Matematik for ingeniører

This monograph provides a comprehensive and self-contained treatment of continuum physics, illustrating a systematic approach to the constitutive equations for wide-ranging classes of materials. Derivations of results are detailed through careful proofs, and the contents have been developed to ensure a self-contained and consistent presentation.Part I reviews the kinematics of continuous bodies and illustrates the general setting of balance laws. Essential preliminaries to continuum physics ¿ such as reference and current configurations, transport relations, singular surfaces, objectivity, and objective time derivatives ¿ are covered in detail. A chapter on balance equations then develops the balance laws of mass, linear momentum, angular momentum, energy, and entropy, as well as the balance laws in electromagnetism.Part II is devoted to the general requirements on constitutive models, emphasizing the application of objectivity and consistency with the second law of thermodynamics. Common models of simple materials are then reviewed, and in this framework, detailed descriptions are given of solids (thermoelastic, elastic, and dissipative) and fluids (elastic, thermoelastic, viscous, and Newtonian).A wide of variety of constitutive models are investigated in Part III, which consists of separate chapters focused on several types of non-simple materials: materials with memory, aging and higher-order grade materials, mixtures, micropolar media, and porous materials. The interaction of the electromagnetic field with deformation is also examined within electroelasticity, magnetoelasticity, and plasma theory.Hysteretic effects and phase transitions are considered in Part IV. A new approach is established by treating entropy production as a constitutive function in itself, as is the case for entropy and entropy flux. This proves to be conceptually and practically advantageous in the modelling of nonlinear phenomena, such as those occurring in hysteretic continua (e.g., plasticity, electromagnetism, and the physics of shape memory alloys).Mathematical Modelling of Continuum Physics will be an important reference for mathematicians, engineers, physicists, and other scientists interested in research or applications of continuum mechanics.

The dynamic behavior of pipelines describes the time-varying continuous response of these structures under extreme effects, that are generated by the surrounding environment (waves and sea currents) and motions imposed by the host floating facility. This book describes all known impacts that affect the behavior and operation of a pipeline conveying an inner flow for underwater applications. "Known Impacts" are those phenomena that are considered important according to practice and experience. Underwater pipelines are typical, unique structures that are attached to unique floating facilities. The design and utilization of underwater pipelines depend strongly on the installation site and the intended application's particulars. It is possible that future technology demands will require us to cope with additional challenges that will be considered important for the design and operation of underwater pipelines, leading inevitably to the enhancement of the "known challenges".

This book is dedicated to the analysis and modelling of fractional behaviours that mainly result from physical stochastic phenomena (diffusion, adsorption or aggregation, etc.) of a population (ions, molecules, people, etc.) in a constrained environment and that can be found in numerous areas. It breaks with the usual approaches based on fractional models since it proposes to use unusual models which have the advantage of overcoming some of the limitations of fractional models.This book is dedicated to postgraduated students and to researchers in the field or those who wish to learn with a fresh perspective. After a review of fractional models and their limitations, it proposes and demonstrates the interest of four other modelling tools to capture fractional behaviours: new kernels in integral operators, Volterra equations, nonlinear models and partial differential equations with spatially variable coefficients. Several applications on real data and devices illustrate their efficiency.

Sowohl im Studium als auch in der täglichen Arbeit benötigt der Physiker eine Vielzahl mathematischer Methoden, die über die Methoden aus den Grundvorlesungen der Analysis und linearen Algebra hinausgehen. Das vorliegende Buch baut auf diesen Vorlesungen auf und stellt die grundlegenden und jeweils einführenden Themen aus der Funktionentheorie, der Funktionalanalysis, der Theorie orthogonaler Funktionen, der Fouriertheorie, der Tensorrechnung und der Distributionen dar. Bei der sehr kompakten Darstellung des Stoffes wurde darauf geachtet, eine einheitliche und gebräuchliche Notation über die verschiedenen Gebiete der Mathematik und Physik hinweg zu verwenden. Besonders wurde auf eine anschauliche Präsentation des Stoffes Wert gelegt, was zum einen durch zahlreiche erklärende farbige Grafiken und zum anderen durch viele praxisrelevante Beispiele und Aufgaben mit Lösungen erreicht wurde. Geschlossene und kompakte Darstellung von elementaren mathematischen Methoden der Physik. Viele anschauliche Beispiele und Aufgaben mit Lösungen im Text integriert, sowie zusätzliche Aufgaben. Zahlreiche komplexe und farbige Plots als Source-Code (MatLab) online frei verfügbar Rezension der 1. Auflage: "Das Buch enthält alles, was für die Ausbildung eines modernen Physikers wichtig ist, inklusive Tensor- und Fourierrechnung, die in vielen anderen Büchern zu kurz behandelt werden. Das Buch kann als Werk für den Dozenten eingesetzt werden und ermöglicht eine Vorlesung auf verschiedenen Niveaus, je nach Möglichkeiten der Teilnehmer."Prof. Simone Sanner, Justus-Liebig-Universität Giessen

¿This book presents a critical overview of statistical fiber bundle models, including existing models and potential new ones. The authors focus on both the physical and statistical aspects of a specific load-sharing example: the breakdown for circuits of capacitors and related dielectrics. In addition, they investigate some areas of open research.This book is designed for graduate students and researchers in statistics, materials science, engineering, physics, and related fields, as well as practitioners and technicians in materials science and mechanical engineering.

This book is aimed to undergraduate STEM majors and to researchers using ordinary differential equations. It covers a wide range of STEM-oriented differential equation problems that can be solved using computational power series methods. Many examples are illustrated with figures and each chapter ends with discovery/research questions most of which are accessible to undergraduate students, and almost all of which may be extended to graduate level research. Methodologies implemented may also be useful for researchers to solve their differential equations analytically or numerically. The textbook can be used as supplementary for undergraduate coursework, graduate research, and for independent study.

This edited volume, with contributions from the Computer Aided Engineering for Batteries (CAEBAT) program, provides firsthand insights into nuances of implementing battery models in actual geometries. It discusses practical examples and gaps in our understanding, while reviewing in depth the theoretical background and algorithms. Over the last ten years, several world-class academics, automotive original equipment manufacturers (OEMs), battery cell manufacturers and software developers worked together under an effort initiated by the U.S. Department of Energy to develop mature, validated modeling tools to simulate design, performance, safety and life of automotive batteries. Until recently, battery modeling was a niche focus area with a relatively small number of experts. This book opens up the research topic for a broader audience from industry and academia alike. It is a valuable resource for anyone who works on battery engineering but has limited hands-on experience with coding.

This book presents a novel design framework for the development of Digital Twin (DT) models for process- and motion-control applications. It is based on system-data acquisition using cutting-edge computing technologies, modelling of physical-system behavior through detailed simultaneous simulation of different aspects of the system, and optimal dynamic behavior-matching of the process. The design framework is enhanced with real-time data analytics to improve the performance of the DT¿s behavior-matching with the real system or physical twin.The methods of creating a DT detailed in Digital-Twin-Enabled Smart Control Engineering make possible the study of a system for real-time controller tuning and fault detection. They also facilitate life-cycle analysis for multiple critical and dangerous conditions that cannot be explored in the corresponding real system or physical twin. The authors show how a DT can be exploited to enable self-optimizing capabilitiesin feedback control systems.The DT framework and the control-performance assessment, fault diagnosis and prognosis, remaining-useful-life analysis, and self-optimizing control abilities it allows are validated with both process- and motion-control systems and their DTs. Supporting MATLAB-based material for a case study and an expanded introduction to the basic elements of DTs can be accessed on an associated website. This book helps university researchers from many areas of engineering to develop new tools for control design and reliability and life-cycle assessment and helps practicing engineers working with robotic, manufacturing and processing, and mechatronic systems to maintain and develop the mechanical tools they use.

< div="">This book introduces undergraduate students of engineering and science to applied mathematics essential to the study of many problems. Topics are differential equations, power series, Laplace transforms, matrices and determinants, vector analysis, partial differential equations, complex variables, and numerical methods. Approximately, 160 examples and 1000 homework problems aid students in their study. This book presents mathematical topics using derivations rather than theorems and proofs. This textbook is uniquely qualified to apply mathematics to physical applications (spring-mass systems, electrical circuits, conduction, diffusion, etc.), in a manner that is efficient and understandable. This book is written to support a mathematics course after differential equations, to permit several topics to be covered in one semester, and to make the material comprehensible to undergraduates. An Instructor Solutions Manual, and also a Student Solutions Manual that provides solutions to select problems, is available.^

The textbook is intended for teaching MATLAB language and its applications. The book is composed of three parts: MATLAB programming, scientific computing with MATLAB, and system simulation with Simulink. Since MATLAB is widely used in all fields of science and engineering, a good introduction to the language can not only help students learn how to use it to solve practical problems, but also provide them with the skills to use MATLAB independently in their later courses and research. The three parts of the book are well-balanced and tailored to the needs of engineering students, and the mathematical problems commonly encountered in engineering can be easily solved using MATLAB. This textbook is suitable for undergraduate and graduate students majoring in science and engineering.The study guide of this textbook could be accessed via: http://sn.pub/thGR7v. This website provides links to recorded teaching videos, MATLAB toolbox for the book, interactive slide decks files in Powerpoint documents, and solution manuals by the authors.

This book focuses on vibration suppression of flexible three-dimensional Euler-Bernoulli beams modeled by PDEs. Boundary control strategy and several control methods are proposed to stabilize the closed-loop system. Besides, some common engineering problems such as input constraint and output constraint are also considered in the control scheme design. This book offers a comprehensive introduction of the modeling process, controller design, stability analysis and numerical simulation. The detailed MATLAB codes in each chapter are also provided, which can make readers better understand the control flow of the system. This book is mainly targeted for researchers, senior undergraduate students and postgraduate students in the field of control theory and control engineering.

This book provides the background and the mathematical methods necessary to understand the basic transforms in signal processing and linear systems and probability and random processes to prepare for in depth study of analog and digital communications systems.This tutorial presentation provides developments of Fourier series and other orthogonal series, including trigonometric and complex exponential Fourier series, least squares approximations and generalized Fourier series, and the spectral content of periodic signals.This text thoroughly covers Fourier transform pairs for continuous time signals, Fourier transform properties, and the magnitude and phase of Fourier transforms.The author includes discussions of techniques for the analysis of continuous time linear systems in the time and frequency domains with particular emphasis on the system transfer function, impulse response, system/filter bandwidth, power and energy calculations, and the time domainsampling theorem.The basics of probability and random processes, including the key concepts of expected value, variance, characteristic functions, common probability distributions, autocorrelation, power spectral densities, wide sense stationarity, and ergodicity, are all developed in some detail. Many examples and problems are included to illustrate and examine these topics.¿ Provides developments of Fourier series and other orthogonal series¿ Presents fundamental Fourier transform properties and example applications¿ Discusses techniques for the analysis of continuous time linear systems in the time and frequency domains¿ Presents a fundamental development of probability and random variables¿ Develops the basic ideas of random processes including autocorrelation, power spectral densities, stationarity, and ergodicity

In the present book, the starting line is defined by a morphogenetic perspective on human communication and culture. The focus is on visual communication, music, religion (myth), and language, i.e., on the ¿symbolic forms¿ at the heart of human cultures (Ernst Cassirer). The term ¿morphogenesis¿ has more precisely the meaning given by René Thom (1923-2002) in his book ¿Morphogenesis and Structural Stability¿ (1972) and the notions of ¿self-organization¿ and cooperation of subsystems in the ¿Synergetics¿ of Hermann Haken (1927- ). The naturalization of communication and cultural phenomena is the favored strategy, but the major results of the involved disciplines (art history, music theory, religious science, and linguistics) are respected.Visual art from the Paleolithic to modernity stands for visual communication. The present book focuses on studies of classical painting and sculpture (e.g., Leonardo da Vinci, William Turner, and Henry Moore) and modern art (e.g., Jackson Pollock and Joseph Beuys). Musical morphogenesis embraces classical music (from J. S. Bach to Arnold Schönberg) and political songwriting (Bob Dylan, Leonhard Cohen). The myths of pre-literary societies show the effects of self-organization in the re-assembly (bricolage) of traditions. Classical polytheistic and monotheistic religions demonstrate the unfolding of basic germs (religious attractors) and their reduction in periods of crisis, the self-organization of complex religious networks, and rationalized macro-structures (in theologies). Significant tendencies are analyzed in the case of Buddhism and Christianism. Eventually, a holistic view of symbolic communication and human culture emerges based on state-of-the-art in evolutionary biology, cognitive science, linguistics, and semiotics (philosophy of symbolic forms).

This thesis works on the topic of fiber-reinforced plastics and discusses the measurement of strain with embedded sensors. Embedding sensors into a structure fundamentally poses challenges arising from the differences in mechanical properties of sensor and structure. This thesis works on the research area of Self-Sensing, where these challenges are overcome by using carbon fibers for both load-carrying and strain-sensing functions. Starting with a literature review, this thesis proposes three research hypotheses, which are targeted to describe the Self-Sensing properties of unidirectional carbon fiber reinforced plastics (CFRPs) for strain measurements. These hypotheses assume, that the electric anisotropy of the material results in a complex voltage distribution within a Self-Sensing specimen. In order to discuss this point further, a two-dimensional piezoresistivity model based on the Laplace equation is introduced. The developed model newly allows to quantify the electricpotential changes in specimens with arbitrary geometrical dimensions and electric anisotropy.Furthermore, this thesis discusses a set of experimental results on the piezoresistive properties of unidirectional CFRP made with the pultrusion process. Overall, the results of the experiments indicate that the most repeatable results are obtained for specimens with electric contacts at their cut-end. This approach allows to manufacture Self-Strain-Sensing rods with a gauge factor of approximately 1.9 that can be used in a multifunctional manner for both load-carrying and strain-sensing purposes. Furthermore, a novel measurement setup is developed, which allows to acquire the electric potential distribution on the surface of electrical conductors with very high spacial resolution. This experimental setup newly reveals that the current flow in specimens can be more complex than assumed in a two-dimensional model.

This book examines some issues involving climate change, human trafficking, and other serious world challenges made worse by climate change. Climate change increases the risk of natural disasters and thus creates poverty and can cause situations of conflict and instability. Displacement can occur giving traffickers an opportunity to exploit affected people. In the fuzzy graph theory part of the book, the relatively new concepts of fuzzy soft semigraphs and graph structures are used to study human trafficking, as well as its time intuitionistic fuzzy sets that have been introduced to model forest fires. The notion of legal and illegal incidence strength is used to analyze immigration to the USA. The examination of return refugees to their origin countries is undertaken. The neighborhood connectivity index is determined for trafficking in various regions in the world. The cycle connectivity measure for the directed graph of the flow from South Americato the USA is calculated. It is determined that there is a need for improvement in government response by countries. Outside the area of fuzzy graph theory, a new approach to examine climate change is introduced. Social network theory is used to study feedback processes that effect climate forcing. Tipping points in climate change are considered. The relationship between terrorism and climate change is examined. Ethical issues concerning the obligation of business organizations to reduce carbon emissions are also considered. Nonstandard analysis is a possible new area that could be used by scholars of mathematics of uncertainty. A foundation is laid to aid the researcher in the understanding of nonstandard analysis. In order to accomplish this, a discussion of some basic concepts from first-order logic is presented as some concepts of mathematics of uncertainty. An application to the theory of relativity is presented.

This book provides practical demonstrations of how to carry out definite integrals with Monte Carlo methods using Mathematica. Random variates are sampled by the inverse transform method and the acceptance-rejection method using uniform, linear, Gaussian, and exponential probability distribution functions. A chapter on the application of the Variational Quantum Monte Carlo method to a simple harmonic oscillator is included. These topics are all essential for students of mathematics and physics. The author includes thorough background on each topic covered within the book in order to help readers understand the subject. The book also contains many examples to show how the methods can be applied.

The Mathematics of Errors presents an original, rigorous and systematic approach to the calculus of errors, targeted at both the engineer and the mathematician.Starting from Gauss's original point of view, the book begins as an introduction suitable for graduate students, leading to recent developments in stochastic analysis and Malliavin calculus, including contributions by the author. Later chapters, aimed at a more mature audience, require some familiarity with stochastic calculus and Dirichlet forms. Sensitivity analysis, in particular, plays an important role in the book. Detailed applications in a range of fields, such as engineering, robotics, statistics, financial mathematics, climate science, or quantum mechanics are discussed through concrete examples. Throughout the book, error analysis is presented in a progressive manner, motivated by examples and appealing to the reader¿s intuition.By formalizing the intuitive concept of error and richly illustrating its scope for application, this book provides readers with a blueprint to apply advanced mathematics in practical settings. As such, it will be of immediate interest to engineers and scientists, whilst providing mathematicians with an original presentation.Nicolas Bouleau has directed the mathematics center of the Ecole des Ponts ParisTech for more than ten years. He is known for his theory of error propagation in complex models. After a degree in engineering and architecture, he decided to pursue a career in mathematics under the influence of Laurent Schwartz. He has also written on the production of knowledge, sustainable economics and mathematical models in finance. Nicolas Bouleau is a recipient of the Prix Montyon from the French Academy of Sciences.

This textbook is aimed at students of non-specialist courses with computer science components. Special emphasis is placed on the so-called life sciences, such as medical technology, rescue engineering, biotechnology, environmental engineering or process engineering. The textbook is suitable for readers in study and practice who want to get an introduction to computer science. The special feature of this book is the problem-based approach, as well as the exercises designed according to different taxonomy levels.