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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.
List of contents
Sets and Functions.- Metric Spaces.- Functions on Metric Spaces.- Differential and Integral Equations.- Convexity.-Convex Optimization.- Measure and Integration.- Bibiography.-Index.-
About the author
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
Summary
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.
Additional text
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)
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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)
