Which one is the best textbook for self-studying differential equations?

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Discussion Overview

The discussion revolves around selecting an appropriate textbook for self-studying differential equations, including both ordinary and partial differential equations. Participants share recommendations, personal experiences with various texts, and considerations regarding rigor, completeness, and applicability of the books.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant suggests checking university libraries to evaluate the recommended textbooks personally before purchasing.
  • Another participant expresses a preference for Boyce and DiPrima's text, while also mentioning Coddington and Carlson as favorable options.
  • Concerns are raised about the rigor of Zill's book, with one participant noting it lacks mathematical rigor compared to other texts.
  • Participants discuss the definition of rigor in the context of differential equations, questioning how to measure it effectively.
  • A participant recommends Birkhoff and Rota's book for its rigor, suggesting a strong calculus background is beneficial for understanding it.
  • There is a mention of the high price of some textbooks, with participants noting that used copies can be found for significantly less.
  • One participant highlights that some readers have reported typos in certain texts, which could affect the learning experience.
  • Another participant shares their experience with various textbooks, asking about the differences in rigor between them.
  • There is a discussion about the balance between theory and application in differential equations, with participants expressing interest in both aspects.
  • Some participants recommend Arnold's book for its rigorous and geometric approach, while others prefer more accessible texts.
  • One participant expresses uncertainty about which textbook to choose, indicating a desire for a solid, rigorous resource with comprehensive coverage.

Areas of Agreement / Disagreement

Participants do not reach a consensus on which textbook is the best for self-studying differential equations. Multiple competing views regarding the rigor and applicability of various texts remain, with some participants favoring more applied approaches while others seek rigorous theoretical foundations.

Contextual Notes

Participants express varying definitions of rigor and completeness in differential equations texts, indicating that personal preferences and mathematical backgrounds may influence their choices. The discussion reflects a range of experiences with different textbooks, highlighting the subjective nature of selecting educational resources.

Who May Find This Useful

This discussion may be useful for individuals interested in self-studying differential equations, particularly those seeking recommendations on textbooks that balance rigor and accessibility. It may also benefit readers considering their mathematical background and learning preferences when selecting a resource.

dijkarte
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I'm considering self-studying differential equations, ordinary and partials, and for this I need a good book that teaches. I checked some universities syllabus and found that the most recommended texts are these:

http://www.amazon.com/dp/0321747747/?tag=pfamazon01-20

http://www.amazon.com/dp/0470458364/?tag=pfamazon01-20

http://www.amazon.com/dp/0470383348/?tag=pfamazon01-20

However I found this one with an excellent review:

http://www.amazon.com/dp/0495383163/?tag=pfamazon01-20

Considering the high price of these texts, I need to pick one that's really excellent, no missing theories, or proofs, and touches as well the qualitative methods, with nice illustrations and figures of course.

Thanks.
 
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I'd say you go to a library (of any nearby university) and check them out for yourself. Those are, as you say, pretty standard texts and won't be difficult to find. Have a look at them first, decide which one you like best, and then buy if you have to.

In my opinion, the best of those you mentioned is Boyce - diPrima. I also like Coddington - Carlson
 


Yes I did already, and based on my very little knowledge of DEs, I found the Zill and Cullen is quite interesting with all these graphs and illustrations. However I'm not sure how it compares to others in terms of mathematical rigor.
 


Zill is the least rigorous ODE book I've experienced but you don't need a lot of rigor for a LD ODE course, particularly if you want to be applied (though you should learn about existence and uniqueness of solutions). I've said it many times but I like Ross, Differential Equations.

https://www.amazon.com/dp/0471032948/?tag=pfamazon01-20

If your library has this one, I'd recommend giving it a shot.
 
Yeah this is very concerning to me, rigorous! I don't want to pay a lot for a text that it's not complete. I prefer a pure mathematical text, but I don't know how to measure rigorous when it comes to DEs. What about the Dover's ODE?
 
Define rigor in DE world? :)
 
The books you posted are mostly for applied/computational differential equations courses.

Ordinary Differential Equations by Garrett Birkhoff and Gian-Carlo Rota is a rigorous textbook. I recommend a background in calculus at the level of Apostol's Calculus or Spivak's Calculus. Linear Algebra would also be beneficial, but it's not required.
 
Thanks. But ~400 pages for ~$233? And old text?
 
And 2.5 out of 5 stars?

Sorry this is overpriced I guess.
 
  • #11
Yup I will go with this one first. Thanks.
 
  • #12
dijkarte said:
Thanks. But ~400 pages for ~$233? And old text?

Sellers on sites like Amazon and AbeBooks usually list it for much less. I picked up a used copy for $10.
dijkarte said:
And 2.5 out of 5 stars?

Sorry this is overpriced I guess.

Yes, it seems as though some readers were not happy with some typos and mistakes toward the end of the book. They shouldn't be a problem to an active reader though. One of the reviews on Amazon sums it up perfectly.

I hope that Tenenbaum and Pollard's book works for you. It's not rigorous, but it's pretty complete. :)
 
  • #13
I've not ordered it yet, but how it differs from the Diprima or Nagle's in terms of math rigor?
What I would benefit from buying the more expensive texts in learning DEs?

Thanks.
 
  • #14
dijkarte said:
I've not ordered it yet, but how it differs from the Diprima or Nagle's in terms of math rigor?
What I would benefit from buying the more expensive texts in learning DEs?

Thanks.

I have never used Nagle, but I have used Birkhoff & Rota, Zill, Boyce & DiPrima, Edwards & Penney, and Tenanbaum & Pollard (yes, I have a lot of differential equations textbooks :biggrin:).

What parts of differential equations interests you? Are you interested in the theory? applications? modeling? And what is your current mathematical background?
 
  • #15
Interested in both theory, and applications in general, with no specific engineering or science area.

I took Calculus courses up to multidimensional and vector calculus. I took a linear algebra and numerical analysis courses.
 
  • #17
Still trying to find a textbook?

That textbook looks similar to the other standard introductory differential equation textbooks: Elementary Differential Equations and Boundary Value Problems by Boyce & DiPrima or Elementary Differential Equations with Boundary Value Problems by Edwards & Penney. Looking back at your course experience, I think that one of those two textbooks would be suitable. You can find copies of previous editions on sites like Amazon or AbeBooks for about $10. The only real difference between the current edition and the most previous edition is a few more exercises and one or two applications.
 
  • #18
[URL="https://www.amazon.com/dp/048667620X/?tag=pfamazon01-20 - Farlow - $10 (USD)
[/URL]
This book is pretty useful at getting you started in PDE's, introducing the different classifications, and how to approach them. It is written for beginners to PDE's, and so is very easy to read compared to most math books, and is short so it doesn't take much time to read. After that, you can pick up a more advanced text. It's also extremely cheap and makes a decent reference. In a pinch, you could probably read most of this painlessly without studying ODE's first (probably not the best idea, though).

ODE's - Arnold - $48
This book is extremely rigorous, and not your average DE book - it emphasizes geometric concepts in DE theory. If you are very strong with calc and linear algebra, this is a great book. Topology/Abstract Algebra would help, but you can get by with looking up things as you go. If you've just taken the first 1 or 2 calc courses in ugrad, you will probably want to hold off on this for a bit.
 
Last edited by a moderator:
  • #19
I still cannot decide...some reviews of the books make me hesitate. :(

I don't mind paying a lot for a book which is solid and rigorous, with a lot of theories, figures, and proofs.

Differential Equations with Boundary-Value Problems by Dennis G. Zill looks promising...

I had the chance to review it and it's full of figures and very rigorous and colorful.

Thanks for advice anyway.
 
  • #20
I used Zill for my intro to DE's course - it was an older version of this one. If the two are anything alike, I don't think it is what you are looking for.
 
  • #21
Now I changed my mind again...so what am I looking for? I don't know really.

Lets say I bought them all, which parts of which books to use for which subjects so that I have rigorous explanation and proofs on each topic?
 
  • #22
How much experience do you have with theorems and proofs?

Have you worked through Spivak's Calculus or Apostol's Calculus?
 
  • #23
IMHO, good enough to understand any decent text :)

Spivak's yes...but not Apostol's.

But at the same time I want something modern, not outdated text in style and content.
 
  • #24
I don't think you need to go through Apostol's calculus if you've already been through spivak's book. Stop wasting time and move on to the more interesting realms of math!
 
  • #25
Yeah my course I assigned to myself is DE :D, which is the one I missed.
 
  • #26
Library.
 
  • #27
Hmmm what about eLibrary? :D
 
  • #28
I'll second Arnold's book: if you know linear algebra and want a rigorous (and very geometric) treatment, this is definitely the best.
 
  • #29
After all searching and reading reviews...I decided to get The Dover's ODE book, which I found very gentle on my brain :D as novice to the subject.

Thanks for all!
 
  • #30
intwo said:
The books you posted are mostly for applied/computational differential equations courses.

Ordinary Differential Equations by Garrett Birkhoff and Gian-Carlo Rota is a rigorous textbook. I recommend a background in calculus at the level of Apostol's Calculus or Spivak's Calculus. Linear Algebra would also be beneficial, but it's not required.

Sorry to bump this thread.

How much more rigorous is this in relation to Ross?
 

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