# Mastering Differential Equations

• Intro Math

## Main Question or Discussion Point

During the summer, I plan on learning differential equations (ODE's and PDE's) from bottom to top, but I am unable to choose books due to a great variety present. Can you suggest books for me to read in the following order (you can add as many books in each section if you like);

Ordinary Differential Equations

(Introduction)

1. ?

1. ?
2. ?
3. ?

1. ?
2. ?

and the same format for partial differential equations.

I would really appreciate it.

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Personally, as an intro, my ODE course used "elementary differential equations with boundary value problems." I thought it was a decent textbook (it also contains specially designated problems that are there to be solved by computer, which is an important thing to learn. Sometimes it's not possible for you to find an explicit solution).

That would cover the undergrad ODE. For a cheap undergrad PDE textbook, look into "partial differential equations for scientists and engineers." It's a Dover book, so it's available for about 10\$.

It's important that you're confortable with derivatives, integrals (especially integration by parts), partial fraction decomposition, Taylor series (or power series in general), determinants and maybe some more linear algebra if possible, and multvariable derivatives and integrals.

This is written assuming you're a physics or engineering student. I don't have any suggestions for graduate or ODE/PDE theory textbooks.

Verty, a fellow member on these boards, introduced me to Shepley L. Ross : Differential Equations. I'm currently reading it and it is very clear. Morris Tennabuan: Ordinary Differential Equations, is another great choice. It is from Dover, so it can be found very cheap. However, the book from Ross is cheaper.

I am not familiar with Simmons Differential book. I have used his pre-calculus and calculus book, and both were well written, intuitive, and did not sacrifice rigor in the problem sets or explanation. Maybe go to a library and check it out.

If you like more theory based, Coddington's: Introduction to Ordinary Differential Equations. Is also great. Although, it is intended for a math major. It is dry and requires a lot of rereading to understand. Not sure how useful Coddington would be for your course, rather read it after you complete your course, to gain a better understanding.

Introduction:
A good physics or engineering textbook, my introduction to Diff Eqs came from an EE book and Giancoli's Physics for Scientists and Engineers. If you've never seen a differential equation before beyond the prototypes of them you might encounter in Calc I and II, I honestly think a science or engineering textbook is best for learning the basic ideas. I struggled endlessly with Diff Eq books at first, even the ones that were supposed to be introductory, because I had no exposure to the ideas.

Simmons, no question. Fantastic book. I especially liked all of the biographies and historical sections, for instance the story of the propriety battle between Newton and Leibniz.

Then Advanced Engineering Mathematics by Kreyszig, not necessarily for ease but for sheer quantity of content.

Finally, there's a Dover book on PDEs by Farlow, Partial Differential Equations for Scientists and Engineers, that I can't recommend enough.

Ordinary Differential Equations

(Introduction)

Any calculus text should offer a basic introduction on ODE's, but this isn't really necessary.

Ross' differential equations is the best book you could wish for. Be sure not to buy his "Introduction to Ordinary Differential equations" which is shorter but doesn't contain the exciting material later on.

Simmons is good too, but is heavily plagiarized.

Arnold's Ordinary Differential Equations is a masterpiece. But not everybody enjoys his style.

Teshl Ordinary Differential Equations and dynamical systems is very good too. A draft version is available for free: https://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf

Partial Differential Equations

(Introductory)

Any ODE book such as Ross will give you a quick intro on PDE.

Evans' Partial Differential Equations is amazingly good, so you might like it. I personally prefer "An introduction to Partial Differential Equations" by Renardy, Rogers: http://www.springer.com/us/book/9780387004440

(Beyond)

Taylor's multi-volume work contains everything you ever want to know on PDE. It does things from the right perspective too: manifolds. I recommend a good knowledge of differential geometry before tackling this: https://www.amazon.com/dp/0387946535/?tag=pfamazon01-20

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Ordinary Differential Equations

(Introduction)

Any calculus text should offer a basic introduction on ODE's, but this isn't really necessary.

Ross' differential equations is the best book you could wish for. Be sure not to buy his "Introduction to Ordinary Differential equations" which is shorter but doesn't contain the exciting material later on.

Simmons is good too, but is heavily plagiarized.

Arnold's Ordinary Differential Equations is a masterpiece. But not everybody enjoys his style.

Teshl Ordinary Differential Equations and dynamical systems is very good too. A draft version is available for free: https://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf

Partial Differential Equations

(Introductory)

Any ODE book such as Ross will give you a quick intro on PDE.

Evans' Partial Differential Equations is amazingly good, so you might like it. I personally prefer "An introduction to Partial Differential Equations" by Renardy, Rogers: http://www.springer.com/us/book/9780387004440

(Beyond)

Taylor's multi-volume work contains everything you ever want to know on PDE. It does things from the right perspective too: manifolds. I recommend a good knowledge of differential geometry before tackling this: https://www.amazon.com/dp/0387946535/?tag=pfamazon01-20
very intriguing post. I own Ross book, and Codington intro book. I like how both of these books complement each other.

I really liked Simmons book, and I'm looking forward to read his Topology book in 2 yrs. What do you mean by Simons ODE book being plagiarized? Is it the same as other generic books?

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