Practical Applied Mathematics Modelling, Analysis, Approximation

Part I. Modelling Techniques: 1. The basics of modelling 2. Units, dimensions and dimensional analysis 3. Non-dimensionalisation 4. Case studies: hair modelling and cable laying 5. Case study: the thermistor (1) 6. Case study: electrostatic painting (1) Part II. Mathematical Techniques: 7. Partial differential equations 8. Case study: traffic modelling 9. Distributions 10. Theory of distributions 11. Case study: the pantograph Part III. Asymptotic techniques: 12. Asymptotic expansions 13. Regular perturbation expansions 14. Case study: electrostatic painting (2) 15. Case study: piano tuning 16. Boundary layers 17. Case study: the thermistor (2) 18. 'Lubrication theory' analysis 19. Case study: continuous casting of steel 20. Lubrication theory for fluids 21. Case study: eggs 22. Methods for oscillators 23. Ray theory and other 'exponential' approaches.

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