Ordinary Differential Equations and Infinite Series 2nd Edition by Sam Melkonian ISBN 9780176716141 0176716149

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Product details:

ISBN 10: 0176716149
ISBN 13: 9780176716141
Author: Sam Melkonian

a comprehensive textbook that bridges the study of differential equations with the theory of infinite series. Structured into two main parts, the book first delves into ordinary differential equations, covering topics such as first-order equations, second-order linear equations, and higher-order linear systems. It then transitions to infinite series, exploring sequences, convergence tests, Taylor series, and Fourier series. A notable feature is its treatment of series solutions to differential equations, including methods like the Frobenius method for equations with regular singular points. The text is rich with examples, exercises, and appendices that reinforce key concepts and provide practical problem-solving techniques. This edition is widely used in undergraduate mathematics and engineering courses, serving as both a learning resource and a reference guide

Ordinary Differential Equations and Infinite Series 2nd Edition Table of contents:

I. Ordinary Differential Equations

1. Introduction

   • Basic Concepts

2. First-Order Equations

   • Separable Equations

   • Homogeneous Equations

   • Linear Equations

   • Bernoulli Equations

   • Exact Equations

3. Second-Order Equations

   • Linear Homogeneous Equations

   • Linear Nonhomogeneous Equations

   • Equations Reducible to First-Order Equations

4. Higher-Order Linear Equations

   • Homogeneous Equations

   • Nonhomogeneous

5. Linear Systems

   • Homogeneous Systems

   • Nonhomogeneous

II. Infinite Series

6. Sequences and Series

   • Sequences

   • Series

7. Taylor Series

   • Power Series

   • Representations of Functions by Power SeriesFourier Series

   • Fourier Series of Periodic Functions

   • Fourier Series of Functions on Finite Intervals

8. Series Solutions of Differential Equations

   • Solutions About Ordinary Points

   • Periodic Solutions

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