You're in luck, lambda-since within the last few years,quite a few excellent advanced ODE texts have been published, in addition to the standard treatises. First, the more standard texts. If you want a strong theoretical course in ODE's, you really need to decide how strong you want it. A full theoretical presentation requires functional analysis and graduate real variables. I don't think you want anything that advanced,a t least not yet. So I'll recommend some of the best "intermediate" level texts - they're the most enjoyable to read, anyway.

My favorite is the beautiful geometric text Ordinary Differential Equations by Vladimir Arnold, in its' third (and sadly final) edition. Not only does it contain a rigorous exposition of ODE's and dynamical systems on manifolds, it contains a wealth of applications to physics,primarily classical mechanics. You'll need a strong background in theoretical calculus and linear algebra to read this one. So worth it.

A book I found immensely helpful when learning this material was Lawrence Perko's Differemtial Equations and Dynamical Systems. Not only does it cover more then Arnold's book, particularly on dynamical systems and nonlinear ODE's, it has a wealth of excellent exercises and diagrams of integral curves in a multitude of solution spaces/dynamical aystems,so important when learning the subject.

The old classic by Smale and Hirsch,Differential Equations,Dynamical Systems and Linear Algebra is best balanced by the second edition coauthored with Steven StrogatzRobert Devaney, Differential Equations,Dynamical Systems and An Introduction To Chaos. The second edition is more applied and less mathematically rigorous,but it contains much more information on nonlinear ODEs and chaotic dynamical systems. It also has many more pictures which are quite helpful in this subject-the sheer complexity of nonlinear systems really makes learning them nongeometrically strikingly noninformative. I would strongly advice getting BOTH books(the first edition is very pricey; I'd recommend borrowing it) and using thier union. Thier union may be the single best textbook that currently exists on the subject.

Lastly, there's James D.Miess' Differential Dynamical Systems, which contains not only a slightly more advanced presentation of the same material as Arnold and Perko, it contains many more applications and computer programming implementations,mainly to chemistry and classical mechanics.

All these books are outstanding and I think you'll find what you're looking for among them.

You're in luck, lambda-since within the last few years,quite a few excellent advanced ODE texts have been published,in published, in addition to the standard treatises.First,the treatises. First, the more standard texts. If you want a strong theoretical course in ODE's,you ODE's, you really need to decide how strong you want it. A full theoretical presentation requires functional analysis and graduate real variables. I don't think you want anything that advanced,at advanced,a t least not yet. So I'll recommend some of the best "intermediate" level texts-they're texts - they're the most enjoyable to read,anyway.My read, anyway.

My favorite is the beautiful geometric text Ordinary Differential Equations by Vladimir Arnold,in Arnold, in its' third (and sadly final) edition. Not only does it contain a rigorous exposition of ODE's and dynamical systems on manifolds,it manifolds, it contains a wealth of applications to physics,primarily classical mechanics.You'll mechanics. You'll need a strong background in theoretical calculus and linear algebra to read this one. So worth it.

A book I found immensely helpful when learning this material was Lawrence Perko's Differemtial Equations and Dynamical Systems. Not only does it cover more then Arnold's book,particularly book, particularly on dynamical systems and nonlinear ODE's,it ODE's, it has a wealth of excellent exercises and diagrams of integral curves in a multitude of solution spaces/dynamical aystems,so important when learning the subject.

The old classic by Smale and Hirsch,Differential Equations,Dynamical Systems and Linear Algebra is best balanced by the second edition coauthored with Steven Strogatz, Differential Equations,Dynamical Systems and An Introduction To Chaos. The second edition is more applied and less mathematically rigorous,but it contains much more information on nonlinear ODEs and chaotic dynamical systems.It systems. It also has many more pictures which are quite helpful in this subject-the sheer complexity of nonlinear systems really makes learning them nongeometrically strikingly noninformative. I would strongly advice getting BOTH books(the first edition is very pricey;I'd pricey; I'd recommend borrowing it) and using thier union. Thier union may be the single best textbook that currently exists on the subject. Lastly,there's

Lastly, there's James D.Miess' Differential Dynamical Systems, which contains not only a slightly more advanced presentation of the same material as Arnold and Perko, it contains many more applications and computer programming implementations,mainly to chemistry and classical mechanics.

All these books are outstanding and I think you'll find what you're looking for among them.

You're in luck, lambda-since within the last few years,quite a few excellent advanced ODE texts have been published,in addition to the standard treatises.First,the more standard texts. If you want a strong theoretical course in ODE's,you really need to decide how strong you want it. A full theoretical presentation requires functional analysis and graduate real variables. I don't think you want anything that advanced,at least not yet. So I'll recommend some of the best "intermediate" level texts-they're the most enjoyable to read,anyway.My favorite is the beautiful geometric text Ordinary Differential Equations by Vladimir Arnold,in its' third (and sadly final) edition. Not only does it contain a rigorous exposition of ODE's and dynamical systems on manifolds,it contains a wealth of applications to physics,primarily classical mechanics.You'll need a strong background in theoretical calculus and linear algebra to read this one. So worth it. A book I found immensely helpful when learning this material was Lawrence Perko's Differemtial Equations and Dynamical Systems. Not only does it cover more then Arnold's book,particularly on dynamical systems and nonlinear ODE's,it has a wealth of excellent exercises and diagrams of integral curves in a multitude of solution spaces/dynamical aystems,so important when learning the subject. The old classic by Smale and Hirsch,Differential Equations,Dynamical Systems and Linear Algebra is best balanced by the second edition coauthored with Steven Strogatz,Differential Equations,Dynamical Systems and An Introduction To Chaos. The second edition is more applied and less mathematically rigorous,but it contains much more information on nonlinear ODEs and chaotic dynamical systems.It also has many more pictures which are quite helpful in this subject-the sheer complexity of nonlinear systems really makes learning them nongeometrically strikingly noninformative. I would strongly advice getting BOTH books(the first edition is very pricey;I'd recommend borrowing it) and using thier union. Thier union may be the single best textbook that currently exists on the subject. Lastly,there's James D.Miess' Differential Dynamical Systems,which contains not only a slightly more advanced presentation of the same material as Arnold and Perko, it contains many more applications and computer programming implementations,mainly to chemistry and classical mechanics. All these books are outstanding and I think you'll find what you're looking for among them.