Real and Convex Analysis [electronic resource] / by Erhan Çınlar, Robert J. Vanderbei.
Contributor(s): Vanderbei, Robert J [author.] | SpringerLink (Online service)Material type: TextSeries: Undergraduate Texts in Mathematics: Publisher: Boston, MA : Springer US : Imprint: Springer, 2013Description: IX, 161 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9781461452577Subject(s): Mathematics | Mathematical analysis | Analysis (Mathematics) | Mathematical optimization | Operations research | Management science | Applied mathematics | Engineering mathematics | Mathematics | Analysis | Appl.Mathematics/Computational Methods of Engineering | Operations Research, Management Science | OptimizationAdditional physical formats: Printed edition:: No titleDDC classification: 515 LOC classification: QA299.6-433Online resources: Click here to access online
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Sets and Functions -- Metric Spaces -- Functions on Metric Spaces -- Differential and Integral Equations -- Convexity.-Convex Optimization -- Measure and Integration -- Bibiography.-Index.-.
This book offers a first course in analysis for scientists and engineers. It can be used at the advanced undergraduate level or as part of the curriculum in a graduate program. The book is built around metric spaces. In the first three chapters, the authors lay the foundational material and cover the all-important “four-C’s”: convergence, completeness, compactness, and continuity. In subsequent chapters, the basic tools of analysis are used to give brief introductions to differential and integral equations, convex analysis, and measure theory. The treatment is modern and aesthetically pleasing. The book contains detailed illustrations, examples and exercises. It lays the groundwork for the needs of classical fields as well as the important new fields of optimization and probability theory.