Real and Convex Analysis

ISBN-13: 9781489998590 / Angielski / Miękka / 2015 / 161 str.

Robert J Vanderbei;Erhan C Nlar

Opis

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. It lays the groundwork for the needs of classical fields as well as the important new fields of optimization and probability theory.

Recenzje

From the reviews:

“The purpose of this slim volume is to serve as a (very quick) introduction to analysis for advanced undergraduate or graduate students in science and engineering. Einlar and Vanderbei (both, Princeton) base this introduction to analysis on metric spaces. … Summing Up: Recommended. Upper-division undergraduates and graduate students.” (D. Robbins, Choice, Vol. 50 (11), July, 2013)

Spis treści

​ ​Sets and Functions.- Metric Spaces.- Functions on Metric Spaces.- Differential and Integral Equations.- Convexity.-Convex Optimization.- Measure and Integration.- Bibiography.-Index.-

O autorze

Erhan Cinlar, Professor and former Chair of Operations Research and Financial Engineering, Princeton University Robert J. Vanderbei, Professor and former Chair of Operations Research and Financial Engineering, Princeton University

Blurb

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.