By Serge Lang

ISBN-10: 0201042231

ISBN-13: 9780201042238

This can be the 5th variation of Lang's caclulus booklet. It covers the entire issues typically taught within the first-year calculus series. The e-book involves 5 components: evaluate of easy fabric, Differention and ordinary capabilities, Integration, Taylor's formulation and sequence and capabilities of numerous Variables. each one component of a primary path IN CALCULUS comprises examples and purposes of the subject lined. moreover, the again of the ebook comprises precise recommendations to loads of the workouts. those can be utilized as worked-out examples, and represent one of many major alterations from past versions.

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Benslimane and Casablanca preserve their first and second rank regardless the curvature. Dakhla preserves its third rank for negative curvature but for positive curvature it loses its position. 8 1 Normalized criterion measurement Fig. 5 Recent Developments of SMAA Recent developments of SMAA include more efficient computational methods and extensions to different decision models. In most cases the SMAA computations can be performed very efficiently using straight forward Monte Carlo simulation.

Syst. Sci. 45(1), 69–81 (2014) 20 R. Lahdelma and P. Salminen 24. : A survey on stochastic multicriteria acceptability analysis methods. J. Multi-Criteria Decis. Anal. 15(1–2), 1–14 (2008) 25. : Implementing stochastic multicriteria acceptability analysis. Eur. J. Oper. Res. 178(2), 500–513 (2007) 26. : A stochastic method for robustness analysis in sorting problems. Eur. J. Oper. Res. 192(1), 236–242 (2009) 27. : Hit-and-run enables efficient weight generation for simulation-based multiple criteria decision analysis.

3) is expressed in a mathematical programming form. t. 4) ∀ xi ∈ C , = 1, . . 5) ∀ xi ∈ C , = 2, . . , q = 1, . . 9) σi+ , σi− ≥ 0 i = 1, . . 10) The objective function minimizes the total weighted classification error, where the weights are defined on the basis of the number of reference alternatives from each class (m1 , . . , mq ). 7) ensures that the class thresholds are defined in a decreasing sequence (ε is a small positive constant). 8) defines the scale of the additive model between 0 and 1 (0 corresponds to the performance of the least preferred 2 Data-Driven Robustness Analysis for Preference Disaggregation 25 alternative x∗ and 1 corresponds to the performance of an ideal action x∗ ).

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A first course in calculus by Serge Lang

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