Mathematical Models And Their Analysis

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Mathematical Models and Their Analysis

Frederick Y. M. Wan
Mathematical Models and Their Analysis Book PDF

Author : Frederick Y. M. Wan
Publisher : SIAM
Page : 404 pages
File Size : 48,8 Mb
Release : 2018-03-20
Category : Computers
ISBN : 9781611975260

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Mathematical Models and Their Analysis by Frederick Y. M. Wan Pdf

A great deal can be learned through modeling and mathematical analysis about real-life phenomena, even before numerical simulations are used to accurately portray the specific configuration of a situation. Scientific computing also becomes more effective and efficient if it is preceded by some preliminary analysis. These important advantages of mathematical modeling are demonstrated by models of historical importance in an easily understandable way. The organization of Mathematical Models and Their Analysis groups models by the issues that need to be addressed about the phenomena. The new approach shows how mathematics effective for one modeled phenomenon can be used to analyze another unrelated problem. For instance, the mathematics of differential equations useful in understanding the classical physics of planetary models, fluid motion, and heat conduction is also applicable to the seemingly unrelated phenomena of traffic flow and congestion, offshore sovereignty, and regulation of overfishing and deforestation. The formulation and in-depth analysis of these and other models on modern social issues, such as the management of exhaustible and renewable resources in response to consumption demands and economic growth, are of increasing concern to students and researchers of our time. The modeling of current social issues typically starts with a simple but meaningful model that may not capture all the important elements of the phenomenon. Predictions extracted from such a model may be informative but not compatible with all known observations; so the model may require improvements. The cycle of model formulation, analysis, interpretation, and assessment is made explicit for the modeler to repeat until a model is validated by consistency with all known facts.

Mathematical Models and Their Analysis

Frederick Y. M. Wan
Mathematical Models and Their Analysis Book PDF

Author : Frederick Y. M. Wan
Publisher : SIAM
Page : 404 pages
File Size : 45,7 Mb
Release : 2018-03-20
Category : Computers
ISBN : 9781611975277

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Mathematical Models and Their Analysis by Frederick Y. M. Wan Pdf

A great deal can be learned through modeling and mathematical analysis about real-life phenomena, even before numerical simulations are used to accurately portray the specific configuration of a situation. Scientific computing also becomes more effective and efficient if it is preceded by some preliminary analysis. These important advantages of mathematical modeling are demonstrated by models of historical importance in an easily understandable way. The organization of Mathematical Models and Their Analysis groups models by the issues that need to be addressed about the phenomena. The new approach shows how mathematics effective for one modeled phenomenon can be used to analyze another unrelated problem. For instance, the mathematics of differential equations useful in understanding the classical physics of planetary models, fluid motion, and heat conduction is also applicable to the seemingly unrelated phenomena of traffic flow and congestion, offshore sovereignty, and regulation of overfishing and deforestation. The formulation and in-depth analysis of these and other models on modern social issues, such as the management of exhaustible and renewable resources in response to consumption demands and economic growth, are of increasing concern to students and researchers of our time. The modeling of current social issues typically starts with a simple but meaningful model that may not capture all the important elements of the phenomenon. Predictions extracted from such a model may be informative but not compatible with all known observations; so the model may require improvements. The cycle of model formulation, analysis, interpretation, and assessment is made explicit for the modeler to repeat until a model is validated by consistency with all known facts.

Mathematical Modeling

Sandip Banerjee
Mathematical Modeling Book PDF

Author : Sandip Banerjee
Publisher : CRC Press
Page : 419 pages
File Size : 46,5 Mb
Release : 2021-11-11
Category : Mathematics
ISBN : 9781351022934

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Mathematical Modeling by Sandip Banerjee Pdf

Mathematical Modeling: Models, Analysis and Applications, Second Edition introduces models of both discrete and continuous systems. This book is aimed at newcomers who desires to learn mathematical modeling, especially students taking a first course in the subject. Beginning with the step-by-step guidance of model formulation, this book equips the reader about modeling with difference equations (discrete models), ODE’s, PDE’s, delay and stochastic differential equations (continuous models). This book provides interdisciplinary and integrative overview of mathematical modeling, making it a complete textbook for a wide audience. A unique feature of the book is the breadth of coverage of different examples on mathematical modelling, which include population models, economic models, arms race models, combat models, learning model, alcohol dynamics model, carbon dating, drug distribution models, mechanical oscillation models, epidemic models, tumor models, traffic flow models, crime flow models, spatial models, football team performance model, breathing model, two neuron system model, zombie model and model on love affairs. Common themes such as equilibrium points, stability, phase plane analysis, bifurcations, limit cycles, period doubling and chaos run through several chapters and their interpretations in the context of the model have been highlighted. In chapter 3, a section on estimation of system parameters with real life data for model validation has also been discussed. Features Covers discrete, continuous, spatial, delayed and stochastic models. Over 250 illustrations, 300 examples and exercises with complete solutions. Incorporates MATHEMATICA® and MATLAB®, each chapter contains Mathematica and Matlab codes used to display numerical results (available at CRC website). Separate sections for Projects. Several exercise problems can also be used for projects. Presents real life examples of discrete and continuous scenarios. The book is ideal for an introductory course for undergraduate and graduate students, engineers, applied mathematicians and researchers working in various areas of natural and applied sciences.

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 : 47,9 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.

Advances in Mathematical Modeling and Analysis

Casper Geller
Advances in Mathematical Modeling and Analysis Book PDF

Author : Casper Geller
Publisher : NY Research Press
Page : 230 pages
File Size : 54,6 Mb
Release : 2021-11-16
Category : Mathematics
ISBN : 1632388758

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Advances in Mathematical Modeling and Analysis by Casper Geller Pdf

The process of developing a mathematical model is known as mathematical modeling. It is characterization of system that uses mathematical concepts and languages. Mathematical models are used in natural science such as physics, chemistry, earth science and biology. They are also used in social sciences such as political science, sociology, economics and psychology. Dynamical systems, statistical models, differential equations or game theoretic models are some forms of mathematical models. There are two primary mathematical modeling problems which are classified as black box models or white box models. A black-box model is a system of model in which there is no priori information available, whereas a white-box model is a system where all necessary information is available. This book contains some path-breaking studies in the field of mathematical modeling. The various advancements in mathematical modeling and analysis are glanced at and their applications as well as ramifications are looked at in detail. For all those who are interested in this discipline, this book can prove to be an essential guide.

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 : 52,6 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.

Mathematical Modeling

Sandip Banerjee
Mathematical Modeling Book PDF

Author : Sandip Banerjee
Publisher : CRC Press
Page : 278 pages
File Size : 51,9 Mb
Release : 2014-02-07
Category : Mathematics
ISBN : 9781439854518

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Mathematical Modeling by Sandip Banerjee Pdf

Almost every year, a new book on mathematical modeling is published, so, why another? The answer springs directly from the fact that it is very rare to find a book that covers modeling with all types of differential equations in one volume. Until now. Mathematical Modeling: Models, Analysis and Applications covers modeling with all kinds of differential equations, namely ordinary, partial, delay, and stochastic. The book also contains a chapter on discrete modeling, consisting of differential equations, making it a complete textbook on this important skill needed for the study of science, engineering, and social sciences. More than just a textbook, this how-to guide presents tools for mathematical modeling and analysis. It offers a wide-ranging overview of mathematical ideas and techniques that provide a number of effective approaches to problem solving. Topics covered include spatial, delayed, and stochastic modeling. The text provides real-life examples of discrete and continuous mathematical modeling scenarios. MATLAB® and Mathematica® are incorporated throughout the text. The examples and exercises in each chapter can be used as problems in a project. Since mathematical modeling involves a diverse range of skills and tools, the author focuses on techniques that will be of particular interest to engineers, scientists, and others who use models of discrete and continuous systems. He gives students a foundation for understanding and using the mathematics that is the basis of computers, and therefore a foundation for success in engineering and science streams.

Model and Mathematics: From the 19th to the 21st Century

Michael Friedman,Karin Krauthausen
Model and Mathematics From the 19th to the 21st Century Book PDF

Author : Michael Friedman,Karin Krauthausen
Publisher : Birkhäuser
Page : 443 pages
File Size : 41,6 Mb
Release : 2022-07-05
Category : Mathematics
ISBN : 303097832X

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Model and Mathematics: From the 19th to the 21st Century by Michael Friedman,Karin Krauthausen Pdf

This open access book collects the historical and medial perspectives of a systematic and epistemological analysis of the complicated, multifaceted relationship between model and mathematics, ranging from, for example, the physical mathematical models of the 19th century to the simulation and digital modelling of the 21st century. The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models. This book is open access under a CC BY 4.0 license.

MATHEMATICAL MODELLING OF SYSTEMS AND ANALYSIS

KAMALANAND, K.,JAWAHAR, P. MANNAR
MATHEMATICAL MODELLING OF SYSTEMS AND ANALYSIS Book PDF

Author : KAMALANAND, K.,JAWAHAR, P. MANNAR
Publisher : PHI Learning Pvt. Ltd.
Page : 264 pages
File Size : 47,7 Mb
Release : 2018-11-01
Category : Computers
ISBN : 9788193593851

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MATHEMATICAL MODELLING OF SYSTEMS AND ANALYSIS by KAMALANAND, K.,JAWAHAR, P. MANNAR Pdf

This book is written with the ideology of providing a simple yet concise explanation on the art of developing mathematical models. This lively and engaging text explicates the basics of mathematical modelling, with special focus on its applications and analysis. Organised in thirteen chapters, the book emphasises the theory and classification of systems, modelling using ordinary differential equations, calculus of variations, stability analysis, system identification and parameter estimation techniques. Also, it includes examples from the areas of mechanics, chemical reactions, biology, population dynamics, epidemiology, and other allied fields of science, engineering and technology. This book is primarily designed for the postgraduate students of mathematics as well as for the undergraduate and postgraduate engineering students of various disciplines for their paper on Modelling and Simulation/Mathematical Modelling and Simulation/Mathematical Modelling. KEY FEATURES • Inclusion of entropy-based modelling, modelling using fractional order ODEs and artificial intelligence along with stability and catastrophe theory is the major highlight of this book. • Figures and tables well support the text. • Numerous worked-out examples make the students aware of problem-solving methodology. • Chapter-end exercises help the students from practice point of view. • References and suggested reading at the end of the book broaden its scope.

Mathematical Modeling of Social Relationships

Urszula Strawinska-Zanko,Larry S. Liebovitch
Mathematical Modeling of Social Relationships Book PDF

Author : Urszula Strawinska-Zanko,Larry S. Liebovitch
Publisher : Springer
Page : 222 pages
File Size : 42,8 Mb
Release : 2018-06-07
Category : Social Science
ISBN : 9783319767659

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Mathematical Modeling of Social Relationships by Urszula Strawinska-Zanko,Larry S. Liebovitch Pdf

This edited volume presents examples of social science research projects that employ new methods of quantitative analysis and mathematical modeling of social processes. This book presents the fascinating areas of empirical and theoretical investigations that use formal mathematics in a way that is accessible for individuals lacking extensive expertise but still desiring to expand their scope of research methodology and add to their data analysis toolbox. Mathematical Modeling of Social Relationships professes how mathematical modeling can help us understand the fundamental, compelling, and yet sometimes complicated concepts that arise in the social sciences. This volume will appeal to upper-level students and researchers in a broad area of fields within the social sciences, as well as the disciplines of social psychology, complex systems, and applied mathematics.

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.

Mathematical Modeling and Simulation

Kai Velten
Mathematical Modeling and Simulation Book PDF

Author : Kai Velten
Publisher : John Wiley & Sons
Page : 362 pages
File Size : 40,6 Mb
Release : 2009-06-01
Category : Science
ISBN : 9783527627615

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Mathematical Modeling and Simulation by Kai Velten Pdf

This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently discussed in detail. Based on the author`s modeling and simulation experience in science and engineering and as a consultant, the book answers such basic questions as: What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? What are simulation, parameter estimation, and validation? The book relies exclusively upon open-source software which is available to everybody free of charge. The entire book software - including 3D CFD and structural mechanics simulation software - can be used based on a free CAELinux-Live-DVD that is available in the Internet (works on most machines and operating systems).

Mathematical Modelling

Seyed M. Moghadas,Majid Jaberi-Douraki
Mathematical Modelling Book PDF

Author : Seyed M. Moghadas,Majid Jaberi-Douraki
Publisher : John Wiley & Sons
Page : 192 pages
File Size : 55,9 Mb
Release : 2018-07-24
Category : Mathematics
ISBN : 9781119483991

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Mathematical Modelling by Seyed M. Moghadas,Majid Jaberi-Douraki Pdf

An 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.

Singular Phenomena and Scaling in Mathematical Models

Michael Griebel
Singular Phenomena and Scaling in Mathematical Models Book PDF

Author : Michael Griebel
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 43,7 Mb
Release : 2013-11-18
Category : Computers
ISBN : 9783319007861

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Singular Phenomena and Scaling in Mathematical Models by Michael Griebel Pdf

The book integrates theoretical analysis, numerical simulation and modeling approaches for the treatment of singular phenomena. The projects covered focus on actual applied problems, and develop qualitatively new and mathematically challenging methods for various problems from the natural sciences. Ranging from stochastic and geometric analysis over nonlinear analysis and modelling to numerical analysis and scientific computation, the book is divided into the three sections: A) Scaling limits of diffusion processes and singular spaces, B) Multiple scales in mathematical models of materials science and biology and C) Numerics for multiscale models and singular phenomena. Each section addresses the key aspects of multiple scales and model hierarchies, singularities and degeneracies, and scaling laws and self-similarity.

Dimensional Analysis In The Identification Of Mathematical Models

Lysik Bertold,Waclaw Kasprzak,Marek Rybaczuk
Dimensional Analysis In The Identification Of Mathematical Models Book PDF

Author : Lysik Bertold,Waclaw Kasprzak,Marek Rybaczuk
Publisher : World Scientific
Page : 206 pages
File Size : 40,7 Mb
Release : 1990-09-12
Category : Mathematics
ISBN : 9789814506779

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Dimensional Analysis In The Identification Of Mathematical Models by Lysik Bertold,Waclaw Kasprzak,Marek Rybaczuk Pdf

This book is the first textbook with the generalization of Dimensional Analysis, specially prepared to solve problems of identification of mathematical models based on experimental data. The generalization gives the possibility of mathematical model invariant with regard to gauge group, groups of rotation and others. The resulting formalism generates the most general and tensor homogeneous form of possible functional dependence.