Books on PDEs: Recommendations for Rigorous Learning

[STEMucator]

I'm wondering if people have recommendations on this topic. It's something I've been meaning to tackle for a long time now. I'm interested in learning how to solve PDEs as well as learn about uniqueness theorems and such. The more rigorous the book is, the better.

I already have good experience with ODEs and I'm pretty comfortable with them. I also have some experience already with BVPs and Fourier series.

 

[R136a1]

A good intro book seems to be Strauss: https://www.amazon.com/dp/0470054565/?tag=pfamazon01-20

More rigorous books (and not exactly meant for a first course) are Evans and Renardy:
https://www.amazon.com/dp/0821849743/?tag=pfamazon01-20
https://www.amazon.com/dp/0387004440/?tag=pfamazon01-20

These books are heavy in functional analysis stuff however. Although Evans has appendices containing everything you need to know to read the book.

The bible on PDE is in my opinion Taylor: https://www.amazon.com/dp/1441970541/?tag=pfamazon01-20 (and the subsequent two volumes)

Strauss is a book that you should be able to read right now. The other three books I mentioned are very mathy, so I kind of doubt they will be much use to you as an electrical engineer (that said, you like math soooo...). As far as I know, none of the books really go into numerical issues.

 

[STEMucator]

Thank you for the plentiful recommendations.

Math gives you wings, so there's no reason not to be serious about it, regardless of the chosen discipline.

I'll read a bit of the Strauss book and then a bit of the Taylor book; then I'll decide which author I enjoy more and read that one.

 

[R136a1]

Thank you for the plentiful recommendations.

Math gives you wings, so there's no reason not to be serious about it, regardless of the chosen discipline.

I'll read a bit of the Strauss book and then a bit of the Taylor book; then I'll decide which author I enjoy more and read that one.

Taylor is extremely mathy. It does PDE's directly on manifolds, so I recommend to know a bit of differential geometry beforehand. So don't be surprised if you find Taylor too much to handle.

 

[STEMucator]

Taylor is extremely mathy. It does PDE's directly on manifolds, so I recommend to know a bit of differential geometry beforehand. So don't be surprised if you find Taylor too much to handle.

I've read calculus on manifolds by Spivak, so I do know some basic stuff. It was a pretty short book though, would it be enough information to tackle Taylor?

Here's a link to the PDF: http://faculty.ksu.edu.sa/fawaz/482/Books/Spivak_Calculus%20on%20manifolds.pdf

 

[R136a1]

I've read calculus on manifolds by Spivak, so I do know some basic stuff. It was a pretty short book though, would it be enough information to tackle Taylor?

I doubt it, but you should try anyway. If it works out then you found a very good book, otherwise you know what you need to work at.

Here's a link to the PDF:

You sure this is legal? You might want to remove it before the mentors see it
But I'm very acquainted with spivak's calc on manifolds, it's a very decent book but it doesn't go very far into differential geometry.

 

[STEMucator]

I doubt it, but you should try anyway. If it works out then you found a very good book, otherwise you know what you need to work at.



You sure this is legal? You might want to remove it before the mentors see it
But I'm very acquainted with spivak's calc on manifolds, it's a very decent book but it doesn't go very far into differential geometry.

If it's uploaded on a .edu website, I don't think there should be any issues as it's public educational knowledge.

I'll give Taylor a go, if I'm not comfortable after the first chapter or so I'll switch to Strauss and see how it feels.

 

[R136a1]

If it's uploaded on a .edu website, I don't think there should be any issues as it's public educational knowledge.

I'll give Taylor a go, if I'm not comfortable after the first chapter or so I'll switch to Strauss and see how it feels.

Good luck!

 

[Xiuh]

R136a1 mentioned some nice books. Evans is sometimes hard to read but it's one of my favorite books.
You should also check out Folland
https://www.amazon.com/dp/0691043612/?tag=pfamazon01-20
and John
https://www.amazon.com/dp/0387906096/?tag=pfamazon01-20