A Concrete Approach to Mathematical Modelling

by Mike Mesterton-Gibbons

Author	: Mike Mesterton-Gibbons
Publisher	: Wiley-Interscience
Total Pages	: 624
Release	: 2007-05-18
Genre	: Mathematics
ISBN	:

GET BOOK

Critical praise for A Concrete Approach to Mathematical Modelling "...a treasure house of material for students and teachers alike...can be dipped into regularly for inspiration and ideas. It deserves to become a classic."--London Times Higher Education Supplement "The author succeeds in his goal of serving the needs of the undergraduate population who want to see mathematics in action, and the mathematics used is extensive and provoking."--SIAM Review "Each chapter discusses a wealth of examples ranging from old standards...to novelty ... Each model is developed critically, analyzed critically, and assessed critically."--Mathematical Reviews Mike Mesterton-Gibbons has done what no author before him could: he has written an in-depth, systematic guide to the art and science of mathematical modelling that's a great read from first page to last. With an abundance of both wit and common sense, he shows readers exactly how the modelling process works, using fascinating real-life examples from virtually every realm of human, machine, natural, and cosmic activity. You'll find models for determining how fast cars drive through a tunnel; how many workers industry should employ; the length of a supermarket checkout line; how birds should select worms; the best methods for avoiding an automobile accident; and when a barber should hire an assistant; just to name a few. Offering more examples, more detailed explanations, and by far, more sheer enjoyment than any other book on the subject, A Concrete Approach to Mathematical Modelling is the ultimate how-to guide for students and professionals in the hard sciences, social sciences, engineering, computers, statistics, economics, politics, business management, and every other discipline in which mathematical modelling plays a role. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department. Cover Design / Illustration: Keithley Associates, Inc.

A Concrete Approach to Mathematical Modelling

by Mike Mesterton-Gibbons

Author	: Mike Mesterton-Gibbons
Publisher	: John Wiley & Sons
Total Pages	: 620
Release	: 2011-02-14
Genre	: Mathematics
ISBN	: 1118030648

GET BOOK

WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists ofselected books that have been made more accessible to consumers inan effort to increase global appeal and general circulation. Withthese new unabridged softcover volumes, Wiley hopes to extend thelives of these works by making them available to future generationsof statisticians, mathematicians, and scientists. " . . . [a] treasure house of material for students and teachersalike . . . can be dipped into regularly for inspiration and ideas.It deserves to become a classic." —London Times Higher Education Supplement "The author succeeds in his goal of serving the needs of theundergraduate population who want to see mathematics in action, andthe mathematics used is extensive and provoking." —SIAM Review "Each chapter discusses a wealth of examples ranging from oldstandards . . . to novelty . . . each model is developedcritically, analyzed critically, and assessed critically." —Mathematical Reviews A Concrete Approach to Mathematical Modelling providesin-depth and systematic coverage of the art and science ofmathematical modelling. Dr. Mesterton-Gibbons shows how themodelling process works and includes fascinating examples fromvirtually every realm of human, machine, natural, and cosmicactivity. Various models are found throughout the book, includinghow to determine how fast cars drive through a tunnel, how manyworkers industry should employ, the length of a supermarketcheckout line, and more. With detailed explanations, exercises, andexamples demonstrating real-life applications in diverse fields,this book is the ultimate guide for students and professionals inthe social sciences, life sciences, engineering, statistics,economics, politics, business and management sciences, and everyother discipline in which mathematical modelling plays a role.

An Introduction to Mathematical Modeling

by Edward A. Bender

Author	: Edward A. Bender
Publisher	: Courier Corporation
Total Pages	: 273
Release	: 2012-05-23
Genre	: Mathematics
ISBN	: 0486137120

GET BOOK

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 and Simulation

by Kai Velten

Author	: Kai Velten
Publisher	: John Wiley & Sons
Total Pages	: 362
Release	: 2009-06-01
Genre	: Science
ISBN	: 3527627618

GET BOOK

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 Education in East and West

by Frederick Koon Shing Leung

Author	: Frederick Koon Shing Leung
Publisher	: Springer Nature
Total Pages	: 666
Release	: 2021-04-26
Genre	: Education
ISBN	: 3030669963

GET BOOK

This book documents ongoing research and theorizing in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in people’s everyday lives as well as sophisticated new problems for society at large. Mathematical tradition in China that emphasizes algorithm and computation has now seen a renaissance in mathematical modelling and applications where China has made significant progress with its economy, science and technology. In recent decades, teaching and learning of mathematical modelling as well as contests in mathematical modelling have been flourishing at different levels of education in China. Today, teachers and researchers in China become keener to learn from their colleagues from Western countries and other parts of the world in research and teaching of mathematical modelling and applications. The book provides a dialogue and communication between colleagues from across the globe with new impetus and resources for mathematical modelling education and its research in both West and East with new ideas on modelling teaching and practices, inside and outside classrooms. All authors of this book are members of the International Community of Teachers of Mathematical Modelling and Applications (ICTMA), the peak research body into researching the teaching, assessing and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace. The book is of interest to researchers, mathematics educators, teacher educators, education administrators, policy writers, curriculum developers, professional developers, in-service teachers and pre-service teachers including those interested in mathematical literacy.

Measuring Professional Competence for the Teaching of Mathematical Modelling

by Raphael Wess

Author	: Raphael Wess
Publisher	: Springer Nature
Total Pages	: 129
Release	: 2021-07-14
Genre	: Education
ISBN	: 3030780716

GET BOOK

This open access book presents a structural model and an associated test instrument designed to provide a detailed analysis of professional competences for teaching mathematical modelling. The conceptualisation is based on the COACTIV model, which describes aspects, areas and facets of professional competences of teachers. The manual provides an overview of the essential teaching skills in application-related contexts and offers the tools needed to capture these aspects. It discusses the objectives and application areas of the instrument, as well as the development of the test. In addition, it describes the implementation and evaluates the quality and results of the structural equation analysis of the model. Teaching mathematical modelling is a cognitively challenging activity for (prospective) teachers. Thus, teacher education requires a detailed analysis of professional competence for teaching mathematical modelling. Measuring this competence requires theoretical models that accurately describe requirements placed upon teachers, as well as appropriate evaluation tools that adequately capture skills and abilities in this field. This book presents an instrument that measures the professional competences in a sample of 349 prospective teachers.

Mathematical Models in Biology

by Elizabeth Spencer Allman

Author	: Elizabeth Spencer Allman
Publisher	: Cambridge University Press
Total Pages	: 388
Release	: 2004
Genre	: Mathematics
ISBN	: 9780521525862

GET BOOK

This introductory textbook on mathematical biology focuses on discrete models across a variety of biological subdisciplines. Biological topics treated include linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction, genetics, and infectious disease models. The coverage of models of molecular evolution and phylogenetic tree construction from DNA sequence data is unique among books at this level. Computer investigations with MATLAB are incorporated throughout, in both exercises and more extensive projects, to give readers hands-on experience with the mathematical models developed. MATLAB programs accompany the text. Mathematical tools, such as matrix algebra, eigenvector analysis, and basic probability, are motivated by biological models and given self-contained developments, so that mathematical prerequisites are minimal.

Principles of Mathematical Modelling

by Alexander A. Samarskii

Author	: Alexander A. Samarskii
Publisher	: CRC Press
Total Pages	: 368
Release	: 2001-12-20
Genre	: Mathematics
ISBN	: 9780415272803

GET BOOK

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..

Teaching and Learning Mathematical Modelling

by Gilbert Greefrath

Author	: Gilbert Greefrath
Publisher	: Springer
Total Pages	: 49
Release	: 2016-08-20
Genre	: Education
ISBN	: 3319450042

GET BOOK

This survey provides an overview of the German discussion on modelling and applications in schools. It considers the development from the beginning of the 20th century to the present, and discusses the term “mathematical model” as well as different representations of the modelling process as modelling cycles. Different trends in the historical and current debate on applications and modelling can be differentiated as perspectives of modelling. Modelling is now one of the six general mathematical competencies defined in the educational standards for mathematics introduced in Germany in 2003, and there have been several initiatives to implement modelling in schools, as well as a whole range of empirical research projects focusing on teachers or students in modelling processes. As a special kind for implementing modelling into school, modelling weeks and days carried out by various German universities have been established.