Book Recommendation for Ordinary Differrential Equations.

[caffeinemachine]

I am doing my first course in Differential Equations and the book the instructor is teaching from is Arnold's Ordinary Differential Equations.
I like the geometric approach taken in the book but I don't like the way the material has been presented.
Can somebody please suggest me another introductory text on ordinary differential equations which takes a geometric approach?

 

[Ackbach]

I would never, ever, teach Introductory Differential Equations from Arnold's book! It looks much too abstract for me. Ironic, considering Arnold was the one who came up with that fantastic quote. (See the footnote at the bottom of page 1 of http://www.math.sunysb.edu/~eitan/menger.pdf.)

I would probably use Zill for an introduction to DE's. Warning, though: I used the sixth edition, and later editions do not appear to be as clear. Go with sixth or seventh. Another great option is Tenenbaum and Pollard.

For a graduate-level course, my teachers (multiple teachers!) kept saying, "Well, that's in Coddington and Levinson". So, there you go.

I'm afraid I haven't at all fundamentally answered your question about a geometric approach. I have no idea whether the books I've recommended would qualify as "a geometric approach". Certainly they appeal to geometry - all of them - from time-to-time. You've got to get a handle on basic solution techniques before you go further - that's my view. And certainly Zill, with Tenenbaum and Pollard as a supplement, would fit that bill.

 

[Fantini]

I second Tenenbaum and Polland. Fantastic! :)

 

[caffeinemachine]

I would never, ever, teach Introductory Differential Equations from Arnold's book! It looks much too abstract for me. Ironic, considering Arnold was the one who came up with that fantastic quote. (See the footnote at the bottom of page 1 of http://www.math.sunysb.edu/~eitan/menger.pdf.)

I would probably use Zill for an introduction to DE's. Warning, though: I used the sixth edition, and later editions do not appear to be as clear. Go with sixth or seventh. Another great option is Tenenbaum and Pollard.

For a graduate-level course, my teachers (multiple teachers!) kept saying, "Well, that's in Coddington and Levinson". So, there you go.

I'm afraid I haven't at all fundamentally answered your question about a geometric approach. I have no idea whether the books I've recommended would qualify as "a geometric approach". Certainly they appeal to geometry - all of them - from time-to-time. You've got to get a handle on basic solution techniques before you go further - that's my view. And certainly Zill, with Tenenbaum and Pollard as a supplement, would fit that bill.

Thank you so much Achbach and Fantini for the recommendations!

 

[blue_raver22]

I highly recommend "Differential Equations: An Introduction to Modern Methods and Applications" by James R. Brannan and William E. Boyce. This textbook also takes a geometric approach to ordinary differential equations, but it is presented in a more clear and organized manner compared to Arnold's book. It includes numerous examples and exercises to help reinforce the concepts, and it also covers a wide range of applications in science and engineering. Overall, I believe this book would be a valuable resource for your first course in differential equations.