The second revised and enlarged edition of this book introduces to the students of B.E., B.Tech., AMIETE and AMIE courses, the important application oriented areas of mathematics, specially in the field of technology and general science. It also caters to the requirements of the B.Sc.(Hons.) and M.Sc. students of Physics and Mathematics as well as institutions offering extended mathematical training and follows the general trend of broadening the curriculum in mathematics. The book comprises 17 chapters. Almost all the chapters have dealt with various aspects of differential equations considering these as effective tools for the modelling of physical and engineering systems. Solution of some special differential equations, viz. the Bessel, Legendre, Hermite, Leguerre and Tschebyscheff, have also been presented. Numerical methods for solving differential equations have been presented and the solution methods to partial differential equations have been thoroughly covered. The Fourier series has been explained in a separate chapter and the theory of functions of complex variables and the variational calculus have been discussed along with their applications in engineering and physical systems. The newly added chapters include Fourier transform, Laplace transform, Z-transform and Probability theory and Statistics. Different aspects of direct and inverse transform have been added. The Laplace transform method, being a very powerful tool for solving linear and non-linear differential equations, has been discussed. Methods of solving integral equations have been discussed in a separate chapter. The book is an indispensable companion to the readers on account of its wide discussion of varied subject matter and solution of plenty of examples in a crystal clear language.