read this to learn functional analysis

read this to learn functional analysis

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Do you want to learn functional analysis? In this video I talk about the book that I used to learn this amazing subject. Note functional analysis is considered to be a graduate level course and does require some background. Ideally you would have already had some advanced calculus and maybe some linear and abstract algebra as well. Some topology before hand would also help. The higher your level of mathematical maturity the better!

Ok so what is the book? It is called "Introductory Functional Analysis with Applications" and it is written by Erwin O. Kreyszig.

Please leave any comments or questions in the comment section below. Thank you:)

[travisporco]

This book is truly a thing of beauty. Kreyszig writes like he wants you to really get it...not just realize *he* gets it!

[JM-tyuq]

This book has been my bible for the last few months thanks to you, I have tried reading Brezis and other FA texts and I just found them impossible to learn from, Kreyszig definitely had pedagogy in mind.

[matthewkehoe]

I also have a copy of Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haïm Brezis and Functional Analysis: Introduction to Further Topics in Analysis by Elias M. Stein and Rami Shakarchi. Kreysig's book is very readable and usually goes into sufficient detail (although he doesn't use any measure theory). This is a great book for an applied mathematician, physicist, or engineer. If you are a pure mathematician then you should read the book by Brezis.

[kshitizmangalbajracharya]

It's extremely easy to follow this textbook. All you need is a familiarity with metric spaces and metric topology. It's the only possible choice to learn Functional Analysis even if you don't have any knowledge of Lebesgue Integration. I love this book. Kreyszig has a great ability to simplify complicated subject matter. His textbook on Differential Geometry is also quite good.

[robertschlesinger]

Kreysig is the author of the most popular Advanced Engineering Mathematics text. Said text is an excellent text and reference. Eventhough Kreysig's Functional Analysis text was published in 1978, it seems to me to be the most accessible functional analysis text for beginners . The edition shown in your video is an international student's edition. The domestic edition is a brown text, for those looking for the text.
As an added comment and heads-up, there are some great more contemporary texts on advanced linear algebra, including considerable functional analysis.

[Prof_Jeff]

Another book we have in common! I took a Functional Analysis course in my doctoral program and this was the text. One of the most enjoyable classes I ever took.

[cueto]

Yes this is a great book, we used the book on our intro to functional analysis course

[midnight]

Currently taking Functional Analysis (kinda on introductory level) course as a junior student majoring in applied mathematics and informatics. This is our core textbook, and, so far, I couldn't find a book better than this one. Others are much harder to comprehend.

[brightsideofmaths]

Greek letters shouldn't be a problem. One just has to learn them once and can use them for your entire mathematical life :)

[thomasblackwell]

Kreyzig is an excellent author. His Advanced Engineering Mathematics book is absolutely the best!

[LucasDimoveo]

Can you make a video explaining exactly what the hell Functional Analysis is? It's referenced a lot in discussions about PDEs, but since my mathematical maturity is quite low I don't understand anything

[williamvalentinmunozlopez]

So I'm neither a Math, nor a Logic student, but I find those symbols and formalism kind of aesthetic and meaningful. Where should I start (given my undergraduate engineering studies) if I want to understand and USE all that?

[sanjursan]

Also good is the book by Bachmann and Narici, and the Riesz book. Both are inexpensive Dover books.

[pinklady]

Only just today, I am exploring functional analysis.

I have ordered five more maths books. Not counting physics books, I probably now have nearly 12, possibly 15. I had previewed the pages before buying the books.

1) Algebraic number theory.
2) Axiomatic set theory.
I am interested in vectors and 3D stuff.

3) Advanced calculus(differential calculus and Strokes' theorem). I ordered this one, as I am almost finished the other calculus book by Ian Stewart.

4) "Special Relativity and Classical Field Theory" by Leonard Susskind. I now have a complete collection of three small books by same author.
I understand just the graphical descriptions of special relativity more than the mathematical description of it. I bought the book straight after watching a TV drama documentary called "Genius, " all 10 series with uncannily lookalike actors like "Albert Einstein" explaining special relativity with CGI graphics. I learned too uncertainty principles and other theorems by Einstein's contemporaries (all acted by lookalike actors). You can see "Genius" on National Graphical via Disney.

5) Concise Oxford Mathematics Dictionary. I had badly needed it. It is good enough for me, though not comprehensive enough for postgraduate students.

[tasneemyaser]

Hello .. Happy to hear you .. I study in Jordan the same subject and book .. I hope to hear the explanation of your lectures and get solutions to the questions kindly ..

[YitzharVered]

This is such a genuinely fun book to read! Up there with Anderson Aerodynamics, a real achievement for a pire math text. Got me through two five hour flights without issue. Much fun.

[jainamkhakhra]

This is amazing... Just in time. Next sem I've got Functional Analysis. Thanks a lot.

[dwchaosfan]

If you know of it, could you compare this book to Stein and Shakarchi's Functional Analysis? Also, a review of all four Princeton Lectures in Analysis series books would be appreciated.

[karanpk]

Sir, please make a video on Completion Theorem on Normed Spaces in this textbook.

[jiahao]

Really thanks for your recommendation, this book is really really good, you save me ton of time!!!