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Titlebook: Computer Aided Proofs in Analysis; Kenneth R. Meyer,Dieter S. Schmidt Book 1991 Springer-Verlag New York Inc. 1991 Mathematica.algebra.alg

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,Lie Transform Tutorial — II,This survey paper is an extension of Meyer (1990) since it contains complete proofs of the main theorems and some generalizations of Lie transform theory. However, the first part of this paper deals with the applications of Lie transforms to various perturbation problems leaving the technical proofs to the later sections.
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Interval Tools for Computer Aided Proofs in Analysis,A brief survey of theory and software implementations of interval and related techniques for computing with machine representable sets is presented with applications to computer aided proofs in analysis. Recent work on variable precision software is discussed.
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Shadowing Trajectories of Dynamical Systems,Computer simulation of the trajectories of deterministic systems involve truncation and rounding errors. A theorem is presented which describes a computer-assisted method for checking whether there is a true trajectory near the computer-generated one.
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MACSYMA Program to Implement Averaging Using Elliptic Functions,tic functions, a process which is most easily and accurately accomplished using computer algebra. We present the listing of a MACSYMA program which implements the method to 0(.), as well as the results of a run for which . is taken as a general cubic polynomial in . and .
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