Real and Convex Analysis [electronic resource] / by Erhan Çınlar, Robert J. Vanderbei. - IX, 161 p. online resource. - Undergraduate Texts in Mathematics, 0172-6056 . - Undergraduate Texts in Mathematics, .

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.

9781461452577

10.1007/978-1-4614-5257-7 doi

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.

Optimization.

QA299.6-433

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