Mathematical Modelling Skills

Author: Dilwyn Edwards,Michael Hamson

Publisher: Macmillan International Higher Education

ISBN: 1349132500

Category: Applied mathematics

Page: 164

View: 4042

The aim of this book is to assist the reader to build up the necessary range of skills needed to be able to solve problems by mathematical modelling. After an introduction to the general principles and advantages of mathematical modelling, chapters 1 to 4 concentrate on the development of basic modelling skills. Each of chapters 5 to 11 isolates a particular modelling concept and provides exercises aimed at developing skills in the use of that concept. The later chapters may be conveniently read in any order as they are self contained. In keeping with the Work Out approach, each chapter contains a large number of examples and exercises, taken from a variety of subject areas and covering a broad range of difficulty. Answers are provided wherever appropriate.

Teaching Mathematical Modelling: Connecting to Research and Practice

Author: Gloria Ann Stillman,Gabriele Kaiser,Werner Blum,Jill P. Brown

Publisher: Springer Science & Business Media

ISBN: 9400765401

Category: Education

Page: 627

View: 8967

This book provides readers with an overview of recent international research and developments in the teaching and learning of modelling and applications from a variety of theoretical and practical perspectives. There is a strong focus on pedagogical issues for teaching and learning of modelling as well as research into teaching and practice. The teaching of applications of mathematics and mathematical modelling from the early years through primary and secondary school and at tertiary level is rising in prominence in many parts of the world commensurate with an ever-increasing usage of mathematics in business, the environment, industry and everyday life. The authors are all members of the International Community of Teachers of Mathematical Modelling and Applications and important researchers in mathematics education and mathematics. The book will be of interest to teachers, practitioners and researchers in universities, polytechnics, teacher education, curriculum and policy.​

Trends in Teaching and Learning of Mathematical Modelling


Author: Gabriele Kaiser,Werner Blum,Rita Borromeo Ferri,Gloria Stillman

Publisher: Springer Science & Business Media

ISBN: 9789400709102

Category: Education

Page: 734

View: 975

This book contains suggestions for and reflections on the teaching, learning and assessing of mathematical modelling and applications in a rapidly changing world, including teaching and learning environments. It addresses all levels of education from universities and technical colleges to secondary and primary schools. Sponsored by the International Community of Teachers of Mathematical Modelling and Applications (ICTMA), it reflects recent ideas and methods contributed by specialists from 30 countries in Africa, the Americas, Asia, Australia and Europe. Inspired by contributions to the Fourteenth Conference on the Teaching of Mathematical Modelling and Applications (ICTMA14) in Hamburg, 2009, the book describes the latest trends in the teaching and learning of mathematical modelling at school and university including teacher education. The broad and versatile range of topics will stress the international state-of-the-art on the following issues: Theoretical reflections on the teaching and learning of modelling Modelling competencies Cognitive perspectives on modelling Modelling examples for all educational levels Practice of modelling in school and at university level Practices in Engineering and Applications

Guide to Mathematical Modelling

Author: Dilwyn Edwards,Mike Hamson

Publisher: Macmillan International Higher Education

ISBN: 1349100420

Category: Applied mathematics

Page: 277

View: 7273

The authors' enthusiasm for their subject is eloquently conveyed in this book, and draws the reader very quickly into active investigation of the problems posed. By providing plenty of modelling examples from a wide variety of fields - most of which are familiar from everyday life - the book shows how to apply mathematical ideas to situations which would not previously have been considered to be 'mathematical' in character.

Mathematical Modelling

Author: John Stephen Berry,Ken Houston

Publisher: Gulf Professional Publishing

ISBN: 0340614048

Category: Mathematics

Page: 142

View: 2485

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.

Mathematical Modelling

Case Studies and Projects

Author: J. Caldwell,Douglas K.S. Ng

Publisher: Springer Science & Business Media

ISBN: 1402019939

Category: Mathematics

Page: 253

View: 996

Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science, engineering, business and management. Recent developments in computer technology and related software have provided the necessary tools of increasing power and sophistication which have significant implications for the use and role of mathematical modelling in the above disciplines. In the past, traditional methods have relied heavily on expensive experimentation and the building of scaled models, but now a more flexible and cost effective approach is available through greater use of mathematical modelling and computer simulation. In particular, developments in computer algebra, symbolic manipulation packages and user friendly software packages for large scale problems, all have important implications in both the teaching of mathematical modelling and, more importantly, its use in the solution of real world problems. Many textbooks have been published which cover the art and techniques of modelling as well as specific mathematical modelling techniques in specialist areas within science and business. In most of these books the mathematical material tends to be rather tailor made to fit in with a one or two semester course for teaching students at the undergraduate or postgraduate level, usually the former. This textbook is quite different in that it is intended to build on and enhance students’ modelling skills using a combination of case studies and projects.

Mathematical Modelling Techniques

Author: Rutherford Aris

Publisher: Courier Corporation

ISBN: 0486138895

Category: Technology & Engineering

Page: 288

View: 1260

Highly useful volume discusses the types of models, how to formulate and manipulate them for best results. Numerous examples.

Mathematical Modelling with Case Studies

A Differential Equations Approach using Maple and MATLAB, Second Edition

Author: B. Barnes,G..R. Fulford

Publisher: CRC Press

ISBN: 9781420083507

Category: Mathematics

Page: 368

View: 5343

Focusing on growth and decay processes, interacting populations, and heating/cooling problems, Mathematical Modelling with Case Studies: A Differential Equations Approach using MapleTM and MATLAB®, Second Edition presents mathematical techniques applicable to models involving differential equations that describe rates of change. Although the authors concentrate on models involving differential equations, the ideas used can be applied to many other areas. The book carefully details the process of constructing a model, including the conversion of a seemingly complex problem into a much simpler one. It uses flow diagrams and word equations to aid in the model building process and to develop the mathematical equations. Employing theoretical, graphical, and computational tools, the authors analyze the behavior of the models under changing conditions. They discuss the validation of the models and suggest extensions to the models with an emphasis on recognizing the strengths and limitations of each model. Through applications and the tools of MapleTM and MATLAB®, this textbook provides hands-on model building skills. It develops, extends, and improves simple models as well as interprets the results.

Effective Learning and Teaching in Mathematics and Its Applications

Author: Peter Kahn,Joseph Kyle

Publisher: Routledge

ISBN: 1135726906

Category: Education

Page: 240

View: 8724

The Effective Learning and Teaching in Higher Education series is packed with up-to-date advice, guidance and expert opinion on teaching in the key subjects in higher education today, and is backed up by the authority of the Institute for Learning and Teaching. This book covers all of the key issues surrounding the effective teaching of maths- a key subject in its own right, and one that forms an important part of many other disciplines. The book includes contributions from a wide range of experts in the field, and has a broad and international perspective.

An Introduction to Mathematical Modeling

Author: Edward A. Bender

Publisher: Courier Corporation

ISBN: 0486137120

Category: Mathematics

Page: 272

View: 6112

Accessible text features over 100 reality-based examples pulled from the science, engineering, and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.

Modelling and Applications in Mathematics Education

The 14th ICMI Study

Author: Peter L. Galbraith,Hans-Wolfgang Henn,Mogens Niss

Publisher: Springer Science & Business Media

ISBN: 9780387298221

Category: Education

Page: 524

View: 3491

The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.

Mathematical Modelling

A Way of Life - ICTMA 11

Author: S J Lamon,W A Parker,S K Houston

Publisher: Elsevier

ISBN: 085709954X

Category: Mathematics

Page: 288

View: 4329

Mathematical modelling is often spoken of as a way of life, referring to habits of mind and to dependence on the power of mathematics to describe, explain, predict and control real phenomena. This book aims to encourage teachers to provide opportunities for students to model a variety of real phenomena appropriately matched to students’ mathematical backgrounds and interests from early stages of mathematical education. Habits, misconceptions, and mindsets about mathematics can present obstacles to university students’ acceptance of a ‘‘models-and-modelling perspective’’ at this stage of mathematics education. Without prior experience in building, interpreting and applying mathematical models, many students may never come to view and regard modelling as a way of life. The book records presentations at the ICTMA 11 conference held in Milwaukee, Wisconsin in 2003. Examines mathematical modelling as a way of life, referring to habits of mind and dependence on the power of mathematics to describe, explain, predict and control real phenomena Encourages teachers to provide students with opportunities to model a variety of real phenomena appropriately matched to students’ mathematical backgrounds and interests from early stages of mathematical education Records presentations at the ICTMA 11 conference held in Milwaukee, Wisconsin in 2003

Mathematical Modelling

A Case Studies Approach

Author: Reinhard Illner

Publisher: American Mathematical Soc.

ISBN: 0821836501

Category: Mathematics

Page: 196

View: 6648

Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem. The presentation is in the form of case studies, which are developed much as they would be in true applications. In many cases, an initial model is created, then modified along the way. Some cases are familiar, such as the evaluation of an annuity. Others are unique, such as the fascinating situation in which an engineer, armed only with a slide rule, had 24 hours to compute whether a valve would hold when a temporary rock plug was removed from a water tunnel. Each chapter ends with a set of exercises and some suggestions for class projects.Some projects are extensive, as with the explorations of the predator-prey model; others are more modest. The text was designed to be suitable for a one-term course for advanced undergraduates. The selection of topics and the style of exposition reflect this choice. The authors have also succeeded in demonstrating just how enjoyable the subject can be. This is an ideal text for classes on modelling. It can also be used in seminars or as preparation for mathematical modelling competitions.

Mathematical modelling

a tool for problem solving in engineering, physical, biological, and social sciences

Author: D. N. P. Murthy,N. W. Page,Ervin Y. Rodin

Publisher: Pergamon

ISBN: 9780080372440

Category: Mathematics

Page: 339

View: 1400

Mathematics of Computing -- Miscellaneous.

Mathematical Modelling

A Case Study Approach

Author: Dick Clements

Publisher: N.A


Category: Mathematics

Page: 176

View: 3290

This book, based on a successful undergraduate course designed by the author, describes mathematical modelling and its application to the solution of problems in industry and commerce. In the early chapters of the book the author first sets out a clear introduction to the principles of mathematical modelling, including sections on the various methodologies of mathematical modelling and their relationship to systems methodologies. He then offers some insights into practical aspects of mathematical modelling and proceeds to describe the development and operation of the undergraduate course upon which the book is based. In the later chapters seven case studies, based on real problems contributed by mathematicians working in industry, are introduced. Each chapter describes a problem, the solution originally adopted and variations on that solution introduced by students over a number of years use of the case studies.

Mathematical Modelling for Earth Sciences

Author: Xin-She Yang

Publisher: Dunedin Academic PressLtd


Category: Mathematics

Page: 310

View: 5810

Mathematical modelling and computer simulations are an essential part of the analytical toolset used by earth scientists. Computer simulations based on mathematical models are routinely used to study geophysical, environmental, and geological processes in many areas of work and research from geophysics to petroleum engineering and from hydrology to environmental fluid dynamics. Author Xin-She Yang has carefully selected the topics which will be of most value to students. Dr. Yang has recognized the need to be careful in his examples while being comprehensive enough to include important topics and popular algorithms. The book is designed to be 'theorem-free' while balancing formality and practicality. Using worked examples and tackling each problem in a step-by-step manner, the text is especially suitable for more advanced students of this aspect of earth sciences. The coverage and level, for instance in the calculus of variation and pattern formation, will be of interest to mathematicians. Topics covered include: vector and matrix analysis â?¢ ordinary differential equations â?¢ partial differential equations â?¢ calculus of variations â?¢ integral equations â?¢ probability â?¢ geostatistics â?¢ numerical integration â?¢ optimization â?¢ finite difference methods â?¢ finite volume methods â?¢ finite element methods â?¢ reaction-diffusion system â?¢ elasticity â?¢ fracture mechanics â?¢ poroelasticity â?¢ flows in porous media.


A Systematic Approach to Mathematical Modelling in the Social Sciences

Author: Wolfgang Weidlich

Publisher: Courier Corporation

ISBN: 0486450279

Category: Mathematics

Page: 380

View: 3961

"Highly recommended. . . . This is an important book in putting the burgeoning field of sociodynamics on a solid footing."—Journal of Artificial Societies and Social Simulation This text deals with general modelling concepts in the social sciences, their applications, and their mathematical methods. The author's well-organized approach offers a clear, coherent introduction to terminology, approaches, and goals in modelling. Appropriate for advanced undergraduates and graduate students, it requires a solid background in algebra and calculus. The three-part treatment begins by addressing general modelling concepts, the second part provides applications, and the third discusses mathematical method. Topics include population dynamics, group interaction, political transitions, evolutionary economics, and urbanization. Guiding students through a series of practical applications that illustrate the methods' potential scope, the text concludes with a detailed look at mathematical methods.

MEI Further Maths: Modelling with Algorithms

Author: Jan Dangerfield

Publisher: Hachette UK

ISBN: 1510451412

Category: Study Aids

Page: 120

View: 946

Develop a deeper understanding of mathematical concepts and their applications with new and updated editions from our bestselling series. - Build connections between topics using real-world contexts that develop mathematical modelling skills, thus providing your students with a fuller and more coherent understanding of mathematical concepts. - Develop fluency in problem-solving, proof and modelling with plenty of questions and well-structured exercises. - Overcome misconceptions and develop mathematical insight with annotated worked examples. - Enhance understanding and map your progress with graduated exercises that support you at every stage of your learning.