MHB Struggling with Advanced ODEs? Here's Some Guidance and Recommended Texts!

[nacho-man]

I am taking and advnaced ODEs course at uni.

The first four weeks have been challenging but doable with some research outside.
As we approach more special functions, it has gotten hectic and I've even fallen two weeks behind :/. Some of the questions we get are insanely scary!

Our lecturer gives uploads some brief notes which are not enough for me to understand the material in the depth I require to do questions.
So far I have tried making use of Advanced Engineering Mathematics by Kreyzig and also Zill & Wright's book.

These have been quite good, but were empty on things like Green's Function and S-L functions. I have yet to see if they contain the other topics we are discussing.

I was hoping someone could recommend some texts which would include the topics that I have provided in the attached image. Additionally, how should I approach this subject, has anyone got any online recommendations? The last time I did a differential equations course was precisely last year so I've gotten a bit rusty.

Any help is appreicated!

 

[Fantini]

I recommend this book. It covers everything you've asked for, the explanations are well thought and much intermediate algebra is done. :)

 

[Euge]

I recommend Norman Lebovitz's notes here

http://people.cs.uchicago.edu/~lebovitz/eodesnotes.html

You should also review some real analysis if you want to tackle some of this material, especially if you're studying Sturm-Liouville theory and stability of solutions.

 

[Fantini]

I'd suggest linear algebra more than anything. I inferred that since he was studying with Advanced Engineering Mathematics by Kreiszig mathematical rigour is not what he's looking for, instead a more operational approach for beginners (which let's agree is not all that easy either). :)

 

[Euge]

I'd suggest linear algebra more than anything. I inferred that since he was studying with Advanced Engineering Mathematics by Kreiszig mathematical rigour is not what he's looking for, instead a more operational approach for beginners (which let's agree is not all that easy either). :)

I certainly agree that linear algebra is important for the study as well, but considering some of the topics in his list, I don't think linear algebra will be enough. Introductory treatments of special functions are usually covered in advanced calculus/real analysis courses, so that's why I mentioned real analysis review.

By the way, great book recommendation!

 

[Euge]

I am taking and advnaced ODEs course at uni.

The first four weeks have been challenging but doable with some research outside.
As we approach more special functions, it has gotten hectic and I've even fallen two weeks behind :/. Some of the questions we get are insanely scary!

Our lecturer gives uploads some brief notes which are not enough for me to understand the material in the depth I require to do questions.
So far I have tried making use of Advanced Engineering Mathematics by Kreyzig and also Zill & Wright's book.

These have been quite good, but were empty on things like Green's Function and S-L functions. I have yet to see if they contain the other topics we are discussing.

I was hoping someone could recommend some texts which would include the topics that I have provided in the attached image. Additionally, how should I approach this subject, has anyone got any online recommendations? The last time I did a differential equations course was precisely last year so I've gotten a bit rusty.

Any help is appreicated!

I also suggest looking through George Carrier and Carl Pearson's book on Ordinary Differential Equations. It's less theoretical than the other book I recommended, but it's concise and has very useful exercises.

 

[nacho-man]

You are all incredible!
Thank you one hundred times over, I will check all of these out!

I'd like to add that I was hoping something with more mathematic rigour than kreyzig (in reference to previous discussion on this post), which is why I've been seeking an alternate resource.

Regardless, I enjoy having more than a one resource at my disposal so it's great different sets of recommendations! :)

 

[nacho-man]

Hey, hope this post isn't considered spam, but I just wanted to thank you all again.

At the time I made this thread I was very distraught. Mathematics does not come easy to me (just check some of my previous threads if you want to see how bad :P) and I was feeling incredibly overwhelmed by this course which I had under-estimated and fallen behind.

I am feeling much better now and more confident after studying hard the past few days, so thank you all again, I couldn't have done it without you.