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.
-->
Request Inspection Copy
-->
Frequently asked questions
Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
Perlego offers two plans: Essential and Complete
Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go. Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access A Friendly Approach to Functional Analysis by Amol Sasane in PDF and/or ePUB format, as well as other popular books in Mathematics & Functional Analysis. We have over one million books available in our catalogue for you to explore.
As we had discussed in the introduction, we wish to do calculus in vector spaces (such as C[a, b], whose elements are functions). In order to talk about the concepts from calculus such as differentiability, we need a notion of closeness between points of a vector space.
Recall for example, that a real sequence (an)n∈N is said to converge with limit L ∈ R if for every
> 0, there exists an N ∈ N such that whenever n > N, |an − L| <
. In other words, the sequence converges to L if no matter what distance
> 0 is given, one can guarantee that all the terms of the sequence beyond a certain index N are at a distance of at most
away from L (this is the inequality |an − L| <
). So we notice that in this notion of “convergence of a sequence”, indeed the notion of distance played a crucial role. After all, we want to say that the terms of the sequence get “close” to the limit, and to measure closeness, we use the distance between points of R. A similar thing happens with continuity and differentiability. Recall that a function f : R → R is said to be continuous at c ∈ R if for every
> 0, there exists a δ > 0 such that whenever |x − c| < δ, |f(x) − f(c)| <
. Roughly, given any distance
, I can find a distance δ such that whenever I choose an x not farther than a distance δ from c, I am guaranteed that f(x) is not farther than a distance of
from f(c). Again notice the key role played by the distance in this definition. The distance between points x, y ∈ R is taken as |x − y|, where | · | : R → [0, ∞) is the absolute value function, given by
If we imagine the real numbers depicted on a “number line”, then |x − y| is the length of line segment joining x, y visualised on the number line. See the following picture.
But now if one wants to also do calculus in a vector space X (for example C[a, b]), there is so far no ready-made available notion of distance between vectors. One way of creating a distance in a vector space is to equip it with a...
