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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!

Dialogues Around Models And Uncertainty: An Interdisciplinary Perspective

Dialogues Around Models And Uncertainty: An Interdisciplinary Perspective

Author: Pauline (The London Sch Of Economics & Political Science, Uk) Barrieu Format: Hardback Release Date: 12/03/2020

This book helps develop a better understanding of how researchers from different scientific backgrounds view models and uncertainty. It provides key steps in fostering and encouraging interdisciplinary research, which is vital in addressing several big issues that society faces today, such as climate change, longevity, financial and actuarial risk management. To make progress in these areas, researchers must develop an understanding of differing perspectives and methods of those working in other disciplines.This title presents the views and understandings of eminent people in their respective fields through interviews on the topic of modelling and uncertainty. Each expert was asked the same set of questions to help readers understand the similarities and differences existing between various disciplines. It also helps to bridge some of the gaps encountered by those carrying out inter- and multi-disciplinary research and suggests new approaches to modelling and uncertainty quantification.

Quantitative Reasoning Thinking in Numbers

Quantitative Reasoning Thinking in Numbers

Author: Eric (Northwestern University, Illinois) Zaslow Format: Hardback Release Date: 31/01/2020

Is college worth the cost? Should I worry about arsenic in my rice? Can we recycle pollution? Real questions of personal finance, public health, and social policy require sober, data-driven analyses. This unique text provides students with the tools of quantitative reasoning to answer such questions. The text models how to clarify the question, recognize and avoid bias, isolate relevant factors, gather data, and construct numerical analyzes for interpretation. Themes and techniques are repeated across chapters, with a progression in mathematical sophistication over the course of the book, which helps the student get comfortable with the process of thinking in numbers. This textbook includes references to source materials and suggested further reading, making it user-friendly for motivated undergraduate students. The many detailed problems and worked solutions in the text and extensive appendices help the reader learn mathematical areas such as algebra, functions, graphs, and probability. End-of-chapter problem material provides practice for students, and suggested projects are provided with each chapter. A solutions manual is available online for instructors.

Quantitative Reasoning Thinking in Numbers

Quantitative Reasoning Thinking in Numbers

Author: Eric (Northwestern University, Illinois) Zaslow Format: Paperback / softback Release Date: 31/01/2020

Is college worth the cost? Should I worry about arsenic in my rice? Can we recycle pollution? Real questions of personal finance, public health, and social policy require sober, data-driven analyses. This unique text provides students with the tools of quantitative reasoning to answer such questions. The text models how to clarify the question, recognize and avoid bias, isolate relevant factors, gather data, and construct numerical analyzes for interpretation. Themes and techniques are repeated across chapters, with a progression in mathematical sophistication over the course of the book, which helps the student get comfortable with the process of thinking in numbers. This textbook includes references to source materials and suggested further reading, making it user-friendly for motivated undergraduate students. The many detailed problems and worked solutions in the text and extensive appendices help the reader learn mathematical areas such as algebra, functions, graphs, and probability. End-of-chapter problem material provides practice for students, and suggested projects are provided with each chapter. A solutions manual is available online for instructors.

Advanced Problem Solving Using Maple Applied Mathematics, Operations Research, Business Analytics, and Decision Analysis

Advanced Problem Solving Using Maple Applied Mathematics, Operations Research, Business Analytics, and Decision Analysis

Author: William P (U.S. Naval Post Graduate School) Fox, William C. Bauldry Format: Hardback Release Date: 21/01/2020

The text applies the mathematical modeling process by formulating, building, solving, analyzing, and criticizing mathematical models. Scenarios are developed within the scope of the problem solving process. The text focuses on discrete dynamical systems, optimization techniques, single-variable unconstrained optimization and applied problems, and numerical search methods. Additional coverage includes multivariable unconstrained and constrained techniques. Linear algebra techniques to model and solve problems such as the Leontief model, advanced regression technique include nonlinear, logistics and Poisson are covered. Game Theory, the Nash equilibrium, Nash arbitration are also included.

Modeling Anomalous Diffusion: From Statistics To Mathematics

Modeling Anomalous Diffusion: From Statistics To Mathematics

This book focuses on modeling the anomalous diffusion phenomena, being ubiquitous in the natural world. Both the microscopic models (stochastic processes) and macroscopic models (partial differential equations) have been built up. The relationships between the two kinds of models are clarified, and based on these models, some statistical observables are analyzed. From statistics to mathematics, the built models show their power with their associated applications.This book is important for students to develop basic skills to be able to succeed in their future research. In addition to introducing the related models or methods, it also provides the corresponding applications and simulation results, which will attract more readers ranging from mathematicians to physicists or chemists, to name a few.

Stochastic Modelling of Reaction-Diffusion Processes

Stochastic Modelling of Reaction-Diffusion Processes

Author: Radek (University of Oxford) Erban, S. Jonathan (University of Oxford) Chapman Format: Paperback / softback Release Date: 31/12/2019

This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.

Stochastic Modelling of Reaction-Diffusion Processes

Stochastic Modelling of Reaction-Diffusion Processes

Author: Radek (University of Oxford) Erban, S. Jonathan (University of Oxford) Chapman Format: Hardback Release Date: 31/12/2019

This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.

The Cahn-Hilliard Equation Recent Advances and Applications

The Cahn-Hilliard Equation Recent Advances and Applications

Author: Alain Miranville Format: Paperback / softback Release Date: 30/12/2019

This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn-Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn-Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn-Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn?Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.

Uncertainty Quantification: Theory, Implementation, and Applications

Uncertainty Quantification: Theory, Implementation, and Applications

Author: Ralph (North Carolina State University) Smith Format: Hardback Release Date: 11/12/2019

The need to quantify and characterise uncertainties arising in mathematical models with unknown parameters leads to the rapidly evolving field of uncertainty quantification. This book provides readers with the concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models. It covers concepts from probability and statistics such as parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, and sensitivity analysis. The book goes on to explore applications and open problems from a wide array of disciplines, particularly those such as climate science, hydrology, and nuclear power where uncertainty quantification is crucial for both scientific understanding and public policy. An accompanying web page provides data used in the exercises and other supplementary material. The text is intended as a coursebook for advanced undergraduates and above, and as a resource for researchers in mathematics, statistics, operations research, science, and engineering.

Classics in Applied Mathematics Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow

Classics in Applied Mathematics Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow

Author: Richard Haberman Format: Paperback / softback Release Date: 09/12/2019

Mathematics is a grand subject in the way it can be applied to various problems in science and engineering. To use mathematics, one needs to understand the physical context. The author uses mathematical techniques along with observations and experiments to give an in-depth look at models for mechanical vibrations, population dynamics, and traffic flow. Equal emphasis is placed on the mathematical formulation of the problem and the interpretation of the results. In the sections on mechanical vibrations and population dynamics, the author emphasizes the nonlinear aspects of ordinary differential equations and develops the concepts of equilibrium solutions and their stability. He introduces phase plane methods for the nonlinear pendulum and for predator-prey and competing species models.

Studies in Applied and Numerical Mathematics Solitons and the Inverse Scattering Transform

Studies in Applied and Numerical Mathematics Solitons and the Inverse Scattering Transform

Author: Mark J. Ablowitz, Harvey Segur Format: Paperback / softback Release Date: 06/12/2019

A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.

The Water Waves Problem Mathematical Analysis and Asymptotics

The Water Waves Problem Mathematical Analysis and Asymptotics

Author: David Lannes Format: Hardback Release Date: 06/12/2019

This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models. Which model provides the best description of waves such as tsunamis or tidal waves? How can water waves equations be transformed into simpler asymptotic models for applications in, for example, coastal oceanography? This book proposes a simple and robust framework for studying these questions. The book should be of interest to graduate students and researchers looking for an introduction to water waves equations or for simple asymptotic models to describe the propagation of waves. Researchers working on the mathematical analysis of nonlinear dispersive equations may also find inspiration in the many (and sometimes new) models derived here, as well as precise information on their physical relevance.