Ordinary Differential Equations

[zeronem]

A nice book for people who are taking Calculus IV(Differential Equations) is
"Ordinary Differential Equations: An Elementary textbook for Students of Mathematics, Engineering, and the Sciences by Morris Tenenbaum and Harry Pollard." This is a Dover book, but it explains in a very straight forward manner, and also reviews some of the properties of a function and such. A very good book full of Definitions and Exercises. I'de recommend it for anyone taking Differential Equations. It is separted into 12 parts, and each part contains a given amount of Lessons.

Parts-
1. Basic Concepts

2. Special Types of Differential Equations of the first order

3. Problems leading to Differential Equations of the first order

4. Linear Differential Equations of Order greater than one

5. Operators and Laplace Transforms

6. Problems leading to Linear Differential Equations of Order two

7. Systems of Differential Equations. Linearization of first order systems

8. Problems giving rise to systems of equations. Special types of second order linear and Non-Linear Equations solvable by reducing to systems

9. Series Methods

10. Numerical Methods

11. Existance and Uniqueness Theorem for the first order differential equation y'=f(x,y). Picard's Method. Envelopes. Clairaut Equations.

12. Existance and Uniqueness Theorems for a system of first order differential equations and for linear and non-linear differential equations of order greater than one. Wronskians.

Definitions are contained in the book, so as you move on you learn a lot of definitions. As well, there are a given amount of theorems with proof for each theorem in the lessons. I would list the lessons in each part, but due to it that there are 12 parts each with about 4 to 5 lessons, is a lot of typing.
There are examples all through out the book. There are also Excercises each with about 14 to 20 problems to solve and questions to answer.

I do understand that the usual Characteristic of Dover books are complex and go right into the material of it. However this Dover book, out of all the Dover books I own is the most straight forward on the material. The book is about 2 inches thick so there is a lot of material. It's a little book in height, but is two inches thick. Anyways, as a Dover book it does dive into the material quickly however it is very straightforward. Since this book is on Differential Equations it assumes you have a background in Calculus.

I'de recommend it for undergraduate students.

 

[graphic7]

I can agree with this review also. I've taken a look at some other ODE texts such as Zill and Cullen. Tenenbaum and Pollard, in my opinion, have the best approach. The first 2 or 3 chapters give the reader a relatively high amount of comfort to conquer ODE. Some parts of the texts, especially the chapters concerning the numerical methods of finding solutions to an ODE are slightly dated. This would be the point where you would want to whip out ZIll and Cullen or some other more recent texts. But all in all, this is an excellent if not the best ODE text that I have seen and for $15, you can't beat it.

 

[hhegab]

Thank you for sharing your recommendation for a textbook on Ordinary Differential Equations. It seems like a comprehensive and well-structured book with a good balance of theory, definitions, examples, and exercises. I appreciate your insight on the Dover books and how this particular one stands out as being more straightforward. It's also helpful to know that it assumes a background in Calculus, as that may influence the level of difficulty for some readers. Overall, it sounds like a valuable resource for undergraduate students studying Differential Equations. Thank you for your recommendation!