Erhan Cınlar, Robert J Vanderbei Real and Convex Analysis

Annotation

This book offers a first course in analysis for scientists and engineers. It can be used at the advanced undergraduate level or as partof 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 briefintroductions to differential and integral equations, convex analysis, and measure theory. The treatment is modern and aesthetically pleasing. It lays the groundwork for the needs of classical fields as well as the important newfields of optimization and probability theory.