Differential Equations: Methods and Applications

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.

Review:

The book presents a concise introduction to the theory of ordinary differential equations that arise in the real world, and the methods used to solve them. Each section or chapter of the book has been followed with examples and exercises with detailed solutions. ... The book is outstanding and will be excellently suited for students who have completed two semesters of differential and integral calculus and need a concise presentation of an introduction to the theory of ordinary differential equations." (Olusola Akinyele, zbMATH 1338.34003, 2016)