Introduction to Piecewise Differentiable Equations [electronic resource] / by Stefan Scholtes.
By: Scholtes, Stefan [author.].
Contributor(s): SpringerLink (Online service).
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BookSeries: SpringerBriefs in Optimization: Publisher: New York, NY : Springer New York : Imprint: Springer, 2012Description: X, 133 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9781461443407.Subject(s): Mathematics | Global analysis (Mathematics) | Functions of complex variables | Mathematical optimization | Mathematics | Analysis | Functions of a Complex Variable | Calculus of Variations and Optimal Control; OptimizationDDC classification: 515 Online resources: Click here to access online
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Springer eBooksSummary: This brief provides an elementary introduction to the theory of piecewise differentiable functions with an emphasis on differentiable equations. In the first chapter, two sample problems are used to motivate the study of this theory. The presentation is then developed using two basic tools for the analysis of piecewise differentiable functions: the Bouligand derivative as the nonsmooth analogue of the classical derivative concept and the theory of piecewise affine functions as the combinatorial tool for the study of this approximation function. In the end, the results are combined to develop inverse and implicit function theorems for piecewise differentiable equations. This Introduction to Piecewise Differentiable Equations will serve graduate students and researchers alike. The reader is assumed to be familiar with basic mathematical analysis and to have some familiarity with polyhedral theory.
This brief provides an elementary introduction to the theory of piecewise differentiable functions with an emphasis on differentiable equations. In the first chapter, two sample problems are used to motivate the study of this theory. The presentation is then developed using two basic tools for the analysis of piecewise differentiable functions: the Bouligand derivative as the nonsmooth analogue of the classical derivative concept and the theory of piecewise affine functions as the combinatorial tool for the study of this approximation function. In the end, the results are combined to develop inverse and implicit function theorems for piecewise differentiable equations. This Introduction to Piecewise Differentiable Equations will serve graduate students and researchers alike. The reader is assumed to be familiar with basic mathematical analysis and to have some familiarity with polyhedral theory.
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