ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS : THEORY AND APPLICATIONS------PHI
Description:
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’.
Contents:
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