Theory of Ordinary Differential Equations by Earl A. Coddington (PDF)

Description

Reprint. Originally published: New York: McGraw-Hill, 1955. (International series in pure and applied mathematics)

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This very famous 1955 book by Coddington and Levinson is deservedly very famous. All of the later books refer to this book when the going gets thorny. It addresses the same trio of issues as the theoretical PDE books: (1) existence, (2) uniqueness, (3) properties. But if you want explicit analytic solutions or numerical solutions, you probably need to read a different book.Personally I use this book as a reference when I need rigorously proved very general theorems for existence and uniqueness. The other ODE books, even theoretical ODE books, tend to be far too brief on the theory because they know that most readers just want to get practical solutions. This is not a practical solutions book. It’s a deep theory book. It applies the same discipline to ODEs that the serious theoretical books on PDEs apply. I think this therefore means that it is only mathematicians who will be interested in this book, and maybe mathematical and theoretical physicists too. But it might be a bit “over the top” for engineering and other real-world applications contexts. This book is packed full of non-trivial theory. Allow at least a year to work through it.By the way, I received this Indian edition in the post directly from India. And I should mention also that the paper, binding and print quality are good.Since there seems to be no preview of this book currently, here are the 17 chapter titles.1. Existence and uniqueness of solutions2. Existence and uniqueness of solutions (continued)3. Linear differential equations4. Linear systems with isolated singularities: Singularities of the first kind5. Linear systems with isolated singularities: Singularities of the second kind6. Asymptotic behavior of linear systems containing a large parameter7. Self-adjoint eigenvalue problems on a finite interval8. Oscillation and comparison theorems for second-order linear equations and applications9. Singular self-adjoint boundary-value problems for second-order equations10. Singular self-adjoint boundary-value problems for n-th-order equations11. Algebraic properties of linear boundary-value problems on a finite interval12. Non-self-adjoint boundary-value problems13. Asymptotic behavior of nonlinear systems: Stability14. Perturbation of systems having a periodic solution15. Perturbation theory of two-dimensional real autonomous systems16. The Poincare-Bendixson theory of two-dimensional autonomous systems17. Differential equations on a torus

⭐This is arguably a classic on the theoretical side of ODEs. The author has covered most of the graduate topics in ODE with clearly written proofs of all main theorems. I like the construction of epsilon-approximate solution to the initial value problem of first-order ordinary differential equations. The author explicitly states the main train of thought behind his elegant, geometric construction, and supplied an illustrative diagram in the same pages. He omits some computational details, though. This is really a matter of personal preference. Some people like to see step-by-step solutions to computational issues, but to me, this is not the crux of most proofs. For me, the crucial thing to be enunciated is rather the main intuition behind, which is the ultimate source of inspiration of most mathematical proofs.

⭐Personal use of a classic. I had a copy. A little mistake, The 1955 edition was dedicated to Fagi and Sue.Best regards.

⭐but thanks!

⭐A book with usable contents ranging from undergraduates to researchers. Coddington and Levinson’s book Theory of Ordinary Differential Equations is definitely not recommended as a first reading on the subject but I am sure this is the best one of them all.

⭐if you want to learn more about ODEs than just how to solve them. I took a course on ODEs in a german university more than 30 years ago and the prof chose Coddington and Levinson. It was tough but I am very thankful now! It is so different from all these new “ODEs for Dummies-type” books with colour pictures all over and matlab, mathematica, maple or whatever in the foreground.

⭐Coddington’s book is a classic and a gold mine of information. I was really grateful to find it and this was an amazingly convenient way to buy it.

⭐Very valuable book. I appreciate the excellent service. Thanks a lot

⭐The book is ok but pages are like they are very much old, yellowish, and some pages are torned. High price

⭐Anche se non è un testo recentissimo, rappresenta un riferimento standard per lo studio delle ODE. Completo e denso di argomento, decisamente ottimo.

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⭐Theoretical book

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