Mathematical modelling : a sourcebook of case studies
著者
書誌事項
Mathematical modelling : a sourcebook of case studies
Oxford University Press, 1990
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内容説明・目次
内容説明
An important component of mathematical education at all levels is the use of mathematics to model real-world situations. In this book the emphasis is on developing models which provide a means to analyze and answer questions posed in practical settings. It provides a compendium of case studies of mathematical models of varying degrees of sophistication and practicality. Teachers and students of mathematical modelling will find it a rich source of examples ranging from insulating houses to basketball and from modelling epidemics to studying the generation of windmill power. The case studies all arise from workshops organized by the editors on the teaching of mathematical modelling and a common feature of the studies is that they provide ample scope for group and project work as well as the use of microcomputers to study the models. The studies are intended to complement undergraduate courses and care has been taken so that any mathematical techniques which are used should be within the capabilities of students. This volume should be valuable to both teachers and practitioners of mathematical modelling by providing a fresh and challenging range of problems to work on with students.
目次
- Preface
- Some aspects of the process of formulation of mathematical models
- Part I: Simple illustrative examples: Estimating route lengths
- Forest management
- Apportionment
- the length of a roll of toilet paper
- Can water in a boat ever make it more stable?
- Part II: Models for class development: Accident investigations
- Insulating a house
- Basketball shooting
- Putting the shot
- Epidemics and the spread of diseases
- Pollution of the Great Lakes
- Quarrying for sand
- The Ruritanian Sports and Social Club
- Indian population projectories
- Biological cell populations
- Marketing a new variety of seed
- Modelling plant growth
- Part III: Extended problems: Valve design in the treatment of hydrocephalus
- Why airlines sometimes overbook flights
- Estimating fertilizer requirements of vegetable crops
- Leylandia vehicles required General Insurance
- Windmill power Arcrite Pipework Limited
- Signal flags
- Part IV: Further problem statements: Emergency evacuation times for educational buildings
- Road safety
- Sheep farming
- Loading tiles into boxes
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