Sasane Amol. Functional analysis and its applications

London School of Economics, 2013. — 92 p.The book is meant for final year undergraduate students. No prerequisites beyond knowledge of linear algebra and ordinary calculus (with e -δ arguments) are needed to read this book. Knowledge of the Lebesgue integration theory or topology is not assumed. Nevertheless, we will include illustrative examples that involve Lebesgue integrals, with the naive under-standing that the Lebesgue integral is simply a generalisation of the usual Riemann integral, which is rather more amenable to limiting processes. We will give a short introduction to the Lebesgue integral, entirely sufficient for treating our subsequent discussion, when we encounter the first such example. parts of the book marked with an asterisk (∗) may be more challenging as compared to the average level of difficulty of the book, and may be skipped, skim-read or studied, depending on the goals of the student. Thus the book should be accessible to a wide spectrum of students, and may also serve to bridge the gap between linear algebra and advanced functional analysis.