Mathematical Modelling

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An Introduction to Mathematical Modeling

Edward A. Bender
An Introduction to Mathematical Modeling Book PDF

Author : Edward A. Bender
Publisher : Courier Corporation
Page : 274 pages
File Size : 54,7 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 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 : 55,9 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 Modelling

Simon Serovajsky
Mathematical Modelling Book PDF

Author : Simon Serovajsky
Publisher : CRC Press
Page : 466 pages
File Size : 45,7 Mb
Release : 2021-11-24
Category : Mathematics
ISBN : 9781000503975

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Mathematical Modelling by Simon Serovajsky Pdf

Mathematical 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.

Introduction to the Foundations of Applied Mathematics

Mark H. Holmes
Introduction to the Foundations of Applied Mathematics Book PDF

Author : Mark H. Holmes
Publisher : Springer Science & Business Media
Page : 477 pages
File Size : 53,5 Mb
Release : 2009-06-18
Category : Mathematics
ISBN : 9780387877655

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Introduction to the Foundations of Applied Mathematics by Mark H. Holmes Pdf

FOAM. This acronym has been used for over ?fty years at Rensselaer to designate an upper-division course entitled, Foundations of Applied Ma- ematics. This course was started by George Handelman in 1956, when he came to Rensselaer from the Carnegie Institute of Technology. His objective was to closely integrate mathematical and physical reasoning, and in the p- cess enable students to obtain a qualitative understanding of the world we live in. FOAM was soon taken over by a young faculty member, Lee Segel. About this time a similar course, Introduction to Applied Mathematics, was introduced by Chia-Ch’iao Lin at the Massachusetts Institute of Technology. Together Lin and Segel, with help from Handelman, produced one of the landmark textbooks in applied mathematics, Mathematics Applied to - terministic Problems in the Natural Sciences. This was originally published in 1974, and republished in 1988 by the Society for Industrial and Applied Mathematics, in their Classics Series. This textbook comes from the author teaching FOAM over the last few years. In this sense, it is an updated version of the Lin and Segel textbook.

The Nature of Mathematical Modeling

Neil A. Gershenfeld
The Nature of Mathematical Modeling Book PDF

Author : Neil A. Gershenfeld
Publisher : Cambridge University Press
Page : 268 pages
File Size : 45,7 Mb
Release : 1999
Category : Science
ISBN : 0521570956

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The Nature of Mathematical Modeling by Neil A. Gershenfeld Pdf

This is a book about the nature of mathematical modeling, and about the kinds of techniques that are useful for modeling. The text is in four sections. The first covers exact and approximate analytical techniques; the second, numerical methods; the third, model inference based on observations; and the last, the special role of time in modeling. Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area. The text is complemented by extensive worked problems.

Mathematical Modelling

John Berry,Ken Houston
Mathematical Modelling Book PDF

Author : John Berry,Ken Houston
Publisher : Gulf Professional Publishing
Page : 157 pages
File Size : 53,5 Mb
Release : 1995-06-17
Category : Mathematics
ISBN : 9780340614044

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Mathematical Modelling by John Berry,Ken Houston Pdf

Assuming virtually no prior knowledge, Modular Mathematics encourages the reader to develop and solve real models, as well as looking at traditional examples. Accessible and concise, it contains tutorial problems, case studies and exercises.

Guide to Mathematical Modelling

David A Towers,Dilwyn Edwards,Mike Hamson
Guide to Mathematical Modelling Book PDF

Author : David A Towers,Dilwyn Edwards,Mike Hamson
Publisher : Bloomsbury Publishing
Page : 326 pages
File Size : 54,6 Mb
Release : 2020-06-06
Category : Mathematics
ISBN : 9781352011272

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Guide to Mathematical Modelling by David A Towers,Dilwyn Edwards,Mike Hamson Pdf

A basic introduction to Mathematical Modelling, this book encourages the reader to participate in the investigation of a wide variety of modelling examples. These are carefully paced so that the readers can identify and develop the skills which are required for successful modelling. The examples also promote an appreciation of the enormous range of problems to which mathematical modelling skills can be usefully applied.

Learning How to Teach Mathematical Modeling in School and Teacher Education

Rita Borromeo Ferri
Learning How to Teach Mathematical Modeling in School and Teacher Education Book PDF

Author : Rita Borromeo Ferri
Publisher : Springer
Page : 153 pages
File Size : 45,5 Mb
Release : 2017-11-26
Category : Education
ISBN : 9783319680729

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Learning How to Teach Mathematical Modeling in School and Teacher Education by Rita Borromeo Ferri Pdf

This timely resource fills a gap in existing literature on mathematical modeling by presenting both theory- and evidence-based ideas for its teaching and learning. The book outlines four key professional competencies that must be developed in order to effectively and appropriately teach mathematical modeling, and in so doing it seeks to reduce the discrepancies between educational policy and educational research versus everyday teaching practice. Among the key competencies covered are: Theoretical competency for practical work. Task competency for instructional flexibility. Instructional competency for effective and quality lessons. Diagnostic competency for assessment and grading. Learning How to Teach Mathematical Modeling in School and Teacher Education is relevant to practicing and future mathematics teachers at all levels, as well as teacher educators, mathematics education researchers, and undergraduate and graduate mathematics students interested in research based methods for teaching mathematical modeling.

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 : 40,6 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.

Concepts of Mathematical Modeling

Walter J. Meyer
Concepts of Mathematical Modeling Book PDF

Author : Walter J. Meyer
Publisher : Courier Corporation
Page : 450 pages
File Size : 55,8 Mb
Release : 2012-10-23
Category : Mathematics
ISBN : 9780486137247

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Concepts of Mathematical Modeling by Walter J. Meyer Pdf

Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each section is preceded by an abstract and statement of prerequisites, and answers or hints are provided for selected exercises. 1984 edition.

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 : 52,6 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.

Mathematical Modelling

Reinhard Illner,REINHARD AUTOR ILLNER,C. Sean Bohun,Samantha McCollum,Thea van Roode
Mathematical Modelling Book PDF

Author : Reinhard Illner,REINHARD AUTOR ILLNER,C. Sean Bohun,Samantha McCollum,Thea van Roode
Publisher : American Mathematical Soc.
Page : 216 pages
File Size : 44,7 Mb
Release : 2005
Category : Mathematical models
ISBN : 9780821836507

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Mathematical Modelling by Reinhard Illner,REINHARD AUTOR ILLNER,C. Sean Bohun,Samantha McCollum,Thea van Roode Pdf

"This is an ideal text for classes on modelling. It can also be used in seminars or as preparation for mathematical modelling competitions."--BOOK JACKET.

Mathematical Modeling

Sandip Banerjee
Mathematical Modeling Book PDF

Author : Sandip Banerjee
Publisher : CRC Press
Page : 419 pages
File Size : 55,6 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.

Mathematical Modelling Techniques

Rutherford Aris
Mathematical Modelling Techniques Book PDF

Author : Rutherford Aris
Publisher : Courier Corporation
Page : 290 pages
File Size : 47,9 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

Mathematical Modelling for Teachers

Keng Cheng Ang
Mathematical Modelling for Teachers Book PDF

Author : Keng Cheng Ang
Publisher : Routledge
Page : 172 pages
File Size : 44,9 Mb
Release : 2018-09-03
Category : Education
ISBN : 9781351247962

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Mathematical Modelling for Teachers by Keng Cheng Ang Pdf

Mathematical 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. 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.