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Textbook in PDF format

Features
The book is very simple to read and it presents the ideas and the methods very clearly
It contains numerous exercises with detailed solutions included
In addition the volume of the book is not very large, so, students can reach the ideas very quickly
This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory.
To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included.
The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations.
Topics:
Difference and Functional Equations
Ordinary Differential Equations