An Introduction to Ordinary Differential Equations (Dover Books on Mathematics) by Earl A. Coddington (PDF)

Description

“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.

User’s Reviews

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

⭐I give this book two stars. Let me prefix this by saying that I am an electrical engineer who has taken multiple semesters of calculus and a course on ordinary differential equations and done well in them. I bought the book because I was looking for a refresher on the subject and chose this item based upon the mostly positive reviews.In short, I would classify the material presentation as sparse and generic to the point where, in my opinion, it would be wholly inadequate for a student unfamiliar with the topic. Additionally, the book tends to have a heavy focus on proofs involving generic solutions, making it much more theoretical than practical in nature.Even the introductory chapter 0 was less than helpful, but did provide a taste of what to expect from the rest of the book. For example, the introduction contained a section on determinants, which are often used to solve systems of simultaneous equations and determine linear independence, as well as in computing the Wronskian used in the solution of certain equations. The book makes a statement about when a the coefficients of system of equations has a non zero determinant that means that there exists a unique solution. One of the practice exercises then proceeds to give a set of equations (to a homogenous) system where the determinant is zero and asks if there is a solution besides the trivial one. The answer to this example being yes, in fact there are an infinite number of them, as the equations are not linearly independent. However, this is not clearly covered in the material and relies upon the reader already having this sort of understanding.The first official chapter of the book deals with first order equation and initially focuses on the subject of linear first order equations. The beginning of the section discusses differential equations in general and has exercise problems where a ‘solution’ is given and you’re asked to prove that it is a solution to a particular equation. This is typical at the start of a differential equations text where the student must take the solution and it’s derivatives and plug them back into the equation to show that it is indeed a solution. It then discusses the concept of initial value problems and gives an exercise to solve a system (y” = 3x + 1) subject to the initial conditions, which can be done by simple polynomial integration and solving for the unknown constants. Had I not already known from my experience with diff eq, this would have been absolutely insufficient in terms of explaining the concept.The next section deals with linear first order equations and this is where I reached the point at which I am now writing this review. As an example, my college textbook on differential equations started out on this same subject by discussing various techniques to solving these types of equations, such as separation of variables. Instead, this book pretty much states that the generic solution will be of the form: e^-ax integral from x0 to x of e^at*b(t) dt + c*e^-ax while going through some derivation and proof of this statement and then asks the student to find all the solutions to various first order equations as an exercise. I found this to be a challenge even having dealt with this subject before and being able to follow and understand at least most of the theory of what the book is describing, however, if this were my initial introduction to the subject I would be absolutely clueless in terms of how to proceed.In short, while the book may be good in terms of dealing with the theory of differential equations and treat it with due mathematical rigor, it most certainly is not what I would call a practical textbook by any means and I would recommend that it be avoided by anyone who is looking for an introductory text on this subject.

⭐TO BE CLEAR: This is an introduction the the THEORY of ODEs, not to the application of ODEs. Uses analytic techniques (presumes you are at least exposed to analysis) and is proof based. There are some exercises and it assumes that you are able to be able to turn theory into practice – that is, that you can read a proof and not only be satisfied that it is valid but also that you will have an intuition and the tools necessary to turn theory into practice.When I was taking my undergraduate ODEs course I showed this to my professor to get his opinion. He said this was a very advanced text suited for study at the PhD level. This is a common thing in mathematics. There are many introductory texts that are very advanced. Be warned.Okay, with that said, I enjoyed this book thoroughly – way more than the over priced text we were using in the course (Kreyszig’s Advanced Engineering Mathematics, weighing in at about 1000 pages and costing 200+ dollars). There was a lot of material covered in Kreyszig that was not covered in Coddington so one is not a replacement for another. However, one is certainly more enjoyable than the other 😀

⭐I think that this book is excellent as a textbook for an Ordinary Differential Equations class. There are plenty of “compute-the-solution” exercises, but there are also a large amount of theoretical exercises. The book is very concise, but it is still legible. It is also very cheap, so students won’t mind buying it :)I think that this book also works well when not used as a textbook. If you are using this to learn ODE’s by yourself, you really need to do some of the exercises since they are essential to the book. I do think that it is $11 well spent, since it teaches all of the basics of ODE’s.In terms of the topics covered, here they are:- Linear, homogeneous, nth-order equations with constant coefficients.- Linear, homogeneous, 1st and 2nd order equations with non-constant coefficients.- Linear, non-homogeneous, nth-order equations with constant coefficients.- Lienar, non-homogeneous, 1st and 2nd order equations with non-constant coefficients.- Solutions to ODEs with regular singular points.- Series solutions.- Existence and uniqueness to linear equations.- Non-linear first order equations.- Existence and uniqueness to first order equations.

⭐I just didn’t like this text. My university uses it almost exclusively to teach intro ODE, I think because it’s inexpensive. Not sure why they wouldn’t opt for

⭐by Tenenbaum/Pollard instead though, which is about the same price, contains more material, and has clearer exposition.My biggest gripe about this text was the strange notation. It’s pretty non-standard, which can make it hard to jump between referencing this text and other ODE material. Also the presentation of the curriculum was a bit unintuitive. Separation of variables isn’t covered until the second to last chapter, though it is a standard beginning technique. Also no mention of the method of undetermined coefficients, which is a standard technique in ODE.If you plan to study ODEs with this book, you may want to buy some supplementary texts.

⭐ODEs are really fun to study and this is a very convenient book. I have taken an ODE class and the textbook was very helpful because it has visuals. The books works for me because I already know a lot of mathematics, but I don’t think this can be a good book for a beginner.If you are a math lover like me, then you will love this excellent book.

⭐This book is a very good introduction to Ordinary Differential Equations as it covers very well the classic elements of the theory of linear ordinary differential equations. Although the book was originally published in 1961, this 1989 Dover edition compares very well with more recent offerings that have glossy and plots/figures in colour. After all, the classic elements of the theory of linear ordinary differential equations have not change a lot since the early 20th century. I particularly enjoyed studying Section 11 of Chapter 2 on a special method for solving non-homogeneous equations with constant coefficients. That method is often called “ the method of annihilator” is quite efficient.

⭐O livro tem uma abordagem interessante, bastante intuitiva, com um grupo de exercícios que ajudam bastante para fixar. É bem fechado em EDOs ,mesmo. Métodos de séries, para mim, foram discutidos de forma rápida. Mas há muitos tópicos abordados. Recomendo.Ottimo testo introduttivo sulle ODE, scritto in modo chiaro e con numerosi esercizi e problemi con soluzione riportati alla fine del testo, (cosa assai utile per gli studenti o chi affronta le equazioni differenziali per la prima volta), più semplice ancora nell’esposizione anche se più elementare forse, l’equivalente sempre della Dover di Tenenbaum e Pollard (Ordinary Differential Equations)I didn’t find this book to be a 5star. It’s an average book on math. As usual, the print for the equations is far too small to be read. Like all the kindle math books, you have to skip the most important part. They all have to be fixed. Worth $10, yes, but it no 5star.

⭐this book is covered the major topics for pg level concepts!, also it is very useful to us!, the time of delivery is too god, thanks to amazon and the packaging is also good, thanks to seller!

Keywords

Free Download An Introduction to Ordinary Differential Equations (Dover Books on Mathematics) in PDF format
An Introduction to Ordinary Differential Equations (Dover Books on Mathematics) PDF Free Download
Download An Introduction to Ordinary Differential Equations (Dover Books on Mathematics) 1989 PDF Free
An Introduction to Ordinary Differential Equations (Dover Books on Mathematics) 1989 PDF Free Download
Download An Introduction to Ordinary Differential Equations (Dover Books on Mathematics) PDF
Free Download Ebook An Introduction to Ordinary Differential Equations (Dover Books on Mathematics)