✍ Scribed by Çınlar, Erhan; Vanderbei, Robert J.
No coin nor oath required. For personal study only.
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.
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This new approach to real analysis stresses the use of the subject with respect to applications, i.e., how the principles and theory of real analysis can be applied in a variety of settings in subjects ranging from Fourier series and polynomial approximation to discrete dynamical systems and nonline