Introduction To Ordinary Differential Equations

An Introduction to Ordinary Differential Equations

Introduction to Ordinary Differential Equations

Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutions, and that should be of interest to the mathematics major, such as the theorems about the existence and uniqueness of solutions. The final chapters discuss the stability of critical points of plane autonomous systems and the results about the existence of periodic solutions of nonlinear equations. This book is great use to mathematicians, physicists, and undergraduate students of engineering and the science who are interested in applications of differential equation.

An Introduction to Ordinary Differential Equations

This book is meant to be a text which can be used for a first course in ordinary differential equations. The student is assumed to have a knowledge of calculus but not what is usually called advanced calculus. The aim is to give an elementary, thorough systematic introduction to the subject. All significant results are stated as theorems, and careful proofs are given. The exercises in the book serve two purposes: to develop the student's technique in solving equations, or to help sharpen the student's understanding of the mathematical structure of the subject. The exercises also introduce the student to a variety of topics not treated in the text: stability, equations with periodic coefficients, and boundary value problems.