Mathematical Modelling Skills

Author: Dilwyn Edwards,Michael Hamson

Publisher: Macmillan International Higher Education

ISBN: 1349132500

Category: Applied mathematics

Page: 164

View: 7250

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: 4956

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: 3537

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

Mathematical Modelling

Author: John Stephen Berry,Ken Houston

Publisher: Gulf Professional Publishing

ISBN: 0340614048

Category: Mathematics

Page: 142

View: 2430

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.

Modelling and Mathematics Education

ICTMA 9 - Applications in Science and Technology

Author: J F Matos,S K Houston,W Blum,S P Carreira

Publisher: Elsevier

ISBN: 0857099655

Category: Mathematics

Page: 432

View: 7256

The articles included in this book are from the ICTMA 9 conference held in Lisbon, attended by delegates from about 30 countries. This work records the 1999 Lisbon Conference of ICTMA. It contains the selected and edited content of the conference and makes a significant contribution to mathematical modelling which is the significant investigative preliminary to all scientific and technological applications from machinery to satellites and docking of space-ships. Contains the selected and edited content of the 1999 Lisbon Conference of ICTMA Makes a significant contribution to mathematical modelling, which is the significant investigative preliminary to all scientific and technological applications from machinery to satellites and docking of space-ships

Effective Learning and Teaching in Mathematics and Its Applications

Author: Peter Kahn,Joseph Kyle

Publisher: Routledge

ISBN: 1135726906

Category: Education

Page: 240

View: 726

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.

Mathematical Modeling

Applications with GeoGebra

Author: Jonas Hall,Thomas Lingefjärd

Publisher: John Wiley & Sons

ISBN: 1119102693

Category: Mathematics

Page: 568

View: 9258

A logical problem-based introduction to the use of GeoGebra for mathematical modeling and problem solving within various areas of mathematics A well-organized guide to mathematical modeling techniques for evaluating and solving problems in the diverse field of mathematics, Mathematical Modeling: Applications with GeoGebra presents a unique approach to software applications in GeoGebra and WolframAlpha. The software is well suited for modeling problems in numerous areas of mathematics including algebra, symbolic algebra, dynamic geometry, three-dimensional geometry, and statistics. Featuring detailed information on how GeoGebra can be used as a guide to mathematical modeling, the book provides comprehensive modeling examples that correspond to different levels of mathematical experience, from simple linear relations to differential equations. Each chapter builds on the previous chapter with practical examples in order to illustrate the mathematical modeling skills necessary for problem solving. Addressing methods for evaluating models including relative error, correlation, square sum of errors, regression, and confidence interval, Mathematical Modeling: Applications with GeoGebra also includes: Over 400 diagrams and 300 GeoGebra examples with practical approaches to mathematical modeling that help the reader develop a full understanding of the content Numerous real-world exercises with solutions to help readers learn mathematical modeling techniques A companion website with GeoGebra constructions and screencasts Mathematical Modeling: Applications with GeoGebrais ideal for upper-undergraduate and graduate-level courses in mathematical modeling, applied mathematics, modeling and simulation, operations research, and optimization. The book is also an excellent reference for undergraduate and high school instructors in mathematics.

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: 396

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.

Guide to Mathematical Modelling

Author: Dilwyn Edwards,Mike Hamson

Publisher: Macmillan International Higher Education

ISBN: 1349100420

Category: Applied mathematics

Page: 277

View: 2795

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 with Case Studies

A Differential Equations Approach using Maple and MATLAB, Second Edition

Author: Belinda Barnes,Glenn Robert Fulford

Publisher: CRC Press

ISBN: 9780415298049

Category: Mathematics

Page: 472

View: 1145

Certain basic modeling skills can be applied to a wide variety of problems. It focuses on those mathematical techniques which are applicable to models involving differential equations. Models in three different areas are considered: growth and decay process, interacting populations and heating/cooling problems. The main mathematical technique is solving differential equations, while the range of applications and mathematical techniques presented provides a broad appreciation of this type of modeling. This book contains three general sections: Compartmental Models, Population Models and Heat Transfer Models. Within each section, the process of constructing a model is presented in full detail. Applications and case studies are integral to this text, and case studies are included throughout. This is a useful course text, and basic calculus and fundamental computing skills are required.

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: 523

View: 4191

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.

MEI Further Maths: Modelling with Algorithms

Author: Jan Dangerfield

Publisher: Hachette UK

ISBN: 1510451412

Category: Study Aids

Page: 120

View: 1676

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.

A First Course in Mathematical Modeling

Author: Frank R. Giordano,William P. Fox,Steven B. Horton

Publisher: Cengage Learning

ISBN: 1285531760

Category: Mathematics

Page: 704

View: 8977

Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 5th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

An Introduction to Mathematical Modeling

Author: Edward A. Bender

Publisher: Courier Corporation

ISBN: 0486137120

Category: Mathematics

Page: 272

View: 6782

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.

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: 1518

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

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: 7222

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 Modeling

Models, Analysis and Applications

Author: Sandip Banerjee

Publisher: CRC Press

ISBN: 1439854513

Category: Mathematics

Page: 276

View: 7449

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.

Mathematical Modelling

A Case Study Approach

Author: Dick Clements

Publisher: N.A


Category: Mathematics

Page: 176

View: 5957

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

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: 2381

Mathematics of Computing -- Miscellaneous.

Modeling in the Neurosciences

From Ionic Channels to Neural Networks

Author: R.R. Poznanski

Publisher: CRC Press

ISBN: 9789057022845

Category: Science

Page: 528

View: 4621

With contributions from more than 40 renowned experts, Modeling in the Neurosciences: From Ionic Channels to Neural Networks is essential for those interested in neuronal modeling and quantitative neiroscience. Focusing on new mathematical and computer models, techniques and methods, this monograph represents a cohesive and comprehensive treatment of various aspects of the neurosciences from the biophysical, cellular and netwrok levels. Many state-of-the-art examples are presented as to how mathematical and computer modeling can contribute to the understanding of mechanisms and systems in the neurosciences. Each chapter also includes suggestions of possible refinements for future modeling in this rapidly changing and expanding field. This book will benefit and inspire the advanced modeler, and give the beginner sufficient confidence to model a wide selection of neuronal systems at the biophysical, cellular and network levels.