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Excerpt from Order of Magnitude Reasoning in Qualitative Differential Equations
The paper is organized as follows: Section 2 presents fundamental definitions and rules that govern the behavior of a solution to a set of qualitative differential equations. The basis of the definitions and the justifications of the rules lie in the theory of non-standard analysis with infinitesimals. Section 3 shows how these rules may be applied in the heavy block on the spring example and other examples. Section 4 presents an algorithm for constructing an envisionment graph from a set of qualitative differential equations. Section 5 discusses the chepachet program, which implements this algorithm. Section 6 makes suggestions for further work. We assume that the reader is familiar with standard theories of envisionment.
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Order of Magnitude Reasoning in Qualitative Differential Equations Classic Reprint
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LX-9781334016677
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Order of Magnitude Reasoning in Qualitative Differential Equations Classic Reprint
Da: PBShop.store UK, Fairford, GLOS, Regno Unito
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LX-9781334016677
Quantità: 15 disponibili
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Order of Magnitude Reasoning in Qualitative Differential Equations
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Paperback. Condizione: New. Print on Demand. This book presents qualitative differential equations, which combines order-of-magnitude reasoning with envisionment of mathematical equations. The theory presented in this book can be applied to dynamical systems containing parameters of various magnitudes. The author proposes two key innovations. Firstly, each state of the system is given a duration and the net change to each parameter during the state. Secondly, the author introduces a set of rules governing the behavior of functions over orders of magnitude. These innovations extend the reader's ability to analyze the dynamic behavior of systems, enabling inferences about systems with quantities of widely varying magnitudes. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Codice articolo 9781334016677_0
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