For introductory courses in Differential Equations. This best-selling text by these well-known authors blends the traditional algebra problem solving skills with the conceptual development and geometric visualisation of a modern differential equations course that is essential to science and engineering students. It reflects the new qualitative approach that is altering the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB. Its focus balances the traditional manual methods with the new computer-based methods that illuminate qualitative phenomena and make accessible a wider range of more realistic applications. Seldom-used topics have been trimmed and new topics added: it starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the text.

The new edition includes additional analytical methods in the classical theory of viscoelasticity. This leads to a new theory of finite linear viscoelasticity of incompressible isotropic materials. Anisotropic viscoplasticity is completely reformulated and extended to a general constitutive theory that covers crystal plasticity as a special case.

This textbook provides the tools for a modern post-graduate introductory course on system reliability theory. It focuses on probabilistic aspects of the theory, including recent results based on signatures, stochastic orders, aging classes, copulas and distortion (or aggregation) functions. The reader requires on an introductory knowledge on probability theory and mathematics. The book serves both for graduate students in mathematics and for engineering students in various disciplines as well as students learning survival analysis, network reliability or simple game theory. Included also are brief introductions to the basic aspects of lifetime modelling, stochastic comparisons, aging classes, mixtures and copula theory. The book develops this knowledge with worked examples and supplies code for the program R so that students can explore its lessons and techniques.

This book addresses the applications of Fourier transform to smile modeling. Smile effect is used generically by ?nancial engineers and risk managers to refer to the inconsistences of quoted implied volatilities in ?nancial markets, or more mat- matically, to the leptokurtic distributions of ?nancial assets and indices. Therefore, a sound modeling of smile effect is the central challenge in quantitative ?nance. Since more than one decade, Fourier transform has triggered a technical revolution in option pricing theory. Almost all new developed option pricing models, es- cially in connection with stochastic volatility and random jump, have extensively applied Fourier transform and the corresponding inverse transform to express - tion pricing formulas. The large accommodation of the Fourier transform allows for a very convenient modeling with a general class of stochastic processes and d- tributions. This book is then intended to present a comprehensive treatment of the Fourier transform in the option valuation, covering the most stochastic factors such as stochastic volatilities and interest rates, Poisson and Levy jumps, including some asset classes such as equity, FX and interest rates, and providing numerical ex- ples and prototype programming codes. I hope that readers will bene't from this book not only by gaining an overview of the advanced theory and the vast large l- erature on these topics, but also by gaining a ?rst-hand feedback from the practice on the applications and implementations of the theory."

This proceedings volume contains a selection of papers presented at the Fourth International Conference on High Performance Scientific Computing held at the Hanoi Institute of Mathematics, Vietnamese Academy of Science and Technology (VAST), March 2-6, 2009. The conference was organized by the Hanoi Institute of Mathematics, the Interdisciplinary Center for Scientific Computing (IWR), Heidelberg, and its Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences, and Ho Chi Minh City University of Technology. The contributions cover the broad interdisciplinary spectrum of scientific computing and present recent advances in theory, development of methods, and applications in practice. Subjects covered are mathematical modelling, numerical simulation, methods for optimization and control, parallel computing, software development, applications of scientific computing in physics, mechanics, biology and medicine, engineering, hydrology problems, transport, communication networks, production scheduling, industrial and commercial problems.

Physiologically Based Pharmacokinetic (PBPK) Modeling: Methods and Applications in Toxicology and Risk Assessment presents foundational principles, advanced techniques and applications of PBPK modeling. Contributions from experts in PBPK modeling cover topics such as pharmacokinetic principles, classical physiological models, the application of physiological models for dose-response and risk assessment, the use of in vitro information, and in silico methods. With end-of-chapter exercises that allow readers to practice and learn the skills associated with PBPK modeling, dose-response, and its applications to safety and risk assessments, this book is a foundational resource that provides practical coverage of PBPK modeling for graduate students, academics, researchers, and more.

This book gathers a selection of invited and contributed lectures from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale methods, numerical linear algebra and discretization techniques for fluid mechanics and optics are presented. As such, the book offers a valuable resource for a wide range of readers looking for a state-of-the-art overview of advanced techniques, algorithms and results in numerical mathematics and scientific computing.

Artificial intelligence (AI) and digital engineering have become prevalent in business, industry, government, and academia. However, the workforce still has a lot to learn on how to leverage them. This handbook presents the preparatory and operational foundations for the efficacy, applicability, risk, and how to take advantage of these tools and techniques. "Handbook of Mathematical and Digital Engineering Foundations for Artificial Intelligence: A Systems Methodology" provides a guide for using digital engineering platforms for advancing AI applications. The book discusses an interface of education and research in the pursuit of AI developments and highlights the facilitation of advanced education through AI and digital engineering systems. It presents an integration of soft and hard skills in developing and using AI and offers a rigorous systems approach to understanding and using AI. This handbook will be the go-to resource for practitioners and students on applying systems methodology to the body of knowledge of understanding, embracing, and using digital engineering tools and techniques.

1) Provides analytical solutions based on a three-phase model for composites of various structures 2) Identifies computational models to solve problems within all applications of composite materials 3) Constructs higher approximations of the Maxwell formula 4) Proposes efficient analytical algorithms ensuring reliable computational analysis

This book is one of the first to include an extensive discussion of integrated public transport planning. In times of growing urban populations and increasing environmental awareness, the importance of optimizing public transport systems is ever-developing. Three different aspects are presented: line planning, timetabling, and vehicle scheduling. Classically, challenges concerning these three aspects of planning are solved sequentially. Due to their high interdependence, the author presents a clear and detailed analysis of innovative, integrated models with accompanied numerical experiments performed to assess, and often support, the benefits of integration. The book will appeal to a wide readership ranging from graduate students to researchers.

This book addresses dynamic modelling methodology and analyses of tree-type robotic systems. Such analyses are required to visualize the motion of a system without really building it. The book contains novel treatment of the tree-type systems using concept of kinematic modules and the corresponding Decoupled Natural Orthogonal Complements (DeNOC), unified representation of the multiple-degrees-of freedom-joints, efficient recursive dynamics algorithms, and detailed dynamic analyses of several legged robots. The book will help graduate students, researchers and practicing engineers in applying their knowledge of dynamics for analysis of complex robotic systems. The knowledge contained in the book will help one in virtual testing of robot operation, trajectory planning and control.

Optimization models based on a nonlinear systems description often possess multiple local optima. The objective of global optimization (GO) is to find the best possible solution of multiextremal problems. This volume illustrates the applicability of GO modeling techniques and solution strategies to real-world problems. The contributed chapters cover a broad range of applications from agroecosystem management, assembly line design, bioinformatics, biophysics, black box systems optimization, cellular mobile network design, chemical process optimization, chemical product design, composite structure design, computational modeling of atomic and molecular structures, controller design for induction motors, electrical engineering design, feeding strategies in animal husbandry, the inverse position problem in kinematics, laser design, learning in neural nets, mechanical engineering design, numerical solution of equations, radiotherapy planning, robot design, and satellite data analysis. The solution strategies discussed encompass a range of practically viable methods, including both theoretically rigorous and heuristic approaches.

Inspired by the Research Collaboration Workshop for Women in Mathematical Biology, this volume contains research and review articles that cover topics ranging from models of animal movement to the flow of blood cells in the embryonic heart. Hosted by the National Institute for Mathematics and Biological Synthesis (NIMBioS), the workshop brought together women working in biology and mathematics to form four research groups that encouraged multidisciplinary collaboration and lifetime connections in the STEM field. This volume introduces many of the topics from the workshop, including the aerodynamics of spider ballooning; sleep, circadian rhythms, and pain; blood flow regulation in the kidney; and the effects of antimicrobial therapy on gut microbiota and microbiota and Clostridium difficile. Perfect for students and researchers in mathematics and biology, the papers included in this volume offer an introductory glimpse at recent research in mathematical biology.

This contributed volume explores innovative research in the modeling, simulation, and control of crowd dynamics. Chapter authors approach the topic from the perspectives of mathematics, physics, engineering, and psychology, providing a comprehensive overview of the work carried out in this challenging interdisciplinary research field. In light of the recent COVID-19 pandemic, special consideration is given to applications of crowd dynamics to the prevention of the spreading of contagious diseases. Some of the specific topics covered in this volume include: - Impact of physical distancing on the evacuation of crowds- Generalized solutions of opinion dynamics models- Crowd dynamics coupled with models for infectious disease spreading- Optimized strategies for leaders in controlling the dynamics of a crowd Crowd Dynamics, Volume 3 is ideal for mathematicians, engineers, physicists, and other researchers working in the rapidly growing field of modeling and simulation of human crowds.

Autonomous Positioning of Piezoactuated Mechanism for Biological Cell Puncture gives a systematic and almost selfcontained description of the many facets of advanced design, optimization, modeling, system identification and advanced control techniques for positioning of cell puncture mechanism with piezoelectric actuator in micro/nanorobotics systems. To achieve biomedical applications, reliability design, modeling, and precision control are vitally important for developing engineering systems. With the advances in mechanical design, dynamic modeling, system identification, and control techniques, exploiting them for the benefit of reliability design, precision control, and quick actuation of micro/nanomanipulation systems to expand the robot's applications at the micro and nanoscales, especially for biomedical applications. This book unifies existing and emerging techniques concerning advanced design, modeling and advanced control methodologies in micropuncture of biological cells using piezoelectric actuator with their practical biomedical applications. The book is an essential resource for researchers within robotics, mechatronics, biomedical engineering, and automatic control society, including both academic and industrial parts. KEY FEATURES * Provides a series of latest results in, including but not limited to, design, modeling, and control of micro/nanomanipulation systems utilizing piezoelectric actuator * Gives recent advances of theory, technological aspects, and applications of advanced modeling, control, and actuation methodologies in cell engineering applications * Presents simulation and experimental results to reflect the micro/nano manipulation practice, and also validate the performances of the developed design, analysis, and synthesis approaches

Exploring Mathematical Modeling in Biology through Case Studies and Experimental Activities provides supporting materials for courses taken by students majoring in mathematics, computer science or in the life sciences. The book's cases and lab exercises focus on hypothesis testing and model development in the context of real data. The supporting mathematical, coding and biological background permit readers to explore a problem, understand assumptions, and the meaning of their results. The experiential components provide hands-on learning both in the lab and on the computer. As a beginning text in modeling, readers will learn to value the approach and apply competencies in other settings. Included case studies focus on building a model to solve a particular biological problem from concept and translation into a mathematical form, to validating the parameters, testing the quality of the model and finally interpreting the outcome in biological terms. The book also shows how particular mathematical approaches are adapted to a variety of problems at multiple biological scales. Finally, the labs bring the biological problems and the practical issues of collecting data to actually test the model and/or adapting the mathematics to the data that can be collected.

The text focuses on mathematical modeling and applications of advanced techniques of machine learning, and artificial intelligence, including artificial neural networks, evolutionary computing, data mining, and fuzzy systems to solve performance and design issues more precisely. Intelligent computing encompasses technologies, algorithms, and models in providing effective and efficient solutions to a wide range of problems including the airport's intelligent safety system. It will serve as an ideal reference text for senior undergraduate, graduate students, and academic researchers in fields including industrial engineering, manufacturing engineering, computer engineering, and mathematics. The book- Discusses mathematical modeling for traffic, sustainable supply chain, vehicular Ad-Hoc networks, internet of things networks with intelligent gateways. Covers advanced machine learning, artificial intelligence, fuzzy systems, evolutionary computing, data mining techniques for real-world problems. Presents applications of mathematical models in chronic diseases such as kidney and coronary artery diseases. Highlights advances in mathematical modeling, strength, and benefits of machine learning and artificial intelligence, including driving goals, applicability, algorithms, and processes involved. Showcases emerging real-life topics on mathematical models, machine learning, and intelligent computing using an interdisciplinary approach. The text presents emerging real-life topics on mathematical models, machine learning, and intelligent computing in a single volume. It will serve as an ideal text for senior undergraduate, graduate students, and researchers in diverse fields domains including industrial and manufacturing engineering, computer engineering, and mathematics.

Machine learning heavily relies on optimization algorithms to solve its learning models. Constrained problems constitute a major type of optimization problem, and the alternating direction method of multipliers (ADMM) is a commonly used algorithm to solve constrained problems, especially linearly constrained ones. Written by experts in machine learning and optimization, this is the first book providing a state-of-the-art review on ADMM under various scenarios, including deterministic and convex optimization, nonconvex optimization, stochastic optimization, and distributed optimization. Offering a rich blend of ideas, theories and proofs, the book is up-to-date and self-contained. It is an excellent reference book for users who are seeking a relatively universal algorithm for constrained problems. Graduate students or researchers can read it to grasp the frontiers of ADMM in machine learning in a short period of time.

Spatial Patterns offers a study of nonlinear higher order model equations that are central to the description and analysis of spatio-temporal pattern formation in the natural sciences. Through a unique combination of results obtained by rigorous mathematical analysis and computational studies, the text exhibits the principal families of solutions, such as kinks, pulses and periodic solutions, and their dependence on critical eigenvalue parameters, and points to a rich structure, much of which still awaits exploration.

The exposition unfolds systematically, first focusing on a single equation to achieve optimal transparency, and then branching out to wider classes of equations. The presentation is based on results from real analysis and the theory of ordinary differential equations.

Key features:

* presentation of a new mathematical method specifically designed for the analysis of multi-bump solutions of reversible systems

* strong emphasis on the global structure of solution branches

* extensive numerical illustrations of complex solutions and their dependence on eigenvalue parameters

* application of the theory to well-known equations in mathematical physics and mechanics, such as the Swift--Hohenberg equation, the nonlinear SchrAdinger equation and the equation for the nonlinearly supported beam

* includes recent original results by the authors

* exercises scattered throughout the text to help illuminate the theory

* many research problems

The book is intended for mathematicians who wish to become acquainted with this new area of partial and ordinary differential equations, for mathematical physicists who wish to learn about the theory developed for aclass of well-known higher order pattern-forming model equations, and for graduate students who are looking for an exciting and promising field of research.

This book presents the theory and computation of open channel flows, using detailed analytical, numerical and experimental results. The fundamental equations of open channel flows are derived by means of a rigorous vertical integration of the RANS equations for turbulent flow. In turn, the hydrostatic pressure hypothesis, which forms the core of many shallow water hydraulic models, is scrutinized by analyzing its underlying assumptions. The book's main focus is on one-dimensional models, including detailed treatments of unsteady and steady flows. The use of modern shock capturing finite difference and finite volume methods is described in detail, and the quality of solutions is carefully assessed on the basis of analytical and experimental results. The book's unique features include: * Rigorous derivation of the hydrostatic-based shallow water hydraulic models * Detailed treatment of steady open channel flows, including the computation of transcritical flow profiles * General analysis of gate maneuvers as the solution of a Riemann problem * Presents modern shock capturing finite volume methods for the computation of unsteady free surface flows * Introduces readers to movable bed and sediment transport in shallow water models* Includes numerical solutions of shallow water hydraulic models for non-hydrostatic steady and unsteady free surface flows This book is suitable for both undergraduate and graduate level students, given that the theory and numerical methods are progressively introduced starting with the basics. As supporting material, a collection of source codes written in Visual Basic and inserted as macros in Microsoft Excel (R) is available. The theory is implemented step-by-step in the codes, and the resulting programs are used throughout the book to produce the respective solutions.

This open access book focuses on robot introspection, which has a direct impact on physical human-robot interaction and long-term autonomy, and which can benefit from autonomous anomaly monitoring and diagnosis, as well as anomaly recovery strategies. In robotics, the ability to reason, solve their own anomalies and proactively enrich owned knowledge is a direct way to improve autonomous behaviors. To this end, the authors start by considering the underlying pattern of multimodal observation during robot manipulation, which can effectively be modeled as a parametric hidden Markov model (HMM). They then adopt a nonparametric Bayesian approach in defining a prior using the hierarchical Dirichlet process (HDP) on the standard HMM parameters, known as the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM). The HDP-HMM can examine an HMM with an unbounded number of possible states and allows flexibility in the complexity of the learned model and the development of reliable and scalable variational inference methods. This book is a valuable reference resource for researchers and designers in the field of robot learning and multimodal perception, as well as for senior undergraduate and graduate university students.

Covers flight mechanics, flight simulation, flight testing, flight control, and aeroservoelasticity. Features artificial neural network and fuzzy logic-based aspects in modeling and analysis of flight mechanics systems: aircraft parameter estimation, and reconfiguration of control. Focuses on a systems-based approach. Includes two new chapters, numerical simulation examples with a MATLAB® based approach, and end-of-chapter exercises. Includes a Solutions Manual and Figure Slides for adopting instructors.

The theory of dynamic games is very rich in nature and very much alive If the reader does not already agree with this statement, I hope he/she will surely do so after having consulted the contents of the current volume. The activities which fall under the heading of 'dynamic games' cannot easily be put into one scientific discipline. On the theoretical side one deals with differential games, difference games (the underlying models are described by differential, respec tively difference equations) and games based on Markov chains, with determin istic and stochastic games, zero-sum and nonzero-sum games, two-player and many-player games - all under various forms of equilibria. On the practical side, one sees applications to economics (stimulated by the recent Nobel prize for economics which went to three prominent scientists in game theory), biology, management science, and engineering. The contents of this volume are primarily based on selected presentations made at the Sixth International Symposium on Dynamic Games and Applica tions, held in St Jovite, Quebec, Canada, 13-15 July 1994. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival technical journals. This conference, as well as its predecessor which was held in Grimentz, 1992, took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. One of the activities of the ISDG is the publication of these Annals. The contributions in this volume have been grouped around five themes."

This volume provides an introduction to the properties of functional differential equations and their applications in diverse fields such as immunology, nuclear power generation, heat transfer, signal processing, medicine and economics. In particular, it deals with problems and methods relating to systems having a memory (hereditary systems). The book contains eight chapters. Chapter 1 explains where functional differential equations come from and what sort of problems arise in applications. Chapter 2 gives a broad introduction to the basic principle involved and deals with systems having discrete and distributed delay. Chapters 3-5 are devoted to stability problems for retarded, neutral and stochastic functional differential equations. Problems of optimal control and estimation are considered in Chapters 6-8. For applied mathematicians, engineers, and physicists whose work involves mathematical modeling of hereditary systems. This volume can also be recommended as a supplementary text for graduate students who wish to become better acquainted with the properties and applications of functional differential equations.

This book is placed at the interface between string theory and elementary particle physics and shows novel results in the search for a heterotic string vacuum that reproduces those matter particles and interactions observed in our universe. The author provides a systematic classification of potentially realistic heterotic covariant lattice vacua, which possess a lower number of moduli fields when compared to conventional compactification methods, by means of number theoretical methods. These methods, while well known to the mathematics community, have not yet found many applications to physics. They are introduced to the degree necessary to understand the computations carried out throughout this work. Furthermore, explicit covariant lattice models with particularly interesting properties are analyzed in detail. Finally, new light is shed on the relation between covariant lattice models and asymmetric orbifold compactifications, the result being a concrete correspondence between certain types of asymmetric orbifolds and those classified covariant lattices.