I'm looking for a gentle an concise introduction to complex-variable differential equations. Eventually, I need to look at complex PDEs, but I assume one starts with complex ODEs.

Mostly, I'm just looking for definitions and basic existence and uniqueness results. Online results, from what I've found, just "leaped" to advanced or specialized topics.


Old classical textbooks cover both real and complex case (with emphasis on the complex case). One of the best is

E. L. Ince, Ordinary differential equations (multiple editions).

Others are

E. A. Coddington and N. Levinson, Theory of Ordinary differential equations (multiple editions),

E. Hille, Lectures on ordinary differential equations, Adison Wesley, 1968.

(This is a different book from the one recommended by Igor Khavkine, and I like it more).


A classic reference is

Hille, Einar, Ordinary differential equations in the complex domain, Pure and Applied Mathematics. New York etc.: John Wiley & Sons, a Wiley-Interscience Publication. XI, 484 p. (1976). ZBL0343.34007.


The books

Ilpo Laine, Nevanlinna Theory and Complex Differential Equations

and Steven G. Krantz, Partial Differential Equations and Complex Analysis (Studies in Advanced Mathematics)

may be useful for you too.


See also e.g. Chapter 4 of the book ODEs and Dynamical systems by Gerald Teschl (note that at this link it can be downloaded free of charge).

  • $\begingroup$ Off-topic, but could you please slow down with your barrage of recent edits to questions (mainly adding tags) since this bumps questions to the front page and pushes other questions off the front page $\endgroup$ – Yemon Choi Sep 9 '18 at 15:10

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.