- •Preface
- •1.1 Introduction
- •1.2 Models and modelling
- •1.3 The learning process for mathematical modelling
- •Summary
- •Aims and objectives
- •2.1 Introduction
- •2.2 Examples
- •2.3 Further examples
- •Appendix 1
- •Appendix 2
- •Aims and objectives
- •3.1 Introduction
- •3.2 Definitions and terminology
- •3.3 Methodology and modelling flow chart
- •3.4 The methodology in practice
- •Background to the problem
- •Summary
- •Aims and objectives
- •4.1 Introduction
- •4.2 Listing factors
- •4.3 Making assumptions
- •4.4 Types of behaviour
- •4.5 Translating into mathematics
- •4.6 Choosing mathematical functions
- •Case 1
- •Case 2
- •Case 3
- •4.7 Relative sizes of terms
- •4.8 Units
- •4.9 Dimensions
- •4.10 Dimensional analysis
- •Summary
- •Aims and objectives
- •5.1 Introduction
- •5.2 First-order linear difference equations
- •5.3 Tending to a limit
- •5.4 More than one variable
- •5.5 Matrix models
- •5.6 Non-linear models and chaos
- •5.7 Using spreadsheets
- •Aims and objectives
- •6.1 Introduction
- •6.2 First order, one variable
- •6.3 Second order, one variable
- •6.4 Second order, two variables (uncoupled)
- •6.5 Simultaneous coupled differential equations
- •Summary
- •Aims and objectives
- •7.1 Introduction
- •7.2 Modelling random variables
- •7.3 Generating random numbers
- •7.4 Simulations
- •7.5 Using simulation models
- •7.6 Packages and simulation languages
- •Summary
- •Aims and objectives
- •8.1 Introduction
- •8.2 Data collection
- •8.3 Empirical models
- •8.4 Estimating parameters
- •8.5 Errors and accuracy
- •8.6 Testing models
- •Summary
- •Aims and objectives
- •9.1 Introduction
- •9.2 Driving speeds
- •Context
- •Problem statement
- •Formulate a mathematical model
- •Rewritten problem statement
- •Obtain the mathematical solution
- •9.3 Tax on cigarette smoking
- •Context
- •Problem statement
- •Formulate a mathematical model
- •Obtain the mathematical solution
- •9.4 Shopping trips
- •Context
- •Problem statement
- •Formulate a mathematical model
- •Obtain the mathematical solution
- •Interpret the mathematical solution
- •Using the model
- •9.5 Disk pressing
- •Context
- •Problem statement
- •Formulate a mathematical model
- •Obtain the mathematical solution
- •Interpret the mathematical solution
- •Further thoughts
- •9.6 Gutter
- •Context and problem statement
- •Formulate a mathematical model
- •Obtain the mathematical solution
- •9.7 Turf
- •Context
- •Problem statement
- •Formulate a mathematical model
- •Obtain the mathematical solution
- •Interpret the solution
- •9.8 Parachute jump
- •Context and problem statement
- •Formulate a mathematical model
- •Obtain the mathematical solution
- •9.9 On the buses
- •Context
- •Problem statement
- •Formulate a mathematical model
- •Obtain the mathematical solution
- •9.10 Further battles
- •Discrete deterministic model
- •Discrete stochastic model
- •Comparing the models
- •9.11 Snooker
- •Context
- •Problem statement
- •Formulate a mathematical model
- •Obtain the mathematical solution
- •Interpret the mathematical solution
- •9.12 Further models
- •Mileage
- •Heads or tails
- •Picture hanging
- •Motorway
- •Vehicle-merging delay at a junction
- •Family names
- •Estimating animal populations
- •Simulation of population growth
- •Needle crystals
- •Car parking
- •Overhead projector
- •Sheep farming
- •Aims and objectives
- •10.1 Introduction
- •10.2 Report writing
- •Preliminary
- •Main body
- •Appendices
- •Summary
- •General remarks
- •10.3 A specimen report
- •Contents
- •1 PRELIMINARY SECTIONS
- •1.1 Summary and conclusions
- •1.2 Glossary
- •2 MAIN SECTIONS
- •2.1 Problem statement
- •2.2 Assumptions
- •2.3 Individual testing
- •2.4 Single-stage procedure
- •2.5 Two-stage procedure
- •2.6 Results
- •2.7 Regular section procedures
- •2.8 Conclusions
- •3 APPENDICES
- •3.1 Possible extensions
- •3.2 Mathematical analysis
- •10.4 Presentation
- •Preparation
- •Giving the presentation
- •Bibliography
- •Solutions to Exercises
- •Chapter 2
- •Example 2.2 – Double wiper overlap problem
- •Chapter 4
- •Chapter 5
- •Chapter 6
- •Chapter 8
- •Index
Bibliography
The following list gives a selection of books currently available, which contain material relevant to this book. Some deal with general topics in mathematics and statistics, but most books cover mathematical modelling at an introductory level.
Barnett, S., Some Modern Applications of Mathematics, Ellis Horwood, 1995. Berry, J., and Houston, S. K., Mathematical Modelling, Edward Arnold, 1995.
Berry, J., Norcliffe, A., and Humble, S., Introductory Mathematics through Science Applications, Cambridge University Press, 1989.
Burghes, D., Galbraith, P., Price, N., and Sherlock, A., Mathematical Modelling, Prentice-Hall, 1996. Daintith, J., and Nelson, R. D., Dictionary of Mathematics, Penguin, 1989.
Daniel, W. W., and Terrell, J. C., Business Statistics, Houghton Mifflin, 1995. Edwards, D., and Hamson M., Mathematical Modelling Skills, Macmillan, 1996.
Fulford, G., Forrester, P., and Jones, A., Modelling with Differential and Difference Equations, Cambridge University Press, 1997.
Galbraith, P., Blum, W., Booker, G., and Huntley, I., Mathematical Modelling: Teaching and Assessment in a Technology Rich World, Horwood Publishing, 1998.
Giordana, F. R., Weir, M. D., and Fox, W. P., A First Course in Mathematical Modelling, (2nd edition), ITP, 1997.
Houston, S. K., Blum, W., Huntley, I., and Neill, N. T., Teaching and Learning Mathematical Modelling, Albion Publishing, 1997.
Matos, J. F., Blum, W., Carreira, S., and Houston, S. K., Modelling, Applications and Mathematics Education – Trend and Issues, Horwood Publishing, 2001.
Medley, D. G., An Introduction to Mechanics and Modelling, Heinemann, 1982.
Oldknow, A., and Ahmed, Afzal (eds), Teaching mathematics and its applications, Journal of the Institute of Mathematics and its Applications, Vol. 19, 2000.
Sandifur, J. T., Discrete Dynamics Systems, Clarendon Press, 1990.
Strang, G., Introduction to Applied Mathematics, Wellesley-Cambridge, 1986.
Townend, M. S., and Pountney, D. C., Learning Modelling with DERIVE, Prentice-Hall, 1995. Tuckwell, H. C., Elementary Applications of Probability Theory, Chapman and Hall, 1988.