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 ...
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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. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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