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Mathematical modelling

See below for a selection of the latest books from Mathematical modelling category. Presented with a red border are the Mathematical modelling books that have been lovingly read and reviewed by the experts at Lovereading. With expert reading recommendations made by people with a passion for books and some unique features Lovereading will help you find great Mathematical modelling books and those from many more genres to read that will keep you inspired and entertained. And it's all free!

Advanced Problem Solving with Maple A First Course

Advanced Problem Solving with Maple A First Course

Author: William P. Fox, William Bauldry Format: Hardback Release Date: 01/08/2019

Problem Solving is essential to solve real-world problems. The text applies the mathematical modeling process by formulating, building, solving, analyzing, and criticizing mathematical models. It is intended for a course introducing students to mathematical topics they will revisit within their further studies. The authors present mathematical modeling topics using Maple as the computer algebra system for solving mathematical equations as well as obtaining plots that help us perform our analyses. The book presents cogent applications demonstrate an effective use of a Maple, provide discussions of the results obtained using Maple, and stimulate thought and analysis of additional applications.

Topics In Biomathematics

Topics In Biomathematics

Author: J. C. Misra Format: Hardback Release Date: 31/07/2019

This book focuses on the integration of mathematical models dealing with the dynamics of the cardiovascular system. The author uses a step-by-step approach to describe different components of the cardiovascular system and provides a variety of information about the dynamical behavior of the cardiovascular system with appropriate diagrams. Various mathematical models for modeling the vascular dynamics of wall tissues, the circulatory system and the flow dynamics of blood in normal as well as pathological states are presented in a systematic manner. This unique work explains technical aspects of the techniques in simple language that is appropriate for novice researchers and scientists. The book bears the potential to suggest further lines of both experimental and theoretical studies.

Modeling with Differential Equations

Modeling with Differential Equations

Author: Vladimir A. Dobrushkin Format: Hardback Release Date: 22/07/2019

Modeling with Differential Equations is an innovative text that bridges the gap between ordinary differential equations and their applications in various areas. It provides a comprehensive introduction from the viewpoint of applied mathematics by engaging readers with real-life problems and scenarios. Readers are shown how to formulate a mathematical model, solve the differential equation, and interpret the result. This sequence of steps is one of the hardest to learn, yet an essential skill to acquire. The book allows students to progress from elementary to more advanced material.

Models for Tropical Climate Dynamics Waves, Clouds, and Precipitation

Models for Tropical Climate Dynamics Waves, Clouds, and Precipitation

Author: Boualem Khouider Format: Hardback Release Date: 20/07/2019

This book is a survey of the research work done by the author over the last 15 years, in collaboration with various eminent mathematicians and climate scientists on the subject of tropical convection and convectively coupled waves. In the areas of climate modelling and climate change science, tropical dynamics and tropical rainfall are among the biggest uncertainties of future projections. This not only puts at risk billions of human beings who populate the tropical continents but it is also of central importance for climate predictions on the global scale. This book aims to introduce the non-expert readers in mathematics and theoretical physics to this fascinating topic in order to attract interest into this difficult and exciting research area. The general thyme revolves around the use of new deterministic and stochastic multi-cloud models for tropical convection and convectively coupled waves. It draws modelling ideas from various areas of mathematics and physics and used in conjunction with state-of-the-art satellite and in-situ observations and detailed numerical simulations. After a review of preliminary material on tropical dynamics and moist thermodynamics, including recent discoveries based on satellite observations as well as Markov chains, the book immerses the reader into the area of models for convection and tropical waves. It begins with basic concepts of linear stability analysis and ends with the use of these models to improve the state-of-the-art global climate models. The book also contains a fair amount of exercises that makes it suitable as a textbook complement on the subject.

Mathematical Modeling of Unsteady Inviscid Flows

Mathematical Modeling of Unsteady Inviscid Flows

Author: Jeff D. Eldredge Format: Hardback Release Date: 18/07/2019

This book builds inviscid flow analysis from an undergraduate-level treatment of potential flow to the level required for research. The tools covered in this book allow the reader to develop physics-based mathematical models for a variety of flows, including attached and separated flows past wings, fins, and blades of various shapes undergoing arbitrary motions. The book covers all of the ingredients of these models: the solution of potential flows about arbitrary body shapes in two- and three-dimensional contexts, with a particular focus on conformal mapping in the plane; the decomposition of the flow into contributions from ambient vorticity and body motion; generalized edge conditions, of which the Kutta condition is a special case; and the calculation of force and moment, with extensive treatments of added mass and the influence of fluid vorticity. The book also contains an extensive primer with all of the necessary mathematical tools. The concepts are demonstrated on several example problems, both classical and modern.

Shapes and Diffeomorphisms

Shapes and Diffeomorphisms

Author: Laurent Younes Format: Hardback Release Date: 15/05/2019

This book covers mathematical foundations and methods for the computerized analysis of shapes, providing the requisite background in geometry and functional analysis and introducing various algorithms and approaches to shape modeling, with a special focus on the interesting connections between shapes and their transformations by diffeomorphisms. A direct application is to computational anatomy, for which techniques such as large-deformation diffeomorphic metric mapping and metamorphosis, among others, are presented. The appendices detail a series of classical topics (Hilbert spaces, differential equations, Riemannian manifolds, optimal control). The intended audience is applied mathematicians and mathematically inclined engineers interested in the topic of shape analysis and its possible applications in computer vision or medical imaging. The first part can be used for an advanced undergraduate course on differential geometry with a focus on applications while the later chapters are suitable for a graduate course on shape analysis through the action of diffeomorphisms. Several significant additions appear in the 2nd edition, most notably a new chapter on shape datasets, and a discussion of optimal control theory in an infinite-dimensional framework, which is then used to enrich the presentation of diffeomorphic matching.

Computational Methods for Approximation of Large-Scale Dynamical Systems

Computational Methods for Approximation of Large-Scale Dynamical Systems

Author: Mohammad Monir Uddin Format: Hardback Release Date: 09/05/2019

These days, computer-based simulation is considered the quintessential approach to exploring new ideas in the different disciplines of science, engineering and technology (SET). To perform simulations, a physical system needs to be modeled using mathematics; these models are often represented by linear time-invariant (LTI) continuous-time (CT) systems. Oftentimes these systems are subject to additional algebraic constraints, leading to first- or second-order differential-algebraic equations (DAEs), otherwise known as descriptor systems. Such large-scale systems generally lead to massive memory requirements and enormous computational complexity, thus restricting frequent simulations, which are required by many applications. To resolve these complexities, the higher-dimensional system may be approximated by a substantially lower-dimensional one through model order reduction (MOR) techniques. Computational Methods for Approximation of Large-Scale Dynamical Systems discusses computational techniques for the MOR of large-scale sparse LTI CT systems. Although the book puts emphasis on the MOR of descriptor systems, it begins by showing and comparing the various MOR techniques for standard systems. The book also discusses the low-rank alternating direction implicit (LR-ADI) iteration and the issues related to solving the Lyapunov equation of large-scale sparse LTI systems to compute the low-rank Gramian factors, which are important components for implementing the Gramian-based MOR. Although this book is primarly aimed at post-graduate students and researchers of the various SET disciplines, the basic contents of this book can be supplemental to the advanced bachelor's-level students as well. It can also serve as an invaluable reference to researchers working in academics and industries alike. Features: Provides an up-to-date, step-by-step guide for its readers. Each chapter develops theories and provides necessary algorithms, worked examples, numerical experiments and related exercises. With the combination of this book and its supplementary materials, the reader gains a sound understanding of the topic. The MATLAB (R) codes for some selected algorithms are provided in the book. The solutions to the exercise problems, experiment data sets and a digital copy of the software are provided on the book's website; The numerical experiments use real-world data sets obtained from industries and research institutes.

An Invitation to Model Theory

An Invitation to Model Theory

Author: Jonathan (University of East Anglia) Kirby Format: Paperback / softback Release Date: 30/04/2019

Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.

An Invitation to Model Theory

An Invitation to Model Theory

Author: Jonathan (University of East Anglia) Kirby Format: Hardback Release Date: 30/04/2019

Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.

Cambridge Monographs on Applied and Computational Mathematics Mathematical Modelling of the Human Cardiovascular System: Data, Numerical Approximation, Clinical Applications

Cambridge Monographs on Applied and Computational Mathematics Mathematical Modelling of the Human Cardiovascular System: Data, Numerical Approximation, Clinical Applications

Mathematical 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 System Resilience

Mathematical Modelling of System Resilience

Almost all the systems in our world, including technical, social, economic, and environmental systems, are becoming interconnected and increasingly complex, and as such they are vulnerable to various risks. Due to this trend, resilience creation is becoming more important to system managers and decision makers, this to ensure sustained performance. In order to be able to ensure an acceptable sustained performance under such interconnectedness and complexity, resilience creation with a system approach is a requirement. Mathematical modeling based approaches are the most common approach for system resilience creation. Mathematical Modelling of System Resilience covers resilience creation for various system aspects including a functional system of the supply chain, overall supply chain systems; various methodologies for modeling system resilience; satellite-based approach for addressing climate related risks, repair-based approach for sustainable performance of an engineering system, and modeling measures of the reliability for a vertical take-off and landing system. Each of the chapters contributes state of the art research for the relevant resilience related topic covered in the chapter. Technical topics covered in the book include: 1. Supply chain risk, vulnerability and disruptions 2. System resilience for containing failures and disruptions 3. Resiliency considering frequency and intensities of disasters 4. Resilience performance index 5. Resiliency of electric Traction system 6. Degree of resilience 7. Satellite observation and hydrological risk 8. Latitude of Resilience 9. On-line repair for resilience 10. Reliability design for Vertical Takeoff and landing Prototype

Nonlocal Modeling, Analysis, and Computation

Nonlocal Modeling, Analysis, and Computation

Author: Qiang Du Format: Paperback / softback Release Date: 30/04/2019

Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to traditional local systems represented by partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives to as well as bridges to existing local continuum and discrete models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on existing discrete models and local continuum models and the connections between them.