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Introduction to Differential Equations

Dr. Debasish Sengupta

First Published: 2016

Third Edition: 2022

ISBN: 978-81-941732-5-0

Pages: 790

**CONTENTS**

- Preliminaries

- Equations of First Order and First Degree: Trajectories

- Equations of First Order but not of First

Degree; Singular Solutions and Extraneous Loci

- Higher Order Linear Differential Equations with constant

Coefficients; Method of Undetermined Coefficients

- Higher Order Homogeneous Linear Differential Equations (Cauchy-Euler and Legendre’s Equations)

- Exact Differential Equations; Some Special Types of differential Equations

- Second Order Linear Differential Equations with Variable Coefficients

- Second Order Initial-value, Boundary-value and Eigen-value Problems

- Simultaneous Linear Differential Equations

- System of Differential Equations

- Planer Linear Autonomous System, Phase Plane

- Total Differential Equations

- Partial Differential Equations of First Order

- Partial Differential Equations of Second Order

- The Laplace Transform

- University Questions

- Index

__ ABOUT THE BOOK__: Introduction to Differential Equations has been designed mainly for the students who study mathematics at the undergraduate and postgraduate levels in any university under the UGC introduced CBCS syllabi. The book contains the basic elements of ordinary differential equations (ODE) as well as the elements of partial differential equations (PDE). A thorough study of ODE containing linear first, second, and higher orders with variable and constant coefficients is incorporated with suitable examples in a lucid way. The method of solving a system of first order ODE with constant coefficients is illustrated with a number of supporting examples. The ideas of determining the local nature of the solutions of certain autonomous systems of ODE in a plane in terms of their stability criterion are described by the phase diagrams with appropriate examples in a fashionable way. Methods of obtaining the series solutions of certain second order ODE having ordinary (regular) and irregular singular points are also discussed with many worked-out examples. Certain particular methods of solving the first order linear and nonlinear PDE are explicitly analysed with many worked-out examples. Canonical representations of the second order PDE and their applications in the study of Heat equation. Wave equation and Laplace equation are discussed separately with a number of standard examples in a simpler way. Finally, methods of determining solution of ODE and PDE by using the method of Laplace transforms are discussed thoroughly with many standard examples in a simpler way. After going through the contents of the book one certainly gains confidence in the techniques of solving problems of ODE and PDE.