Ordinary Differential Equations and Stability Theory: An Introduction (Dover Books on Mathematics)

Book Details:

• Publisher: Dover

• Author: David A. Sanchez

• Language: English

• Binding: Paperback

• ISBN: 9780486638287

• Pages: 192

• Edition: New

• Release Date: 29-02-2012

About The Book:

"Ordinary Differential Equations: A Modern Introduction" by David A. Sanchez offers a concise and accessible introduction to the subject of ordinary differential equations (ODEs), with a focus on stability theory. This book is ideal as a supplementary text for advanced undergraduate or beginning graduate students who have already taken an introductory course in ODEs.

The book begins with a general discussion of linear equations, introducing the concept of a fundamental system of solutions and the Wronskian. It moves on to the nonhomogeneous linear equation and provides the crucial variation of parameters formula for solving nth-order linear equations.

In-depth attention is given to the linear equation with constant coefficients in a dedicated chapter. The next sections focus on stability theory for both autonomous and nonautonomous systems, featuring key results for nonlinear systems and introducing Liapunov’s direct method. The book concludes with an exploration of the existence and uniqueness of solutions.

Key features of this book include:

• Clear explanations of linear equations and nonhomogeneous linear equations.

• An introduction to stability theory with results for nonlinear systems.

• Coverage of Liapunov’s direct method and its applications.

• Two appendices on series solutions of second-order linear equations and linear systems with periodic coefficients.

• Problems at the end of each chapter to reinforce learning.

This book is a perfect resource for students aiming to strengthen their understanding of differential equations and stability theory, providing foundational knowledge and preparing readers for advanced studies in mathematics and engineering.