ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS: THEORY AND APPLICATIONS

by NITA H. SHAH

Overview

This revised and updated text, now in its second edition, continues to present the theoretical concepts of methods of solutions of ordinary and partial differential equations. It equips students with the various tools and techniques to model different physical problems using such equations.The book discusses the basic concepts of ordinary and partial differential equations. It contains different methods of solving ordinary differential equations of first order and higher degree. It gives the solution methodology for linear differential equations with constant and variable coefficients and linear differential equations of second order. The text elaborates simultaneous linear differential equations, total differential equations, and partial differential equations along with the series solution of second order linear differential equations. It also covers Bessel’s and Legendre’s equations and functions, and the Laplace transform. Finally, the book revisits partial differential equations to solve the Laplace equation, wave equation and diffusion equation, and discusses the methods to solve partial differential equations using the Fourier transform. A large number of solved examples as well as exercises at the end of chapters help the students comprehend and strengthen the underlying concepts.The book is intended for undergraduate and postgraduate students of Mathematics (B.A./B.Sc., M.A./M.Sc.), and undergraduate students of all branches of engineering (B.E./B.Tech.), as part of their course in Engineering Mathematics.New to the SECOND Edition• Includes new sections and subsections such as applications of differential equations, special substitution (Lagrange and Riccati), solutions of non-linear equations which are exact, method of variation of parameters for linear equations of order higher than two, and method of undetermined coefficients• Incorporates several worked-out examples and exercises with their answers• Contains a new Chapter 19 on ‘Z-Transforms and its Applications’.

Product Details

ISBN-13:	9788120350878
Publisher:	PHI Learning
Publication date:	01/17/2015
Sold by:	Barnes & Noble
Format:	eBook
File size:	29 MB
Note:	This product may take a few minutes to download.

About the Author

Nita H. Shah, Ph.D., is Professor in the Department of Mathematics, Gujarat University. She is a post-doctoral visiting fellow of University of New Brunswick, Canada, and visits many universities for research oriented programmes. Dr. Shah has published over 250 research articles in various national and international journals.

Table of Contents

Preface1. Introduction of Ordinary Differential Equation2. Differential Equations of the First Order and First Degree3. Differential Equations of First Order and of Higher Degree4. Linear Differential Equations with Constant Coefficients5. Homogeneous Linear Differential Equations with Variable Coefficients6. Exact Differential Equations and Differential Equations of Higher Order7. Linear Differential Equations of Second Order8. Simultaneous Linear Differential Equations9. Total Differential Equations10. Partial Differential Equations (PDE) of First Order11. Linear Partial Differential Equations with Constant Coefficients12. Partial Differential Equations of Order Two with Variable Coefficients13. Power Series Method14. Bessel’s Equation and Bessel’s Function15. Legendre’s Equation and its Polynomials16. Laplace Transform and its Applications17. Applications of Partial Differential Equations of Order Two18. Fourier Transforms and its Applications to Partial Differential Equations19. Z-Transforms and its ApplicationsIndex