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