Ordinary And Partial Differential Equations: Theory And Applications

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.

• 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’.

Preface

1. Introduction of Ordinary Differential Equation

2. Differential Equations of the First Order and First Degree

3. Differential Equations of First Order and of Higher Degree

4. Linear Differential Equations with Constant Coefficients

5. Homogeneous Linear Differential Equations with Variable Coefficients

6. Exact Differential Equations and Differential Equations of Higher Order

7. Linear Differential Equations of Second Order

8. Simultaneous Linear Differential Equations

9. Total Differential Equations

10. Partial Differential Equations (PDE) of First Order

11. Linear Partial Differential Equations with Constant Coefficients

12. Partial Differential Equations of Order Two with Variable Coefficients

13. Power Series Method

14. Bessel’s Equation and Bessel’s Function

15. Legendre’s Equation and its Polynomials

16. Laplace Transform and its Applications

17. Applications of Partial Differential Equations of Order Two

18. Fourier Transforms and its Applications to Partial Differential Equations

19. Z-Transforms and its Applications

Index