Are All PDE Books a NIGHTMARE?!

[@actuariallurker9650]

As a Math and Physics double degree undergrad- I used Boyce and DiPrima back in the 8Os for my math major and used the problem solving books for some applied PDE courses. That way I could get BOTH theory and practice. Once I got to junior year I took Hilbert spaces and Lie Group courses at the grad level as an undergrad using Knapp's text for the latter.

[@CrazyShores]

Which title the book by Knapp?

[@MathematicalToolbox]

Today, we’re discussing PDE books and whether there exist PDE books that are not a nightmare. The answer, of course, is both yes and no. Feel free to share books and give your input in the comment section below! Watching the video back I need to make a clarification. I say "problem solving" type PDE books to indicate the usual run of the mill undergraduate level PDE book (Farlow). These are the books that cover separation of variables, Fourier Transforms, etc. I also use "theory" to mean PDE books that are more rigorous (Evans). i.e. they are much more formal and have more theorems and proofs. Many times their exercises are more involved and ask the reader to show certain results or prove theorems. Note that there are books that try to do both (Pivato). Patreon: patreon.com/MathematicalToolbox Discord: discord.gg/gqhRwfhXMM Check out our affiliate links in the description too!

[@edwardgraham-j8l]

Really smooth and most helpful! Thank you. My degrees are in engineering but I've had a few analysis courses and Measure theory ... love the books you are recommending. If you don't mind, I's appreciate your sharing your background and career ... I am retired so I study mathematics for fun!

[@MathematicalToolbox]

I talk about my background a little more in depth in another video, but my formal background is a minor in applied math. Since graduating (non technical degree), I've learned a handful of subjects and dabbled in a bunch of other ones. kzbin.info/www/bejne/f5iXeXSbjJyqY6csi=IwBfIc4uAKfT0tkJ

[@dacianbonta2840]

yes. pde theory IS a nightmare a tower'o'babel-style nightmare, a Godly gift to remind us how little we know and how little we can know.

[@jedediahjehoshaphat]

What's worse yet? PDE books that assumes you have working knowledge in Advanced Functional Analysis from the get go 😂

[@MathematicalToolbox]

😂 yikes

[@Galaxia496]

Have you heard of Partial Differential Equations: A First Course by Rustum Choksi? It's supposed to require just real analysis, basic familiarity with multivariable calculus, and linear algebra.

[@MathematicalToolbox]

The professor actually reached out and told me about it. It's actually VERY good. I would even say it's the most readable book on the theory of PDEs. This is a great book and great recommendation. Thank you for sharing it with us.

[@lalrinpuia_tlau]

Check out Intro to Partial Differential Equations - Sankara Rao. It's a diluted version of Sneddon's book. PDE by Nandakumaran & Datti is also good.

[@keithwald5349]

For physics, a really nice book, focusing on inhomogeneous problems, is "Elements of Green's Functions and Propagation" by Gabriel Barton. It's a very friendly, straightforward, easy to read book with lots of worked examples that goes through most of the linear PDE Green's function techniques (for potentials, diffusion, waves, and Helmholtz equations) relevant to physics.

[@MathematicalToolbox]

Thanks for this one! Looks cool.

[@encapsulatio]

Can you please link videos or if not make videos with your up to date recommendations for the best books that explain the clearest all the prerequisites that are needed before buying the books you recommended in this video for PDEs? Thank you so much as always.

[@CrazyShores]

"the best books" is subjective... Are you a mathematician looking for a formal textbook on the theory of PDEs, or do you just want to be able to solve some PDEs for applications in physics and engineering? The books to use and the prerequisites are very different in the two cases!

[@MathematicalToolbox]

You're gonna want at least Calculus I-III, ODEs, and Linear Algebra for any book on PDEs. Most theory of PDE books will require at least real analysis in addition. If you want to understand the theory books fully, then you'll want measure theory and functional analysis. The amount of measure theory and/or functional analysis required will vary from book to book. Some theory of PDE books will even give you the functional analysis and/or measure theory in text. Past this point, you'll find more specialized books, and you'll know what you need once you get there. As @Crazyshores says, there are only best books for a particular person, not in general.

[@encapsulatio]

@@MathematicalToolbox Thanks for replying so fast. What books do you find to be the best at teaching how ODEs, and Linear Algebra are used practically in the real world?

[@AdityaNair-c7t]

Do you have a recommendation for a pde book for someone just getting into the theory behind cfd?

[@MathematicalToolbox]

Tbh I am not knowledgeable enough to give you a good recommendation. I would suggest you ask on Reddit. If I had to give a suggestion, I would start with the Evans book first and then Salsa and Verzini there after. I just found the one by Herron and Foster. It looks a little elementary early on, though. Let me know if that works for you or not.

[@eliasmai6170]

wait what are these books gear towards to?

[@MathematicalToolbox]

I'm not sure what you mean exactly. There are three different types of books in this video with at least two different target audiences. With the exception of the last set of PDE books everything else here is at the undergraduate level. Scientists and engineers should be able to understand everything except for the theory of PDE books. I recommend analysis for this.

[@awindwaker4130]

Oh thank God, it's not just me. I bought a PDE book, and I struggled to get through the first few pages. It assumed too much prior physics knowledge for me.

[@MathematicalToolbox]

What book was it? Some books might bamboozle you into thinking you need to have a background in physics. They will usually tell you in the preface, though. I almost dropped ODEs early on because of that exact same situation. We were using Boyce and Diprima, and I also had a terrible professor. All the dumb applications and direction fields in the beginning really overwhelmed me early on. Having some background on the subject can really help, but picking the right book is essential. Thanks for sharing, and stay strong!

[@hubomba]

I used Strauss for my undergrad PDE course and honestly it felt like a 4 month blackout where I woke up with a 3.5 on the other end. Seemed like I learned nothing and we had a great professor for the course. I couldn't tell you what the goal of the Strauss book is honestly, really overpriced too. Glad it didn't make the cut for this video xD.

[@MathematicalToolbox]

I've had a LOT of people tell me that Strauss was a nightmare. I'm glad I never had to use it. Respect for making it through!

[@αηομαλψ]

Thoughts on PDEs by Fritz John?

[@MathematicalToolbox]

I've skimmed through it, and it's not my thing. I like books that are a little easier and straightforward to read with plenty of examples. Your thoughts on it?

[@TheIllerX]

I bought that one a long time ago for a course in PDE. Thankfully I took the course later on when they had changed the book. In my opinion this is one of the worst books on PDEs ever written for several reasons. 1. It uses some notation it does not explain. 2. Some claims are given without explanation. 3. Does not go deeper into the topics to bring a better understanding, but instead tries to obscure simple concepts. 4. Not much explanation on what is actually going on. If you already have taken courses in PDE so that you really understand the stuff, then you will still have problems understanding his explanations. Also, you will then gain nothing new, since you already know the stuff on a deeper level. So this is a book that is not really for anybody, neither the beginner (due to the confusing presentation) or the advanced reader (since he does not present the stuff in a rigorous way and it does not contain any advanced materials anyway). There are tons of other PDE books out there. Almost all of them better than this.

[@CrazyShores]

Hi great video as always! I wanted to buy the book from Wazwaz but it's insanely priced 😢 you didn't mention Asnar and Haberman this time! They're not your favourites? I bought Pivato thanks to your review (found it new but half price) and Asnar used, now I'm waiting to find a reasonably priced copy of Haberman!

[@MathematicalToolbox]

Wazwaz has another book that doesn't have the Solitary Waves Theory stuff, but it's still a little pricey. I used Asmar as a reference when I took my BVP course. Maybe I'll do a video on it at some point. I've actually only looked at Haberman a couple of times. I don't really have an opinion on it. What are your thoughts on the Pivato book? Here's an affiliate link to the Wazwaz book: amzn.to/4h5VGud

[@CrazyShores]

@@MathematicalToolbox yes please a video on Asmar 🙏🏼 never even started with Pivato 😁 i'm still working through complex analysis, but I'm on pause since half November...

[@CrazyShores]

​@@MathematicalToolbox actually Asmar didn't came as a recommendation, I really checked the PDF and liked it. The one by Haberman too I checked the PDF and looks pretty accessible, but I also saw your video and you seemed to like it!

[@CrazyShores]

@@MathematicalToolbox Yesterday I saw a video by @OceansofMath and he highly recommends the book by Haberman!

[@CrazyShores]

@@MathematicalToolbox I recently saw a video from another KZbin channel, @OceansofMath, and Haberman comes as highly recommended... Yesterday I was finally able to find it used at an affordable price and ordered it!

[@farhanniazi94]

Differential equations have always been an elusive topic for me, perhaps owing to my interests (biostatistics and psychometrics) which don’t require them outside of specialized topics like time series, but even that is more relevant to finance. I do notice that dynamical systems are popular though… i wonder if anyone here has tried the book “Introductory Mathematical Analysis for Quantitative Finance” by Ritelli. It has chapters on DE and PDE and is the closest thing to a statistics oriented intro to DE that i can find … would be nice to find a DE book purely for statistics students because i don’t really care about physics or engineering.

[@MathematicalToolbox]

You can check out the book Partial Differential Equations for Probabilists by Stroock. It is a little advanced, but let me know what you think. Thanks for sharing!

[@farhanniazi94]

@ thanks for the recommendation! I’ll check it out 🙏🏽

[@dimwit818]

A recommendation: Partial Differential Equations 3 volume set 3rd edition by Michael Taylor.

[@CrazyShores]

I checked it out and it looks like a very comprehensive trilogy on PDE! It seems pretty tough though, very formal for pure mathematicians

[@TranquilSeaOfMath]

A nice book overview. I love the AMS grad series, a lot of interesting topics; they're pricey though.

[@MathematicalToolbox]

Indeed! Which AMS book is your favorite?

[@TranquilSeaOfMath]

@@MathematicalToolbox I have a GSM book on Tropical Algebra, which I haven't read much of. I have an Analysis book, from the Sally series I thnk, which is an undergrad text.

[@kamalhaider397]

Great! I think farlow pde, salsa in action and then Lawrence Evans are good choices but later two books required good foundations in real analysis and measure theory in order to have learn pde in pure domain

[@MathematicalToolbox]

Yeah, if you want to understand everything, you'll need a more technical background! Thanks for sharing.

[@paraseth]

Book by courant and hilbert were very helpful for me ( physicist)

[@Andrew_J123]

Hey! You should check out Robert Ash's books. I'm quite liking them and they have solutions attached to them as well.

[@MathematicalToolbox]

Indeed. I talk about his Analysis book here, and I even had his Measure Theory book at one point, but I ended up returning it as the spine was starting to sag. Never bought it again as it was a little pricey. I also have his book on Probability and his wife's book on Probability. Which of theirs is your favorite?

[@frankjohnson123]

I'm so relieved you said Evans was on the more difficult side, had a lot of trouble with that one.

[@MathematicalToolbox]

I'm happy that you feel validated. This is one of my goals for the channel. There are some individuals within the mathematics community that will attempt to shame or belittle those of us that have difficulty with popular books such as Evans or Rudin. In reality, some of these books might not be appropriate for us given our current background in mathematics. This can look like giving Rudin to an undergraduate engineering student that wants to pick up analysis in their free time. Or in the case of Evans, giving it to an engineering student without a background in analysis. Both are a bad idea, I would argue. By the way, just out of curiosity, what year were you (in undergrad or grad school) when you used Evans, what were the prerequisites, and how much of it were you required to read? I've heard some guys say they used the first part of Evans as an undergrad. Couldn't imagine it! Thank you for sharing.

[@frankjohnson123]

@@MathematicalToolbox I was self-learning the subject after graduating undergrad in Physics. I had taken a few upper level math courses but never took an actual course in real analysis, moreso just picking up bits of it as I needed. Reading Evans was one of those instances where it hurt to not have a more solid foundation, because while I could understand it on a line-by-line basis, it became too much to keep track of at once.

[@sieni221]

Ive mainly just used evans.

[@adryanblack13]

What is the need to learn PDEs?

[@walter274]

Thanks. I'm not a DE guy, so i don;t know much about them.

[@40yearoldman]

Boundary Value Problems by David Powers

[@byronwilliams7977]

I really could have used this video 4 years ago.

[@MathematicalToolbox]

rip XD. What book did you use back then?