J. Caldwell – författare

Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science and engineering. There has been a constant movement in the emphasis from developing proficiency in purely mathematical techniques to an approach which caters for industrial and scientific applications in emerging new technologies. In this textbook we have attempted to present the important fundamental concepts of mathematical modelling and to demonstrate their use in solving certain scientific and engineering problems. This text, which serves as a general introduction to the area of mathematical modelling, is aimed at advanced undergraduate students in mathematics or closely related disciplines, e.g., students who have some prerequisite knowledge such as one-variable calculus, linear algebra and ordinary differential equations. Some prior knowledge of computer programming would be useful but is not considered essential. The text also contains some more challenging material which could prove attractive to graduate students in engineering or science who are involved in mathematical modelling. In preparing the text we have tried to use our experience of teaching mathematical modelling to undergraduate students in a wide range of areas including mathematics and computer science and disciplines in engineering and science. An important aspect of the text is the use made of scientific computer software packages such as MAPLE for symbolic algebraic manipulations and MA TLAB for numerical simulation.

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.

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.

In recent years, mathematical modelling allied to computer simulation has emerged as en effective and invaluable design tool for industry and a discipline in its own right. This has been reflected in the popularity of the growing number of courses and conferences devoted to the area. The North East Polytechnics Mathematical Modelling and Computer Simulation Group has a balanced representation of academics and industrialists and, as a Group, has the objective of promoting a continuing partnership between the Polytechnics in the North East and local industry. Prior to the present conference the Group has organised eight conferences with a variety of themes related to mathematical modelling and computer simulation. The theme chosen for the Polymodel 9 Conference held in Newcastle upon Tyne in May 1986 was Industrial Vibration Modelling, which is particularly approp riate for 'Industry Year' and is an area which continues to present industry and academics with new and challenging problems. The aim of the Conference was to calIon and use the modelling experience of eminent academics and industrialists who are deeply involved in the solution of vibration problems. To this end the following four sessions were organised: (1) Vehicular Vibrations led by keynote speaker Dr S King (Westland Helicopters Ltd) (2) Acoustics led by Dr M Petyt (Southampton University) (3) Fluid/Structural Vibrations led by G T Willshare (British Maritime Technology) (4) Special Problems and Developing Areas to include nonlinearities, ultrasonics, transients, elastic stability, etc.

Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science and engineering. There has been a constant movement in the emphasis from developing proficiency in purely mathematical techniques to an approach which caters for industrial and scientific applications in emerging new technologies. In this textbook we have attempted to present the important fundamental concepts of mathematical modelling and to demonstrate their use in solving certain scientific and engineering problems. This text, which serves as a general introduction to the area of mathematical modelling, is aimed at advanced undergraduate students in mathematics or closely related disciplines, e.g., students who have some prerequisite knowledge such as one-variable calculus, linear algebra and ordinary differential equations. Some prior knowledge of computer programming would be useful but is not considered essential. The text also contains some more challenging material which could prove attractive to graduate students in engineering or science who are involved in mathematical modelling. In preparing the text we have tried to use our experience of teaching mathematical modelling to undergraduate students in a wide range of areas including mathematics and computer science and disciplines in engineering and science. An important aspect of the text is the use made of scientific computer software packages such as MAPLE for symbolic algebraic manipulations and MA TLAB for numerical simulation.

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.

In recent years, mathematical modelling allied to computer simulation has emerged as en effective and invaluable design tool for industry and a discipline in its own right. This has been reflected in the popularity of the growing number of courses and conferences devoted to the area. The North East Polytechnics Mathematical Modelling and Computer Simulation Group has a balanced representation of academics and industrialists and, as a Group, has the objective of promoting a continuing partnership between the Polytechnics in the North East and local industry. Prior to the present conference the Group has organised eight conferences with a variety of themes related to mathematical modelling and computer simulation. The theme chosen for the Polymodel 9 Conference held in Newcastle upon Tyne in May 1986 was Industrial Vibration Modelling, which is particularly approp riate for ''Industry Year'' and is an area which continues to present industry and academics with new and challenging problems. The aim of the Conference was to calIon and use the modelling experience of eminent academics and industrialists who are deeply involved in the solution of vibration problems. To this end the following four sessions were organised: (1) Vehicular Vibrations led by keynote speaker Dr S King (Westland Helicopters Ltd) (2) Acoustics led by Dr M Petyt (Southampton University) (3) Fluid/Structural Vibrations led by G T Willshare (British Maritime Technology) (4) Special Problems and Developing Areas to include nonlinearities, ultrasonics, transients, elastic stability, etc.

During the past few years the rapid development of computer tech­ nology has made high power computing facilities more readily accessible to a greater proportion of our industrial and academic community. This development coupled with the recent upsurge in mathematical modelling and computer simulation has led to signif­ icant developments in electromagnetic field theory and its applic­ ations to industry. In view of such developments and the present high interest to both academics and industry the theme chosen for the Polymodel 6 Conference held at Newcastle upon Tyne in May 1983 was Industrial Electromagnetics Modelling. To date the North East Polytechnics Mathematical Modelling and Computer Simulation Group has organised five successful Polymodel. conferences each with a different theme. The objectives of the Polymodel group include the promotion of collaborative research between Newcastle, Sunderland and Teesside Polytechnics and industry in the areas of mathematical modelling and computer simulation. The aim of the Polymodel 6 Conference was to call on and use the modelling and computer.simulation expertise of eminent academics and industrialists who are deeply involved in the area of electro­ magnetics. These proceedings have a twofold purpose in that they contain current analytical and numerical techniques relevant to electromagnetic field problems and useful ideas on the modelling and simulation techniques which are most appropriate. It was also felt important to include implications. of. computer developments (both hardware and software) on such work.

During the past few years the rapid development of computer tech­ nology has made high power computing facilities more readily accessible to a greater proportion of our industrial and academic community. This development coupled with the recent upsurge in mathematical modelling and computer simulation has led to signif­ icant developments in electromagnetic field theory and its applic­ ations to industry. In view of such developments and the present high interest to both academics and industry the theme chosen for the Polymodel 6 Conference held at Newcastle upon Tyne in May 1983 was Industrial Electromagnetics Modelling. To date the North East Polytechnics Mathematical Modelling and Computer Simulation Group has organised five successful Polymodel. conferences each with a different theme. The objectives of the Polymodel group include the promotion of collaborative research between Newcastle, Sunderland and Teesside Polytechnics and industry in the areas of mathematical modelling and computer simulation. The aim of the Polymodel 6 Conference was to call on and use the modelling and computer.simulation expertise of eminent academics and industrialists who are deeply involved in the area of electro­ magnetics. These proceedings have a twofold purpose in that they contain current analytical and numerical techniques relevant to electromagnetic field problems and useful ideas on the modelling and simulation techniques which are most appropriate. It was also felt important to include implications. of. computer developments (both hardware and software) on such work.

In recent years, mathematical modelling allied to computer simulation has emerged as en effective and invaluable design tool for industry and a discipline in its own right. This has been reflected in the popularity of the growing number of courses and conferences devoted to the area. The North East Polytechnics Mathematical Modelling and Computer Simulation Group has a balanced representation of academics and industrialists and, as a Group, has the objective of promoting a continuing partnership between the Polytechnics in the North East and local industry. Prior to the present conference the Group has organised eight conferences with a variety of themes related to mathematical modelling and computer simulation. The theme chosen for the Polymodel 9 Conference held in Newcastle upon Tyne in May 1986 was Industrial Vibration Modelling, which is particularly approp riate for 'Industry Year' and is an area which continues to present industry and academics with new and challenging problems. The aim of the Conference was to calIon and use the modelling experience of eminent academics and industrialists who are deeply involved in the solution of vibration problems. To this end the following four sessions were organised: (1) Vehicular Vibrations led by keynote speaker Dr S King (Westland Helicopters Ltd) (2) Acoustics led by Dr M Petyt (Southampton University) (3) Fluid/Structural Vibrations led by G T Willshare (British Maritime Technology) (4) Special Problems and Developing Areas to include nonlinearities, ultrasonics, transients, elastic stability, etc.