Friendly Approach To Functional Analysis, A (Essential Textbooks in Mathematics)

This book constitutes a concise introductory course on Functional Analysis for students who have studied calculus and linear algebra. The topics covered are Banach spaces, continuous linear transformations, Frechet derivative, geometry of Hilbert spaces, compact operators, and distributions. In addition, the book includes selected applications of functional analysis to differential equations, optimization, physics (classical and quantum mechanics), and numerical analysis. The book contains 197 problems, meant to reinforce the fundamental concepts. The inclusion of detailed solutions to all the exercises makes the book ideal also for self-study. A Friendly Approach to Functional Analysis is written specifically for undergraduate students of pure mathematics and engineering, and those studying joint programmes with mathematics.

"The book is written very clearly and notions are described via many illustrations and examples. I consider the book very useful for (undergraduate) students in mathematics, physics and engineering, who have passed some courses on metric spaces and linear algebra." -- zbMATH

"This is a nice and modern introduction to the topic ... If the reader is a student who wants to be become proficient in the subject, then solving the exercises, or as many as possible, is an excellent way to acquire the necessary skills. The flexible possibilities provided — the text can be used as lecture notes for a course, or as a tool for self study, and even as a handbook to look up some definitions or theorems." -- European Mathematical Society

"The book is unusual among functional analysis books in devoting a lot of space to the derivative. The 'friendly' aspect promised in the title is not explained, but there are three things I think would strike most students as friendly: the slow pace, the enormous number of examples, and complete solutions to all the exercises." -- MAA Reviews