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Introduction
Book chapter

Introduction

P. Mohana Shankar
Differential Equations, pp 1-4
2018
DOI: https://doi.org/10.1201/b22396-1

Abstract

Order Linear Differential Equation Characteristic Polynomial Differential Equations Second Order Linear Differential Equation Order Differential Equations Generalized Eigenvectors Phase Plane Analysis Higher Order Differential Equations Non-homogeneous Differential Equation Defective Matrices Separable Differential Equation Homogeneous Differential Equation Linear Algebra Depth Coverage Row Reduced Echelon Forms MATLAB Script Geometric Multiplicities Laplace Transforms Phase Portraits Order Equation Runge Kutta Method Engineering Education Autonomous Differential Equations Fundamental Matrix Cramer’s Rule
An overview of the book and its contents has been given. The uniqueness of the approach followed in subsequent chapters and appendices has been articulated to demonstrate the breadth, depth and scope of the coverage of the topics from the points of view of the students and instructors. This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book examines the study of first order differential equations with special emphasis on autonomous systems to develop an appreciation and understanding of the equilibrium conditions of associated systems. It deals with method of integrating factors and the method of separable functions for obtaining the solution of first order differential equations. MATLAB scripts for solving example problems, creating phase plots and obtaining Laplace transforms are given for the benefit of the reader. Appendices provide in depth coverage of topics such as numerical methods for solving differential equations, theory of Laplace transforms and applications to differential equations and phase plane analysis. An additional approach for obtaining the solution based on converting the second order equation into a pair of coupled first order differential equations is also offered as yet another level of verification of the solutions along with numerical solution obtained using Runge-Kutta methods.

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