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Theory of Ordinary Differential Equations, by Earl A. Coddington, Norman Levinson
Download Theory of Ordinary Differential Equations, by Earl A. Coddington, Norman Levinson
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The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable. It has been developed from courses given by the authors and probably contains more material than will ordinarily be covered in a one-year course. It is hoped that the book will be a useful text in the application of differential equations as well as for the pure mathematician.
- Sales Rank: #582216 in Books
- Brand: Brand: Krieger Pub Co
- Published on: 1984-06
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 6.25" w x .75" l, 1.63 pounds
- Binding: Hardcover
- 429 pages
- Used Book in Good Condition
Most helpful customer reviews
9 of 10 people found the following review helpful.
Not for beginners
By Pedro Tomas Hasdeu
Definitely not for the faint hearted or beginners. You need a reasonable command of Lebesgue integration, the Jordan normal form of matrices, asymptotic series, complex variables, Laplace integrals etc, to read this book, which deals with the theory of ODE.
The book was written half a century ago, and may be considered an update of E. L. Ince's treatise which was written before WW2, so you will find no mention of distributional or weak solutions, chaos or bifurcation theory. Numerical solutions and analytical methods of closed form solutions are given rather scant attention.
Insofar as it goes I find it a very thorough book, similar in spirit to I. G. Petrovski's book Ordinary Differential Equations, which might be read concurrently.
22 of 25 people found the following review helpful.
A Comprehensive Text
By A Customer
The text is a standard reference on the theory of ordinary differential equations (it is not easy reading but comprehensive and accurate). Topics covered include: existence and uniqueness theorems for equations with various degrees of smoothness; dependence of solutions on parameters and initial conditions; singular equations; Sturm-Liouville theory (completeness of the eigenfunctions, convergence of eigenfunction expansions and asymptotic distribution of eigenvalues); asymptotic solutions; o.d.e's in the complex plane and much, much more. The text includes at the end of each chapter a collection of problems which extend the theory developed in the chapter and lead the reader to explore related areas.
2 of 2 people found the following review helpful.
I like the construction of epsilon-approximate solution to the initial value ...
By Shen Zeyu
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.
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