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Mathematical Modelling Techniques


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Table of Contents

1. What is a model? 1.1 The idea of a mathematical model and its relation to other uses of the word 1.2 Relations between models with respect to origins 1.3 Relations between models with respect to purpose and conditions 1.4 How should a model be judged? 2. The Different types of model 2.1 Verbal models and mechanical analogies 2.2 Finite models 2.3 Fuzzy subsets 2.4 Statistical models 2.5 Difference and differential equations 2.6 Stochastic models 3. How to formulate a model 3.1 Laws and conservation principles 3.2 Constitutive relations 3.3 Discrete and continuous models 4. How should a model be manipulated into its most responsive form? 4.1 Introductory suggestions 4.2 Natural languages and notations 4.3 Rendering the variables and parameters dismensionless 4.4 Reducing the number of equations and simplifying them 4.5 Getting partial insights into the form of the solution 4.5.1 The phase plane and competing populations 4.5.2 Coarse numerical methods and their uses 4.5.3 The interaction of easier and more difficult problems 5. How should a model be evaluated? 5.1 Effective presentation of a model 5.2 Extension of models 5.3 Observable quantities 5.4 Comparison of models and prototypes and of models among themselves Appendices A. Longitudinal diffusion in a packed bed B. The coated tube chromatograph and Taylor diffusion C. The stirred tank reactor References Subject index Name idex Appendices to the Dover Edition I. "Re, k and p: A Conversation on Some Aspects of Mathematical Modelling" II. The Jail of Shape III. The Mere Notion of a Model IV. "Ut Simulacrum, Poesis" V. Manners Makyth Modellers VI. How to Get the Most Out of an Equation without Really Trying

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