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’‎.‎