This book provides a clear and precise exposition of modern techniques in engineering. It is designed as a suitable text-book for engineering and science students up to the graduate level. Each method is illustrated by a number of solved examples followed by properly graded problems, some of which have been selected from various University and professional examination papers. Beginning with different methods of finding inverse and Eigen values of a matrix and few iterative methods to solve system of linear equations have been discussed. Thereafter methods to obtain general and particular solutions of ordinary differential equations have been illustrated. Addition to that Fourier series expansion of periodic functions in different intervals has been discussed.