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Mathematical Modelling: A Graduate Textbook
by Seyed M. Moghadas Majid Jaberi-DourakiAn important resource that provides an overview of mathematical modelling Mathematical Modelling offers a comprehensive guide to both analytical and computational aspects of mathematical modelling that encompasses a wide range of subjects. The authors provide an overview of the basic concepts of mathematical modelling and review the relevant topics from differential equations and linear algebra. The text explores the various types of mathematical models, and includes a range of examples that help to describe a variety of techniques from dynamical systems theory. The book’s analytical techniques examine compartmental modelling, stability, bifurcation, discretization, and fixed-point analysis. The theoretical analyses involve systems of ordinary differential equations for deterministic models. The text also contains information on concepts of probability and random variables as the requirements of stochastic processes. In addition, the authors describe algorithms for computer simulation of both deterministic and stochastic models, and review a number of well-known models that illustrate their application in different fields of study. This important resource: Includes a broad spectrum of models that fall under deterministic and stochastic classes and discusses them in both continuous and discrete forms Demonstrates the wide spectrum of problems that can be addressed through mathematical modelling based on fundamental tools and techniques in applied mathematics and statistics Contains an appendix that reveals the overall approach that can be taken to solve exercises in different chapters Offers many exercises to help better understand the modelling process Written for graduate students in applied mathematics, instructors, and professionals using mathematical modelling for research and training purposes, Mathematical Modelling: A Graduate Textbook covers a broad range of analytical and computational aspects of mathematical modelling.
Mathematical Modelling
by Simon SerovajskyMathematical Modelling sets out the general principles of mathematical modelling as a means comprehending the world. Within the book, the problems of physics, engineering, chemistry, biology, medicine, economics, ecology, sociology, psychology, political science, etc. are all considered through this uniform lens. The author describes different classes of models, including lumped and distributed parameter systems, deterministic and stochastic models, continuous and discrete models, static and dynamical systems, and more. From a mathematical point of view, the considered models can be understood as equations and systems of equations of different nature and variational principles. In addition to this, mathematical features of mathematical models, applied control and optimization problems based on mathematical models, and identification of mathematical models are also presented. Features Each chapter includes four levels: a lecture (main chapter material), an appendix (additional information), notes (explanations, technical calculations, literature review) and tasks for independent work; this is suitable for undergraduates and graduate students and does not require the reader to take any prerequisite course, but may be useful for researchers as well Described mathematical models are grouped both by areas of application and by the types of obtained mathematical problems, which contributes to both the breadth of coverage of the material and the depth of its understanding Can be used as the main textbook on a mathematical modelling course, and is also recommended for special courses on mathematical models for physics, chemistry, biology, economics, etc.
Mathematical Modelling and Applications
by Gabriele Kaiser Werner Blum Gloria Ann StillmanThis volume documents on-going research and theorising in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in the life world of people whether these range from the everyday individual numeracy level to sophisticated new problems for society at large. Mathematical modelling and real world applications are considered as having potential for multi-disciplinary work that involves knowledge from a variety of communities of practice such as those in different workplaces (e. g. , those of educators, designers, construction engineers, museum curators) and in different fields of academic endeavour (e. g. , history, archaeology, mathematics, economics). From an educational perspective, researching the development of competency in real world modelling involves research situated in crossing the boundaries between being a student engaged in modelling or mathematical application to real word tasks in the classroom, being a teacher of mathematical modelling (in or outside the classroom or bridging both), and being a modeller of the world outside the classroom. This is the focus of many of the authors of the chapters in this book. All authors of this volume are members of the International Community of Teachers of Mathematical Modelling (ICTMA), the peak research body into researching the teaching and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace.
Mathematical Modelling and Biomechanics of the Brain (Fields Institute Monographs #37)
by Corina Drapaca Siv SivaloganathanThis monograph aims to provide a rigorous yet accessible presentation of some fundamental concepts used in modeling brain mechanics and give a glimpse of the insights and advances that have arisen as a result of the nascent interaction of the mathematical and neurosurgical sciences. It begins with some historical perspective and a brief synopsis of the biomedical/biological manifestations of the clinical conditions/diseases considered. Each chapter proceeds with a discussion of the various mathematical models of the problems considered, starting with the simplest models and proceeding to more complex models where necessary. A detailed list of relevant references is provided at the end of each chapter. With the beginning research student in mind, the chapters have been crafted to be as self-contained as possible while addressing different clinical conditions and diseases. The book is intended as a brief introduction to both theoreticians and experimentalists interested in brain mechanics, with directions and guidance for further reading, for those who wish to pursue particular topics in greater depth. It can also be used as a complementary textbook in a graduate level course for neuroscientists and neuroengineers.
Mathematical Modelling and Computing in Physics, Chemistry and Biology: Fundamentals and Applications (Studies in Systems, Decision and Control #495)
by Zdzislaw TrzaskaThis book keeps an eye in the direction of applications of advanced and high performance scientific computing in describing the behavior of natural and constructed systems, e.g. chaos, bifurcation, fractal, Lyapunov exponent, period doubling, Poincaré map, strange attractor etc. With the aid of powerful computers the modem theory of chaos and its geometry, the fractals, and attractors are developed. The concepts of object oriented computing are introduced early in the text and steadily expanded as one progresses through the chapters. The beginning of each chapter is of an introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on nonlinear stability and convergence. This is the first complete introduction to process modelling and computing that fully integrates software tools — enabling professionals and students to master critical techniques hands on through computer simulations based on the popular MATLAB environment. The book offers a simple tool for all those oscillations that are travelling through the world, helping them discover its hidden beauty. Many applications as well as results of computer simulations are presented. The center of concern is set on existing as well as emerging continuous methods of investigations useful for researchers, engineers and practitioners active in many and often interdisciplinary fields, where physics, electrochemistry, biology and medicine play a key role. Coverage includes: • Dynamic behavior of nonlinear systems, • Fundamental descriptions of processes exhibiting nonlinear oscillations, • Mechanism and function of structures of nonlinear oscillations’ patterns, • Analysis of dynamical oscillations in electric circuits and systems, • Artificial intelligence models of natural systems, • Nonlinear oscillations in chemistry, biology and medicine, • Oscillations in mechanics and transport systems, • Oscillations in fractional-order systems, • Energy harvesting systems from the surrounding environment. With an insatiable appetite for exploring the surrounding world and doing research, this book can help readers quickly find ways to use new computers and facilitate the quest for greater knowledge and understanding of reality. The reach of novelty of the book ranges from new mathematical ideas to motivating questions and science issues in many subject areas.
Mathematical Modelling and Nonstandard Schemes for the Corona Virus Pandemic (BestMasters)
by Sarah Marie TreibertThis book deals with the prediction of possible future scenarios concerning the COVID-19 pandemic. Based on the well-known SIR model by Kermack and McKendrick a compartment model is established. This model comprises its own assumptions, transition rates and transmission dynamics, as well as a corresponding system of ordinary differential equations. Making use of numerical methods and a nonstandard-finite-difference scheme, two submodels are implemented in Matlab in order to make parameter estimations and compare different scenarios with each other.
Mathematical Modelling and Optimization of Engineering Problems (Nonlinear Systems and Complexity #30)
by Dumitru Baleanu J. A. Tenreiro Machado Necati ÖzdemirThis book presents recent developments in modelling and optimization of engineering systems and the use of advanced mathematical methods for solving complex real-world problems. It provides recent theoretical developments and new techniques based on control, optimization theory, mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena including latest technologies such as additive manufacturing. Specific topics covered in detail include combinatorial optimization, flow and heat transfer, mathematical modelling, energy storage and management policy, artificial intelligence, optimal control, modelling and optimization of manufacturing systems.
Mathematical Modelling and Scientific Computing with Applications: ICMMSC 2018, Indore, India, July 19–21 (Springer Proceedings in Mathematics & Statistics #308)
by Santanu Manna Biswa Nath Datta Sk. Safique AhmadThis book contains original research papers presented at the International Conference on Mathematical Modelling and Scientific Computing, held at the Indian Institute of Technology Indore, India, on 19–21 July 2018. Organized into 30 chapters, the book presents the recent progress and the most advanced innovations, trends, and real-world challenges encountered and solutions embraced in the applications of mathematics and scientific computing. The book will be of interests to a wide variety of researchers, students and the practicing engineers working in diverse areas of science and engineering, ranging from applied and computational mathematics, vibration problem, computer science, and numerical optimization to physics, chemistry, biology, electrical, civil, mechanical, chemical, seismology, aerospace, and medical sciences. The aim of the conference is to bring together leading academicians, scientists, researchers, engineers, and industry partners from all over the globe to exchange and share their experiences and research results on various aspects of applied mathematics and scientific computation, like, differential equation, modeling, simulation, dynamical systems, numerical analysis, matrix theory, inverse problems, and solid and fluid mechanics, computational engineering.
Mathematical Modelling, Applied Analysis and Computation: ICMMAAC 2018, Jaipur, India, July 6-8 (Springer Proceedings in Mathematics & Statistics #272)
by Jagdev Singh Devendra Kumar Hemen Dutta Dumitru Baleanu Sunil Dutt PurohitThis book contains original research papers presented at the International Conference on Mathematical Modelling, Applied Analysis and Computation, held at JECRC University, Jaipur, India, on 6-8 July, 2018. Organized into 20 chapters, the book focuses on theoretical and applied aspects of various types of mathematical modelling such as equations of various types, fuzzy mathematical models, automata, Petri nets and bond graphs for systems of dynamic nature and the usage of numerical techniques in handling modern problems of science, engineering and finance. It covers the applications of mathematical modelling in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science and finance. A wide variety of dynamical systems like deterministic, stochastic, continuous, discrete or hybrid, with respect to time, are discussed in the book. It provides the mathematical modelling of various problems arising in science and engineering, and also new efficient numerical approaches for solving linear and nonlinear problems and rigorous mathematical theories, which can be used to analyze a different kind of mathematical models. The conference was aimed at fostering cooperation among students and researchers in areas of applied analysis, engineering and computation with the deliberations to inculcate new research ideas in their relevant fields. This volume will provide a comprehensive introduction to recent theories and applications of mathematical modelling and numerical simulation, which will be a valuable resource for graduate students and researchers of mathematical modelling and industrial mathematics.
Mathematical Modelling Education and Sense-making (International Perspectives on the Teaching and Learning of Mathematical Modelling)
by Gabriele Kaiser Gloria Ann Stillman Christine Erna LampenThis volume documents on-going research and theorising in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in people’s everyday lives as well as sophisticated new problems for society at large. Mathematical modelling and real world applications are considered as having potential for cultivating sense making in classroom settings. This book focuses on the educational perspective, researching the complexities encountered in effective teaching and learning of real world modelling and applications for sense making is only beginning. All authors of this volume are members of the International Community of Teachers of Mathematical Modelling (ICTMA), the peak research body into researching the teaching and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace.
Mathematical Modelling Education in East and West (International Perspectives on the Teaching and Learning of Mathematical Modelling)
by Gabriele Kaiser Gloria Ann Stillman Frederick Koon Shing Leung Ka Lok WongThis book documents ongoing research and theorizing in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in people’s everyday lives as well as sophisticated new problems for society at large. Mathematical tradition in China that emphasizes algorithm and computation has now seen a renaissance in mathematical modelling and applications where China has made significant progress with its economy, science and technology. In recent decades, teaching and learning of mathematical modelling as well as contests in mathematical modelling have been flourishing at different levels of education in China. Today, teachers and researchers in China become keener to learn from their colleagues from Western countries and other parts of the world in research and teaching of mathematical modelling and applications. The book provides a dialogue and communication between colleagues from across the globe with new impetus and resources for mathematical modelling education and its research in both West and East with new ideas on modelling teaching and practices, inside and outside classrooms.All authors of this book are members of the International Community of Teachers of Mathematical Modelling and Applications (ICTMA), the peak research body into researching the teaching, assessing and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace. The book is of interest to researchers, mathematics educators, teacher educators, education administrators, policy writers, curriculum developers, professional developers, in-service teachers and pre-service teachers including those interested in mathematical literacy.
Mathematical Modelling for Next-Generation Cryptography
by Tsuyoshi Takagi Masato Wakayama Keisuke Tanaka Noboru Kunihiro Kazufumi Kimoto Dung Hoang DuongThis book presents the mathematical background underlying security modeling in the context of next-generation cryptography. By introducing new mathematical results in order to strengthen information security, while simultaneously presenting fresh insights and developing the respective areas of mathematics, it is the first-ever book to focus on areas that have not yet been fully exploited for cryptographic applications such as representation theory and mathematical physics, among others. Recent advances in cryptanalysis, brought about in particular by quantum computation and physical attacks on cryptographic devices, such as side-channel analysis or power analysis, have revealed the growing security risks for state-of-the-art cryptographic schemes. To address these risks, high-performance, next-generation cryptosystems must be studied, which requires the further development of the mathematical background of modern cryptography. More specifically, in order to avoid the security risks posed by adversaries with advanced attack capabilities, cryptosystems must be upgraded, which in turn relies on a wide range of mathematical theories. This book is suitable for use in an advanced graduate course in mathematical cryptography, while also offering a valuable reference guide for experts.
Mathematical Modelling for Teachers: Resources, Pedagogy and Practice
by Keng Cheng AngMathematical Modelling for Teachers: Resources, Pedagogy and Practice provides everything that teachers and mathematics educators need to design and implement mathematical modelling activities in their classroom. Authored by an expert in Singapore, the global leader in mathematics education, it is written with an international readership in mind. <P><P>This book focuses on practical classroom ideas in mathematical modelling suitable to be used by mathematics teachers at the secondary level. As they are interacting with students all the time, teachers generally have good ideas for possible mathematical modelling tasks. However, many have difficulty translating those ideas into concrete modelling activities suitable for a mathematics classroom. In this book, a framework is introduced to assist teachers in designing, planning and implementing mathematical modelling activities, and its use is illustrated through the many examples included. Readers will have access to modelling activities suitable for students from lower secondary levels (Years 7 and 8) onwards, along with the underlying framework, guiding notes for teachers and suggested approaches to solve the problems. The activities are grouped according to the types of models constructed: empirical, deterministic and simulation models. Finally, the book gives the reader suggestions of different ways to assess mathematical modelling competencies in students.
Mathematical Modelling in Education Research and Practice
by Gloria Ann Stillman Werner Blum Maria Salett BiembengutIn this volume cultural, social and cognitive influences on the research and teaching of mathematical modelling are explored from a variety of theoretical and practical perspectives. The authors of the current volume are all members of the International Community of Teachers of Mathematical Modelling and Applications, the peak research body in this field. A distinctive feature of this volume is the high number of authors from South American countries. These authors bring quite a different perspective to modelling than has been showcased in previous books in this series, in particular from a cultural point of view. As well as recent international research, there is a strong emphasis on pedagogical issues including those associated with technology and assessment, in the teaching and learning of modelling. Applications at various levels of education are exemplified. The contributions reflect common issues shared globally and represent emergent or on-going challenges.
Mathematical Modelling in Health, Social and Applied Sciences (Forum for Interdisciplinary Mathematics)
by Hemen DuttaThis book discusses significant research findings in the field of mathematical modelling, with particular emphasis on important applied-sciences, health, and social issues. It includes topics such as model on viral immunology, stochastic models for the dynamics of influenza, model describing the transmission of dengue, model for human papillomavirus (HPV) infection, prostate cancer model, realization of economic growth by goal programming, modelling of grazing periodic solutions in discontinuous systems, modelling of predation system, fractional epidemiological model for computer viruses, and nonlinear ecological models. A unique addition in the proposed areas of research and education, this book is a valuable resource for graduate students, researchers and educators associated with the study of mathematical modelling of health, social and applied-sciences issues. Readers interested in applied mathematics should also find this book valuable.
Mathematical Modelling in One Dimension
by Jacek BanasiakMathematical Modelling in One Dimension demonstrates the universality of mathematical techniques through a wide variety of applications. Learn how the same mathematical idea governs loan repayments, drug accumulation in tissues or growth of a population, or how the same argument can be used to find the trajectory of a dog pursuing a hare, the trajectory of a self-guided missile or the shape of a satellite dish. The author places equal importance on difference and differential equations, showing how they complement and intertwine in describing natural phenomena.
Mathematical Modelling in Plant Biology
by Richard J. MorrisProgress in plant biology relies on the quantification, analysis and mathematical modeling of data over different time and length scales. This book describes common mathematical and computational approaches as well as some carefully chosen case studies that demonstrate the use of these techniques to solve problems at the forefront of plant biology. Each chapter is written by an expert in field with the goal of conveying concepts whilst at the same time providing sufficient background and links to available software for readers to rapidly build their own models and run their own simulations. This book is aimed at postgraduate students and researchers working the field of plant systems biology and synthetic biology, but will also be a useful reference for anyone wanting to get into quantitative plant biology.
Mathematical Modelling in Real Life Problems: Case Studies from ECMI-Modelling Weeks (Mathematics in Industry #33)
by Ewald Lindner Alessandra Micheletti Cláudia NunesThis book is intended to be a useful contribution for the modern teaching of applied mathematics, educating Industrial Mathematicians that will meet the growing demand for such experts. It covers many applications where mathematics play a fundamental role, from biology, telecommunications, medicine, physics, finance and industry. It is presented in such a way that can be useful in Modelation, Simulation and Optimization courses, targeting master and PhD students. Its content is based on many editions from the successful series of Modelling Weeks organized by the European Consortium of Mathematics in Industry (ECMI). Each chapter addresses a particular problem, and is written in a didactic way, providing the description of the problem, the particular way of approaching it and the proposed solution, along with the results obtained.
Mathematical Modelling, Nonlinear Control and Performance Evaluation of a Ground Based Mobile Air Defence System (Mechanisms and Machine Science #76)
by Constantinos FrangosIn this book, the author deals with the mathematical modelling, nonlinear control and performance evaluation of a conceptual anti-aircraft gun based mobile air defence system engaging an attacking three-dimensional aerial target.This book is of interest to academic faculty, graduate students and industry professionals working in the fields of mathematical modelling and control, ground vehicles, mobile air defence systems and other related topics.
Mathematical Modelling of Chromosome Replication and Replicative Stress
by Jens KarschauDNA replication is arguably the most crucial process at work in living cells. It is the mechanism by which organisms pass their genetic information from one generation to the next and life on Earth would be unthinkable without it. Despite the discovery of DNA structure in the 1950s, the mechanism of its replication remains rather elusive. This work makes important contributions to this line of research. In particular, it addresses two key questions in the area of DNA replication: which evolutionary forces drive the positioning of replication origins in the chromosome and how is the spatial organization of replication factories achieved inside the nucleus of a cell?. A cross-disciplinary approach uniting physics and biology is at the heart of this research. Along with experimental support, statistical physics theory produces optimal origin positions and provides a model for replication fork assembly in yeast. Advances made here can potentially further our understanding of disease mechanisms such as the abnormal replication in cancer.
Mathematical Modelling of Fluid Dynamics and Nanofluids
by Katta Ramesh Fateh Mebarek-Oudina Basma SouayehMathematical Modelling of Fluid Dynamics and Nanofluids serves as a comprehensive resource for various aspects of fluid dynamics simulations, nanofluid preparation, and numerical techniques.The book examines the practical implications and real-world applications of various concepts, including nanofluids, magnetohydrodynamics, heat and mass transfer, and radiation. By encompassing these diverse domains, it offers readers a broad perspective on the interconnectedness of these fields.The primary audience for this book includes researchers and graduate students who possess a keen interest in interdisciplinary studies within the realms of fluid dynamics, nanofluids, and biofluids. Its content caters to those who wish to deepen their knowledge and tackle complex problems at the intersection of these disciplines.
Mathematical Modelling of Haemodialysis: Cardiovascular Response, Body Fluid Shifts, and Solute Kinetics
by Leszek Pstras Jacek WaniewskiBeginning with an introduction to kidney function, renal replacement therapies, and an overview of clinical problems associated with haemodialysis, this book explores the principles of the short-term baroreflex regulation of the cardiovascular system and the mechanisms of water and solute transport across the human body from a mathematical model perspective. It synthesizes theoretical physiological concepts and practical aspects of mathematical modelling needed for simulation and quantitative analysis of the haemodynamic response to dialysis therapy.Including an up-to-date review of the literature concerning the modelled physiological mechanisms and processes, the book serves both as an overview of transport and regulatory mechanisms related to the cardiovascular system and body fluids and as a useful reference for the study and development of mathematical models of dynamic physiological processes.Mathematical Modelling of Haemodialysis: Cardiovascular Response, Body Fluid Shifts, and Solute Kinetics is intended for researchers and graduate students in biomedical engineering, physiology, or medicine interested in mathematical modelling of cardiovascular dynamics and fluid and solute transport across the human body, both under physiological conditions and during haemodialysis therapy.
Mathematical Modelling of Solids with Nonregular Boundaries (Mathematical Modeling Ser. #3)
by A.B. Movchan N.V. MovchanMathematical Modelling of Solids with Nonregular Boundaries demonstrates the use of asymptotic methods and other analytical techniques for investigating problems in solid mechanics. Applications to solids with nonregular boundaries are described in detail, providing precise and rigorous treatment of current methods and techniques. The book addresses problems in fracture mechanics of inhomogeneous media and illustrates applications in strength analysis and in geophysics. The rigorous approach allows the reader to explicitly analyze the stress-strain state in continuous media with cavities or inclusions, in composite materials with small defects, and in elastic solids with sharp inclusions. Effective asymptotic procedures for eigenvalue problems in domains with small defects are clearly outlined, and methods for analyzing singularly perturbed boundary value problems are examined.Introductory material is provided in the first chapter of Mathematical Modelling of Solids with Nonregular Boundaries, which presents a survey of relevant and necessary information, including equations of linear elasticity and formulations of the boundary value problems. Background information - in the form of definitions and general solutions - is also provided on elasticity problems in various bounded and unbounded domains. This book is an excellent resource for students, applied scientists, and engineers.
Mathematical Modelling of the Human Cardiovascular System: Data, Numerical Approximation, Clinical Applications (Cambridge Monographs on Applied and Computational Mathematics #33)
by Alfio Quarteroni Luca Dede' Andrea Manzoni Christian VergaraMathematical and numerical modelling of the human cardiovascular system has attracted remarkable research interest due to its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. This book addresses the two principal components of the cardiovascular system: arterial circulation and heart function. It systematically describes all aspects of the problem, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, reviewing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiovascular system and the need for computational methods that are stable, reliable and efficient. The final part is devoted to control and inverse problems, including parameter estimation, uncertainty quantification and the development of reduced-order models that are important when solving problems with high complexity, which would otherwise be out of reach.
Mathematical Modelling of Waves in Multi-Scale Structured Media (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by Alexander B. Movchan Natasha V. Movchan Ian S. Jones Daniel J. ColquittMathematical Modelling of Waves in Multi-Scale Structured Media presents novel analytical and numerical models of waves in structured elastic media, with emphasis on the asymptotic analysis of phenomena such as dynamic anisotropy, localisation, filtering and polarisation as well as on the modelling of photonic, phononic, and platonic crystals.