useful resource for students, researchers and faculty as well as practitioners.

This book is to provide readers with up-to-date advances in applied and interdisciplinary engineering science and technologies related to nonlinear dynamics, vibration, control, robotics, and their engineering applications, developed in the most recent years. All the contributed chapters come from active scholars in the area, which cover advanced theory & methods, innovative technologies, benchmark experimental validations and engineering practices. Readers would benefit from this state-of-the-art collection of applied nonlinear dynamics, in-depth vibration engineering theory, cutting-edge control methods and technologies, and definitely find stimulating ideas for their on-going R&D work. This book is intended for graduate students, research staff and scholars in academics, and also provides useful hand-up guidance for professional and engineers in practical engineering missions.

Structural Analysis with Finite Elements reveals the theory behind the finite element (FE) method as it relates to structural engineering and explains how to overcome commonly encountered problems and errors found in everyday structural modelling with finite element software.

This open access book offers comprehensive, self-contained knowledge on Digital Twin (DT), which is a very promising technology for achieving digital intelligence in the next-generation wireless communications and computing networks. DT is a key technology to connect physical systems and digital spaces in Metaverse.The objectives of this book are to provide the basic concepts of DT, to explore the promising applications of DT integrated with emerging technologies, and to give insights into the possible future directions of DT. For easy understanding, this book also presents several use cases for DT models and applications in different scenarios.The book starts with the basic concepts, models, and network architectures of DT. Then, we present the new opportunities when DT meets edge computing, Blockchain and Artificial Intelligence, anddistributed machine learning (e.g., federated learning, multi-agent deep reinforcement learning). We also present a wide application of DT as an enabling technology for 6G networks, Aerial-Ground Networks, and Unmanned Aerial Vehicles (UAVs).The book allows an easy cross-reference owing to the broad coverage on both the principle and applications of DT. The book is written for people interested in communications and computer networks at all levels. The primary audience includes senior undergraduates, postgraduates, educators, scientists, researchers, developers, engineers, innovators and research strategists.

This book publishes the work presented at the 1st Olympiad in Engineering Science (OES 2023), an international congress and contest aiming to disseminate and evaluate the recent advances in Engineering Science. The book covers diverse domains of engineering. From Machine Learning applications in Thrust Bearings' behavior to Optimization Techniques for space applications, each chapter presents innovative solutions to complex challenges. The Automatic Control section explores distributed intelligence in watercraft and supervisory control for manufacturing systems. In Data-Driven Engineering, simulations assess pedestrian comfort and model reconstruction. The Diagnostic-Prognostic Methods section delves into unbalance identification and steel truss bridge validation. Finally, Numerical and Analytical Methods in Engineering Mathematics cover everything from boundary integral methods to analytical solutions for fluid flows.

The monograph is devoted to the construction of the high-order finite difference and finite element methods for numerical solving multidimensional boundary-value problems (BVPs) for different partial differential equations, in particular, linear Helmholtz and wave equations, nonlinear Burgers¿ equations, and elliptic (Schrödinger) equation. Despite of a long history especially in development of the theoretical background of these methods there are open questions in their constructive implementation in numerical solving the multidimensional BVPs having additional requirement on physical parameters or desirable properties of its approximate solutions. Over the last two decades many papers on this topics have been published, in which new constructive approaches to numerically solving the multidimensional BVPs were proposed, and its highly desirable to systematically collect these results. This motivate us to write thus monograph based on our research results obtained in collaboration with the co-authors. Since the topic is importance we believe that this book will be useful to readers, graduate students and researchers interested in the field of computational physics, applied mathematics, numerical analysis and applied sciences

This book provides readers with up-to-date advances in applied and interdisciplinary engineering science and technologies related to nonlinear dynamics, vibration, control, robotics, and their engineering applications, developed in the most recent years. All the contributed chapters come from active scholars in the area, which cover advanced theory and methods, innovative technologies, benchmark experimental validations and engineering practices. Readers would benefit from this state-of-the-art collection of applied nonlinear dynamics, in-depth vibration engineering theory, cutting-edge control methods and technologies and definitely find stimulating ideas for their on-going R&D work. This book is intended for graduate students, research staff, and scholars in academics and also provides useful hand-up guidance for professionals and engineers in practical engineering missions.

This book offers a comprehensive overview of the latest advancements in the field of applied mathematics as it relates to finance, marketing, and economics. It covers a range of topics including the effective utilization of applied mathematics and mathematical modeling in finance, economics, and marketing. Additionally, it explores the intersection between applied mathematics and practical applications in various scientific fields. The book targets a multidisciplinary audience, fostering the exchange of diverse ideas and showcasing the broad appeal of different subjects. It delves into recent developments in areas such as mathematical modeling in finance, mathematical modeling in marketing, the modeling of financial and economic fundamentals (e.g., interest rates, asset prices), market behavior modeling, modeling market imperfections, pricing financial derivative securities, hedging strategies, numerical methods, and financial engineering.The book features selected contributions presented at the first edition of the International Conference in Applied Mathematics to Finance, Marketing and Economics, which took place at the National School of Commerce and Management in El Jadida, Morocco, from November 26 to 27, 2020.

This book focuses on nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs (BG) statistical mechanics.Conceived nearly 150 years ago by Maxwell, Boltzmann and Gibbs, the BG theory, one of the greatest monuments of contemporary physics, exhibits many impressive successes in physics, chemistry, mathematics, and computational sciences. Presently, several thousands of publications by scientists around the world have been dedicated to its nonextensive generalization. A variety of applications have emerged in complex systems and its mathematical grounding is by now well advanced.Since the first edition release thirteen years ago, there has been a vast amount of new results in the field, all of which have been incorporated in this comprehensive second edition. Heavily revised and updated with new sections and figures, the second edition remains the go-to text on the subject.A pedagogical introduction to the BG theory concepts and their generalizations ¿ nonlinear dynamics, extensivity of the nonadditive entropy, global correlations, generalization of the standard CLT¿s, complex networks, among others ¿ is presented in this book, as well as a selection of paradigmatic applications in various sciences together with diversified experimental verifications of some of its predictions. Introduction to Nonextensive Statistical Mechanics is suitable for students and researchers with an interest in complex systems and statistical physics.

This book publishes select papers presented at the 4th International Conference on Frontiers in Industrial and Applied Mathematics (FIAM-2021), held at the Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India, from 21¿22 December 2021. Most of the papers deal with mathematical theory embedded with its applications to engineering and sciences. This book illustrates numerical simulation of scientific problems and the state-of-the-art research in industrial and applied mathematics, including various computational and modeling techniques with case studies and concrete examples. Graduate students and researchers, who are interested in real applications of mathematics in the areas of computational and theoretical fluid dynamics, solid mechanics, optimization and operations research, numerical analysis, bio-mathematics, fuzzy, control and systems theory, dynamical systems and nonlinear analysis, algebra and approximation theory, will find the book useful.

Petri nets model concurrent and distributed systems where active components communicate through the production and absorption of various kinds of resources. Although the dynamic properties of such systems may be very complex, they may sometimes be connected to the static structure of a Petri net. Many properties are decidable, but their complexity may be huge. It is often opportune to restrict oneself to classes of systems, to partial algorithms, and to similar but simpler properties. Instead of analysing a given system, it is also possible to search for a system satisfying some desired properties by construction. This comprehensive textbook/reference presents and discusses these issues in-depth in the context of one of the most fundamental Petri net models, called place/transition nets. The presentation is fortified by means of many examples and worked exercises. Among topics addressed: ¿ In which order may actions may be generated and scheduled? ¿ What states and configurations may be reached in a concurrent system? ¿ Which interesting classes of systems can be analysed relatively efficiently? ¿ Is it possible to synthesise a system of some class from its behaviour? ¿ How can systems be represented algebraically, compositionally, and concisely? This unique text, based on introductory as well as on advanced courses on distributed systems, will serve as an invaluable guide for students and (future) researchers interested in theoretical¿as well as in practical¿aspects of Petri nets and related system models. Eike Best has been a full professor (now retired) affiliated to Carl von Ossietzky Universität Oldenburg, Germany. Raymond Devillers has been a full professor (now retired) affiliated to Université Libre de Bruxelles, Belgium. The authors have a long record as collaborators in the fields of Petri nets and the semantics of concurrency.

These are the proceedings of the 27th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in Prague, Czech Republic, in July 2022.Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems.The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2022.

This book focuses on Krylov subspace methods for solving linear systems, which are known as one of the top 10 algorithms in the twentieth century, such as Fast Fourier Transform and Quick Sort (SIAM News, 2000). Theoretical aspects of Krylov subspace methods developed in the twentieth century are explained and derived in a concise and unified way. Furthermore, some Krylov subspace methods in the twenty-first century are described in detail, such as the COCR method for complex symmetric linear systems, the BiCR method, and the IDR(s) method for non-Hermitian linear systems.The strength of the book is not only in describing principles of Krylov subspace methods but in providing a variety of applications: shifted linear systems and matrix functions from the theoretical point of view, as well as partial differential equations, computational physics, computational particle physics, optimizations, and machine learning from a practical point of view.The book is self-contained in that basic necessary concepts of numerical linear algebra are explained, making it suitable for senior undergraduates, postgraduates, and researchers in mathematics, engineering, and computational science. Readers will find it a useful resource for understanding the principles and properties of Krylov subspace methods and correctly using those methods for solving problems in the future.