Mathematical modelling / J.N. Kapur. Author. Kapur, Jagat Narain, Published. New York, N.Y.: Wiley, Physical Description. xi, p.: ill. ; 25 cm. Mathematical Modelling, by J. N. Kapur, New York: John Wiley, , xi + pp. , $ The most interesting thing that I have learned from this book. Mathematical Modelling book. Read 4 reviews from the world's largest community for readers. The application of mathematical modelling to physical, econom.
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A mathematical model is a description of a system using Mathematical Elements of a mathematical model .. 3. Mathematical Modelling: by J. N. Kapur . Download Citation on ResearchGate | Mathematical modelling / J.N. Kapur | Incluye bibliografía e índice. Jagat Narain Kapur Request Full-text Paper PDF. 𝗣𝗗𝗙 | Mathematical model on the industrial pollution and spread of infection Kapur, J. N., " Mathematical modeling in biology and medicine ".
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Open Preview See a Problem? Details if other: Thanks for telling us about the problem. Return to Book Page. Preview — Mathematical Modelling by J. Mathematical Modelling by J. The application of mathematical modelling to physical, economic, and social systems is growing rapidly. This book describes the more important techniques of mathematical modelling, and shows how to apply these techniques to a variety of problems.
Each chapter covers a different mathematical technique, discusses the kinds of situations in which it is useful, and shows how t The application of mathematical modelling to physical, economic, and social systems is growing rapidly.
Each chapter covers a different mathematical technique, discusses the kinds of situations in which it is useful, and shows how to apply the technique to different fields. Examples are drawn from many subjects, including physics, chemistry, economics, demography, biology, medicine, ecology, traffic flow, and others.
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Continuous-variate models appear to be easier to handle than the discrete-variate models, due to the development of calculus and differential equations. In fact in many disciplines, these were developed first. However continuous models are simple only when analytical solutions are available, otherwise we have to approximate a continuous model also by a discrete model so that these can be handled numerically.
For many situations presented in real life and specifically in Petroleum engineering, the discrete models are severally used due to the complexity of the models that are developed. We want a mathematical model to be as realistic as possible and to represent reality as closely as possible.
However if a model is very realistic, it may not be mathematically tractable. In making a mathematical model, there has to be a trade-off between tractability and reality. Mathematical modelling is not one-shot affair. Models are constantly improved to make the more realistic. Thus for every situation, we get hierarchy of models, each more realistic than the preceding and each likely to be followed by a better one.
Different models differ in their precision and their agreement with observations. A mathematical model is said to be robust if small changes in the parameters lead to small changes in the behaviour of the model. The decision is made using sensitivity analysis for the models. A mathematical model involves equations and in equations and these must be consistent. Sometimes the inconsistency results from inconsistency of basic assumptions.
Since mathematical inconsistency is relatively easier to find out, this gives a method of finding inconsistency in requirements which social or biological scientists may require of their models. It has been said that mathematics that is certain does not refer to reality and mathematics that refer to reality is not certain.
A model may not represent reality because it is oversimplified. A model may also be overambitious in the sense that it may involve too many complications and many give results accurate to ten decimal places whereas the observations may be correct to two decimal places only. This can be increased by subdividing variables, by taking more variables and by considering more details.
Increase of complexity need not always lead to increase of insight as after stage, diminishing returns begin to set in. The art of mathematical modelling consists in stopping before this stage.
Comparison of predictions with observations reveals the need for new experiments to collect needed data. Mathematical models can also lead to development of new concepts. If known mathematical techniques are not adequate to deduce results from the mathematical model new mathematical techniques have to be developed. Thus we may need different models for explaining different aspects of the same situation or even for different ranges of the variables.
Of course in this case, search for a unified model continues.
Usually models give predictions expected on common sense considerations, but the model predictions are more quantitative in nature. Sometimes they give unexpected predictions and they may lead to break-through or deep thinking about assumptions.
Sometimes models give prediction completely at variance with observations and then these models have to be drastically revised. Models may lead to nice and elegant mathematical results, but only those models are acceptable which can explain, predict or control simulations.
A model may also fit one situation very well and may give hopeless fit for another situation.
Before making a mathematical model, one has to clear about the structure and essentials of the situation. A model helps thinking, but it can also direct thinking in one narrow channel only.
Sometimes insight is obtained by breaking with traditional models and designing entirely new ones with new concepts. Since they lead us to search for aspects which may be been neglected at first. Failures can be prelude to successes if we can find the reasons of these failures.
A model must include the possibility of its improvement in the light of the experimental or observational data. Before making a model for the whole system, it may be convenient to make partial models of subsystems, test their validity and then integrate these partial models into a complete model. Sometimes existing models are combined to give models for bigger systems.
Often models are unified so that the general model includes the earlier models and special cases. One may think of models for small modules and by combining them in different ways, one may get models for a large number of systems.
No model is perfect and every model can be improved. However each such improvement may cost time and money. The improvement in the model must justify the investment made in this process.
For making a mathematical model, one has first to identify the state variables and then specify the relations between them. The right choice is of the most importance. Every model contains some parameters and these have to be estimated. The model must itself suggest experiments or observations and the methods of calculation of these parameters.
Without this explicit specification, the model is incomplete.