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Introduction to Differential Geometry for Engineers
This outstanding guide supplies important mathematical tools for diverse engineering applications, offering engineers the basic concepts and terminology of modern global differential geometry. Suitable for independent study as well as a supplementary text for advanced undergraduate and graduate courses, this volume also constitutes a valuable reference for control, systems, aeronautical, electrical, and mechanical engineers.The treatment's ideas are applied mainly as an introduction to the Lie theory of differential equations and to examine the role of Grassmannians in control systems analysis. Additional topics include the fundamental notions of manifolds, tangent spaces, vector fields, exterior algebra, and Lie algebras. An appendix reviews concepts related to vector calculus, including open and closed sets, compactness, continuity, and derivative.
NASA Technical Note
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Proceedings
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Expected Number of Maxima and Minima of a Stationary Random Process with Non-Gaussian Frequency Distribution
A method is outlined for calculating the expected number of maxima or minima of a random process with non-Gaussian frequency distribution from the statistical moments of the process and its first two derivatives. This method is based on an estimate of the joint frequency function of the process and its first two derivatives given by mesm of a generalized form of Edgeworth's series; the procedure thus consists essentially in applying a correction to the results for a Gaussian process. The functions required in this procedure are calculated for the first two correction terms; therefore, the effects of skewness and kurtosis can be calculated, provided the required moments are known. Expressions are given for these moments in terms of multiple correlation functions and multi-spectra, and the relations between these functions for a random output of a linear system and those for the random input are indicated.
Monthly Catalog, United States Public Documents
February issue includes Appendix entitled Directory of United States Government periodicals and subscription publications; September issue includes List of depository libraries; June and December issues include semiannual index
