An Introduction to Ordinary Differential Equationsby Earl A. Coddington
This concise text offers undergraduates in mathematics and science a thorough and systematic first course in elementary differential equations. Presuming a knowledge of basic calculus, the book first reviews the mathematical essentials required to master the materials to/i>
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"Written in an admirably cleancut and economical style." — Mathematical Reviews.
This concise text offers undergraduates in mathematics and science a thorough and systematic first course in elementary differential equations. Presuming a knowledge of basic calculus, the book first reviews the mathematical essentials required to master the materials to be presented.
The next four chapters take up linear equations, those of the first order and those with constant coefficients, variable coefficients, and regular singular points. The last two chapters address the existence and uniqueness of solutions to both first order equations and to systems and n-th order equations.
Throughout the book, the author carries the theory far enough to include the statements and proofs of the simpler existence and uniqueness theorems. Dr. Coddington, who has taught at MIT, Princeton, and UCLA, has included many exercises designed to develop the student's technique in solving equations. He has also included problems (with answers) selected to sharpen understanding of the mathematical structure of the subject, and to introduce a variety of relevant topics not covered in the text, e.g. stability, equations with periodic coefficients, and boundary value problems.
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i am tired of the game publishers play of releasing a new edition every year or so of basically the same book, and jacking up the price, while letting the old cheap ones go out of existence, while the professors cooperate by requiring the new one. mathematically and pedagogically there is often no difference, except the newer ones may be dumbed down more, which is arguably harmful. this is a fine little treatment of the elementary aspects of o.d.e. with clear full proofs and examples, in the same form it took early on in its life. we used this at harvard in an undergrad course in 1963. it only lacks the phase plane theory, for the qualitative analysis of equations that cannot be solved explicitly, and that I like to present. my solution may be to combine this clean treatment of the theory of easily solved equations, with another reasonable but high quality dover book, like hurewicz or waltman, for the qualitative theory.