Ordinary Differential Equations Books

[Falgun]

I am trying to self study Ordinary Differential Equations and am totally fed up of "cookbook style ODEs". I have recently finished Hubbard's Multivariable Calculus Book and Strang's Linear algebra book. I would like a rigorous and Comprehensive book on ODEs. I have shortlisted a few books below however feel free to suggest others. Please also tell the reason for liking/disliking a book.

1. Tenenbaum & Pollard
2. Ince
3. Coddington & Levinson (Theory of ODEs)
4. Coddington & Levinson (Intro to ODEs)
5. Hirsch & Smale
6. Hirsch, Smale & Devaney
7. Birkhoff & Rota
8. Hurewicz
9. George Simmons (Not the 3rd edition which I hear is horrible)
10. Hale
11. Hubbard & West
    
    P.S. Also sorry for any mistakes , this is my first thread.

 

[S.G. Janssens]

3. Recommended (essential?) reading as a basis for research in ODEs and classical analysis.
5. Good for the dynamical systems approach towards ODEs, particularly for its beautiful connection with linear algebra.
6. More modern than 5. but with less emphasis on linear algebra. Since even nonlinear (semilinear) theory depends a lot on linear results, I would prefer 5, but this is a matter of taste.
10. Recommended reading as a basis for research in ODEs as well as various classes of DDEs and other infinite dimensional systems. Proofs may lack detail or even contain small factual errors, but the ideas are essential.

More recommendations: Amann (directs towards research, particularly if you are interested in extending towards infinite dimensions), Logemann and Ryan (for an introduction to systems and control), Chicone (directs towards research and with a particular focus on applications to physics), books by Arnol'd (geometric theory, Russian school).

I could go on... Super that you are interested in learning about this subject. If you need more specific pointers, let me know.

 

[Falgun]

3. Recommended (essential?) reading as a basis for research in ODEs and classical analysis.
5. Good for the dynamical systems approach towards ODEs, particularly for its beautiful connection with linear algebra.
6. More modern than 5. but with less emphasis on linear algebra. Since even nonlinear (semilinear) theory depends a lot on linear results, I would prefer 5, but this is a matter of taste.
10. Recommended reading as a basis for research in ODEs as well as various classes of DDEs and other infinite dimensional systems. Proofs may lack detail or even contain small factual errors, but the ideas are essential.

More recommendations: Amann (directs towards research, particularly if you are interested in extending towards infinite dimensions), Logemann and Ryan (for an introduction to systems and control), Chicone (directs towards research and with a particular focus on applications to physics), books by Arnol'd (geometric theory, Russian school).

I could go on... Super that you are interested in learning about this subject. If you need more specific pointers, let me know.

Thanks a lot I'll definitely check out your other recommendations especially arnol'd (as I have heard about it before) .

Also , I have heard 1 is quite comprehensive, so would i be better off starting with 1 & 7 and then moving on to arnol'd & 10 or should i start with 3 and then move to more advanced books. (I would love to read everything but I'm a bit short on time.

 

[MidgetDwarf]

I am trying to self study Ordinary Differential Equations and am totally fed up of "cookbook style ODEs". I have recently finished Hubbard's Multivariable Calculus Book and Strang's Linear algebra book. I would like a rigorous and Comprehensive book on ODEs. I have shortlisted a few books below however feel free to suggest others. Please also tell the reason for liking/disliking a book.

1. Tenenbaum & Pollard
2. Ince
3. Coddington & Levinson (Theory of ODEs)
4. Coddington & Levinson (Intro to ODEs)
5. Hirsch & Smale
6. Hirsch, Smale & Devaney
7. Birkhoff & Rota
8. Hurewicz
9. George Simmons (Not the 3rd edition which I hear is horrible)
10. Hale
11. Hubbard & West
    
    P.S. Also sorry for any mistakes , this is my first thread.

I would recommend Ross: Ordinary Differential Equations. It is similar in style to Hubbard (the tone of writing). ie., gives a mentions as to why we care, great care explaining the steps, and its very concise and offers some insights.

Its not a rigorous math book per say. But its a well written book. I think you need a bit more math to get into a more theoretical book.

I am familiar with Simmons book. Its also good, but I prefer Ross, due to being more "gentle."

I think you need at least Analysics on Metric Spaces, Linear Algebra, and a bit of Topology to start reading more theory based ODE books.

 

[Falgun]

I would recommend Ross: Ordinary Differential Equations. It is similar in style to Hubbard (the tone of writing). ie., gives a mentions as to why we care, great care explaining the steps, and its very concise and offers some insights.

Its not a rigorous math book per say. But its a well written book. I think you need a bit more math to get into a more theoretical book.

I am familiar with Simmons book. Its also good, but I prefer Ross, due to being more "gentle."

I think you need at least Analysics on Metric Spaces, Linear Algebra, and a bit of Topology to start reading more theory based ODE books.

I have Baby Rudin & Apostol Analysis Book with me right now . I could probably spend a month getting the topology from first few chapters of apostol and save rudin for when I want to deep fry my brain. Would that be enough background to study ODEs in more depth?

 

[S.G. Janssens]

Thanks a lot I'll definitely check out your other recommendations especially arnol'd (as I have heard about it before) .

Also , I have heard 1 is quite comprehensive, so would i be better off starting with 1 & 7 and then moving on to arnol'd & 10 or should i start with 3 and then move to more advanced books. (I would love to read everything but I'm a bit short on time.

The answer depends a bit on your goal. You wrote that you are self-studying. Do you have in mind taking a test or exam on this material? If so, then maybe you could give a list of required topics. (And I should have asked for that right away.)

On the other hand, if there are no formal constraints, then it really depends on your own goals and interests. ODEs is a large field, with many ties to other fields. Keeping in mind that

• you seek an entry point to the subject,
• you want it to be rigorous,
• you have some background knowledge in analysis, but you still need to learn that subject proper,
• I prefer to comment only on books that I read (at least in part) myself,

then I would recommend beginning with 5. or 6., with a mild preference for 6. unless you prefer a stronger focus on the relationship between ODEs and LA. You will have fun, see examples and learn a lot. Afterwards, you will be better prepared to choose how to continue.

The more advanced books such as 3. and 10. (and some books that I mentioned, such as Amann) are best for cherry picking instead of integral reading. Doing the former is motivating, but doing the latter can be quite dull.

(Note that books such as 5. and 6. and 10. contain hardly any (or no) material on ODE boundary value problems: The focus is strongly on the ODE initial value problem, the generated dynamics and its geometry. In that sense, I believe that no single book can be truly comprehensive.)

 

[Falgun]

No , I don't have to give an exam as I am not in university yet . I just find myself with free time and want to cover as much material as possible with my background. Right now I am more interested in breadth than depth. I will go into much more depth when I take a course on ODEs. Though my primary goal is physics , I find pure math worth learning on its own.

Right now I am leaning heavily to using 1 & 3 (using 1 to ease me into 3) and then moving on to arnol'd if I have the time and maybe even stopping by to flip through 5 or 6 .

PS Do you have some lecture series you find particularly relevant?

 

[Frabjous]

Braun was one of standards back in the 90’s. It has some wonderful ‘real world’ examples.

 

[MidgetDwarf]

I have Baby Rudin & Apostol Analysis Book with me right now . I could probably spend a month getting the topology from first few chapters of apostol and save rudin for when I want to deep fry my brain. Would that be enough background to study ODEs in more depth?

I don't think a month is enough time. You would still need to learn about the other parts of Analysis.
You stated your goal was Physics. I believe a better use of your time, would be working through an ODE book like Ross or Simmons. Learning LA from say Linear Algebra Done Right. You could also practice Analysis during this time.

Linear Algebra Done Right has the pitfall of dealing with determinants at the end. But since you read Strang it should be a nonissue.

Then try to learn ODE from a theoretical pov.