Methods Of Mathematical Modelling

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Methods of Mathematical Modelling

Thomas Witelski,Mark Bowen
Methods of Mathematical Modelling Book PDF

Author : Thomas Witelski,Mark Bowen
Publisher : Springer
Page : 305 pages
File Size : 51,9 Mb
Release : 2015-09-18
Category : Mathematics
ISBN : 9783319230429

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Methods of Mathematical Modelling by Thomas Witelski,Mark Bowen Pdf

This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

Methods of Mathematical Modelling

Harendra Singh,Devendra Kumar,Dumitru Baleanu
Methods of Mathematical Modelling Book PDF

Author : Harendra Singh,Devendra Kumar,Dumitru Baleanu
Publisher : CRC Press
Page : 255 pages
File Size : 55,7 Mb
Release : 2019-09-17
Category : Mathematics
ISBN : 9781000596786

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Methods of Mathematical Modelling by Harendra Singh,Devendra Kumar,Dumitru Baleanu Pdf

This book features original research articles on the topic of mathematical modelling and fractional differential equations. The contributions, written by leading researchers in the field, consist of chapters on classical and modern dynamical systems modelled by fractional differential equations in physics, engineering, signal processing, fluid mechanics, and bioengineering, manufacturing, systems engineering, and project management. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate level students, educators, researchers, and scientists interested in mathematical modelling and its diverse applications. Features Presents several recent developments in the theory and applications of fractional calculus Includes chapters on different analytical and numerical methods dedicated to several mathematical equations Develops methods for the mathematical models which are governed by fractional differential equations Provides methods for models in physics, engineering, signal processing, fluid mechanics, and bioengineering Discusses real-world problems, theory, and applications

Methods of Mathematical Modelling and Computation for Complex Systems

Jagdev Singh,Hemen Dutta,Devendra Kumar,Dumitru Baleanu,Jordan Hristov
Methods of Mathematical Modelling and Computation for Complex Systems Book PDF

Author : Jagdev Singh,Hemen Dutta,Devendra Kumar,Dumitru Baleanu,Jordan Hristov
Publisher : Springer Nature
Page : 433 pages
File Size : 54,6 Mb
Release : 2021-08-26
Category : Technology & Engineering
ISBN : 9783030771690

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Methods of Mathematical Modelling and Computation for Complex Systems by Jagdev Singh,Hemen Dutta,Devendra Kumar,Dumitru Baleanu,Jordan Hristov Pdf

This book contains several contemporary topics in the areas of mathematical modelling and computation for complex systems. The readers find several new mathematical methods, mathematical models and computational techniques having significant relevance in studying various complex systems. The chapters aim to enrich the understanding of topics presented by carefully discussing the associated problems and issues, possible solutions and their applications or relevance in other scientific areas of study and research. The book is a valuable resource for graduate students, researchers and educators in understanding and studying various new aspects associated with complex systems. Key Feature • The chapters include theory and application in a mix and balanced way. • Readers find reasonable details of developments concerning a topic included in this book. • The text is emphasized to present in self-contained manner with inclusion of new research problems and questions.

Mathematical Modelling Techniques

Rutherford Aris
Mathematical Modelling Techniques Book PDF

Author : Rutherford Aris
Publisher : Courier Corporation
Page : 290 pages
File Size : 45,6 Mb
Release : 2012-06-29
Category : Mathematics
ISBN : 9780486138893

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Mathematical Modelling Techniques by Rutherford Aris Pdf

"Engaging, elegantly written." — Applied Mathematical Modelling Mathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models. The author begins with a discussion of the term "model," followed by clearly presented examples of the different types of models (finite, statistical, stochastic, etc.). He then goes on to discuss the formulation of a model and how to manipulate it into its most responsive form. Along the way Dr. Aris develops a delightful list of useful maxims for would-be modellers. In the final chapter he deals not only with the empirical validation of models but also with the comparison of models among themselves, as well as with the extension of a model beyond its original "domain of validity." Filled with numerous examples, this book includes three appendices offering further examples treated in more detail. These concern longitudinal diffusion in a packed bed, the coated tube chromatograph with Taylor diffusion and the stirred tank reactor. Six journal articles, a useful list of references and subject and name indexes complete this indispensable, well-written guide. "A most useful, readable-and stimulating-book, to be read both for pleasure and for enlightenment." — Bulletin of the Institute of Mathematics and Its Applications

An Introduction to Mathematical Modeling

Edward A. Bender
An Introduction to Mathematical Modeling Book PDF

Author : Edward A. Bender
Publisher : Courier Corporation
Page : 273 pages
File Size : 49,6 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486137124

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An Introduction to Mathematical Modeling by Edward A. Bender Pdf

Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.

Methods and Models in Mathematical Programming

S. A. MirHassani,F. Hooshmand
Methods and Models in Mathematical Programming Book PDF

Author : S. A. MirHassani,F. Hooshmand
Publisher : Springer Nature
Page : 389 pages
File Size : 52,5 Mb
Release : 2019-12-09
Category : Mathematics
ISBN : 9783030270452

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Methods and Models in Mathematical Programming by S. A. MirHassani,F. Hooshmand Pdf

This book focuses on mathematical modeling, describes the process of constructing and evaluating models, discusses the challenges and delicacies of the modeling process, and explicitly outlines the required rules and regulations so that the reader will be able to generalize and reuse concepts in other problems by relying on mathematical logic.Undergraduate and postgraduate students of different academic disciplines would find this book a suitable option preparing them for jobs and research fields requiring modeling techniques. Furthermore, this book can be used as a reference book for experts and practitioners requiring advanced skills of model building in their jobs.

Principles of Mathematical Modelling

Alexander A. Samarskii,Alexander P. Mikhailov
Principles of Mathematical Modelling Book PDF

Author : Alexander A. Samarskii,Alexander P. Mikhailov
Publisher : CRC Press
Page : 368 pages
File Size : 46,9 Mb
Release : 2001-12-20
Category : Mathematics
ISBN : 0415272807

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Principles of Mathematical Modelling by Alexander A. Samarskii,Alexander P. Mikhailov Pdf

Mathematical modeling is becoming increasingly versatile and multi-disciplinary. This text demonstrates the broadness of this field as the authors consider the principles of model construction and use common approaches to build models from a range of subject areas. The book reflects the interests and experiences of the authors, but it explores mathematical modeling across a wide range of applications, from mechanics to social science. A general approach is adopted, where ideas and examples are favored over rigorous mathematical procedures. This insightful book will be of interest to specialists, teachers, and students across a wide range of disciplines..

Mathematical Modelling

Seppo Pohjolainen,Matti Heiliö,Timo Lähivaara,Erkki Laitinen,Timo Mantere,Jorma Merikoski,Kimmo Raivio,Risto Silvennoinen,Antti Suutala,Tanja Tarvainen,Timo Tiihonen,Jukka Tuomela,Esko Turunen,Marko Vauhkonen
Mathematical Modelling Book PDF

Author : Seppo Pohjolainen,Matti Heiliö,Timo Lähivaara,Erkki Laitinen,Timo Mantere,Jorma Merikoski,Kimmo Raivio,Risto Silvennoinen,Antti Suutala,Tanja Tarvainen,Timo Tiihonen,Jukka Tuomela,Esko Turunen,Marko Vauhkonen
Publisher : Springer
Page : 242 pages
File Size : 53,5 Mb
Release : 2016-07-14
Category : Mathematics
ISBN : 9783319278360

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Mathematical Modelling by Seppo Pohjolainen,Matti Heiliö,Timo Lähivaara,Erkki Laitinen,Timo Mantere,Jorma Merikoski,Kimmo Raivio,Risto Silvennoinen,Antti Suutala,Tanja Tarvainen,Timo Tiihonen,Jukka Tuomela,Esko Turunen,Marko Vauhkonen Pdf

This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

Modelling in Mathematical Programming

José Manuel García Sánchez
Modelling in Mathematical Programming Book PDF

Author : José Manuel García Sánchez
Publisher : Springer Nature
Page : 291 pages
File Size : 46,5 Mb
Release : 2020-10-31
Category : Business & Economics
ISBN : 9783030572501

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Modelling in Mathematical Programming by José Manuel García Sánchez Pdf

This book provides basic tools for learning how to model in mathematical programming, from models without much complexity to complex system models. It presents a unique methodology for the building of an integral mathematical model, as well as new techniques that help build under own criteria. It allows readers to structure models from the elements and variables to the constraints, a basic modelling guide for any system with a new scheme of variables, a classification of constraints and also a set of rules to model specifications stated as logical propositions, helping to better understand models already existing in the literature. It also presents the modelling of all possible objectives that may arise in optimization problems regarding the variables values. The book is structured to guide the reader in an orderly manner, learning of the components that the methodology establishes in an optimization problem. The system includes the elements, which are all the actors that participate in the system, decision activities that occur in the system, calculations based on the decision activities, specifications such as regulations, impositions or actions of defined value and objective criterion, which guides the resolution of the system.

Modelling Mathematical Methods and Scientific Computation

Nicola Bellomo,Luigi Preziosi
Modelling Mathematical Methods and Scientific Computation Book PDF

Author : Nicola Bellomo,Luigi Preziosi
Publisher : CRC Press
Page : 516 pages
File Size : 46,9 Mb
Release : 1994-12-22
Category : Mathematics
ISBN : 0849383315

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Modelling Mathematical Methods and Scientific Computation by Nicola Bellomo,Luigi Preziosi Pdf

Addressed to engineers, scientists, and applied mathematicians, this book explores the fundamental aspects of mathematical modelling in applied sciences and related mathematical and computational methods. After providing the general framework needed for mathematical modelling-definitions, classifications, general modelling procedures, and validation methods-the authors deal with the analysis of discrete models. This includes modelling methods and related mathematical methods. The analysis of models is defined in terms of ordinary differential equations. The analysis of continuous models, particularly models defined in terms of partial differential equations, follows. The authors then examine inverse type problems and stochastic modelling. Three appendices provide a concise guide to functional analysis, approximation theory, and probability, and a diskette included with the book includes ten scientific programs to introduce the reader to scientific computation at a practical level.

Methods and Models in Mathematical Biology

Johannes Müller,Christina Kuttler
Methods and Models in Mathematical Biology Book PDF

Author : Johannes Müller,Christina Kuttler
Publisher : Springer
Page : 711 pages
File Size : 41,8 Mb
Release : 2015-08-13
Category : Mathematics
ISBN : 9783642272516

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Methods and Models in Mathematical Biology by Johannes Müller,Christina Kuttler Pdf

This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.

A Primer on Mathematical Modelling

Alfio Quarteroni,Paola Gervasio
A Primer on Mathematical Modelling Book PDF

Author : Alfio Quarteroni,Paola Gervasio
Publisher : Springer Nature
Page : 238 pages
File Size : 52,9 Mb
Release : 2020-10-09
Category : Mathematics
ISBN : 9783030445416

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A Primer on Mathematical Modelling by Alfio Quarteroni,Paola Gervasio Pdf

In this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers. A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites. This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasio This book is addressed to any student interested in learning how to construct and apply mathematical models.

Mathematical Methods in Engineering and Applied Sciences

Taylor & Francis Group
Mathematical Methods in Engineering and Applied Sciences Book PDF

Author : Taylor & Francis Group
Publisher : CRC Press
Page : 308 pages
File Size : 40,6 Mb
Release : 2021-09-30
Category : Electronic
ISBN : 1032175915

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Mathematical Methods in Engineering and Applied Sciences by Taylor & Francis Group Pdf

This book covers tools and techniques used for developing mathematical methods and modelling related to real-life situations. It brings forward significant aspects of mathematical research by using different mathematical methods such as analytical, computational, and numerical with relevance or applications in engineering and applied sciences.

Mathematical Modeling

Ludmilla A. Uvarova,Anatolii V. Latyshev
Mathematical Modeling Book PDF

Author : Ludmilla A. Uvarova,Anatolii V. Latyshev
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 55,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475733976

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Mathematical Modeling by Ludmilla A. Uvarova,Anatolii V. Latyshev Pdf

This volume contains review articles and original results obtained in various fields of modern science using mathematical simulation methods. The basis of the articles are the plenary and some section reports that were made and discussed at the Fourth International Mathematical Simulation Conference, held in Moscow on June 27 through July 1, 2000. The conference was devoted to the following scientific areas: • mathematical and computer discrete systems models; • non-linear excitation in condensed media; • complex systems evolution; • mathematical models in economics; • non-equilibrium processes kinematics; • dynamics and structure of the molecular and biomolecular systems; • mathematical transfer models in non-linear systems; • numerical simulation and algorithms; • turbulence and determined chaos; • chemical physics of polymer. This conference was supported by the Russian Ministry of Education, Russian foundation for Basic Research and Federal Program "Integration". This volume contains the following sections: 1. models of non-linear phenomena in physics; 2. numerical methods and computer simulations; 3. mathematical computer models of discrete systems; 4. mathematical models in economics; 5. non-linear models in chemical physics and physical chemistry; 6. mathematical models of transport processes in complex systems. In Sections One and Five a number of fundamental and sufficiently general problems, concerning real physical and physical-chemical systems simulation, is discussed.

Mathematical and Computational Methods for Modelling, Approximation and Simulation

Domingo Barrera,Sara Remogna,Driss Sbibih
Mathematical and Computational Methods for Modelling Approximation and Simulation Book PDF

Author : Domingo Barrera,Sara Remogna,Driss Sbibih
Publisher : Springer
Page : 0 pages
File Size : 43,8 Mb
Release : 2023-05-09
Category : Mathematics
ISBN : 3030943410

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Mathematical and Computational Methods for Modelling, Approximation and Simulation by Domingo Barrera,Sara Remogna,Driss Sbibih Pdf

This book contains plenary lectures given at the International Conference on Mathematical and Computational Modeling, Approximation and Simulation, dealing with three very different problems: reduction of Runge and Gibbs phenomena, difficulties arising when studying models that depend on the highly nonlinear behaviour of a system of PDEs, and data fitting with truncated hierarchical B-splines for the adaptive reconstruction of industrial models. The book includes nine contributions, mostly related to quasi-interpolation. This is a topic that continues to register a high level of interest, both for those working in the field of approximation theory and for those interested in its use in a practical context. Two chapters address the construction of quasi-interpolants, and three others focus on the use of quasi-interpolation in solving integral equations. The remaining four concern a problem related to the heat diffusion equation, new results on the notion of convexity in probabilistic metric spaces (which are applied to the study of the existence and uniqueness of the solution of a Volterra equation), the use of smoothing splines to address an economic problem and, finally, the analysis of poverty measures, which is a topic of increased interest to society. The book is addressed to researchers interested in Applied Mathematics, with particular reference to the aforementioned topics.