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During his imprisonment Poncelet studied projective geometry and wrote Applications d'analyse et de géométrie, 2 vol. (1862 64; "Applications of Analysis and Geometry").
The applications of analysis were also varied, including the theory of the vibrating string, particle dynamics, the theory of rigid bodies, the mechanics of flexible and elastic media, and the theory of compressible and incompressible fluids.
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His early mathematical research was mainly concerned with the Dirichlet series, a series introduced by Peter Dirichlet of Germany in the application of analysis to the theory of numbers.
The main vehicles for the application of analysis are differential equations, which relate the rates of change of various quantities to their current values, making it possible in principle and often in practice to predict future behaviour.
Put differently, the course aimed at equipping students with conceptual knowledge (an understanding of scientific methods), and procedural knowledge (application of analysis methods and scientific writing).
In his Essay on the Application of Analysis to the Probability of Majority Decisions (1785), he advocated a particular voting system, pairwise majority voting, and presented his two most prominent insights.
Statistical significance between groups was performed by the application of analysis of variance ANOVA followed by Bonferroni's test.
Considerations in the choice and application of analysis methods are briefly summarized here and reviewed in depth elsewhere [ 59].
Many of the greatest applications of speech analysis will come at the nexus of qualitative behavioral analysis and quantitative lexical analysis.
The applications of spectral analysis in power systems can be found in power quality analysis, protection and control.
The applications of systems analysis in civil government obviously still have far to go before their potentialities are exhausted.
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