This is a Lecture Notes on a one semester course on Engineering Mathematics. This consists of Differential equations, Laplace Transforms and Fourier Series.This Lecture Notes is based on lectures given to first year students of Engineering institute. Here are the salient features of the Lecture Notes. All conccepts with examples are completely given in a lucid student friendly manner. A large number of solved exercises are included. I hope this book would invite the students to the subject of Mathematics and would inspire them to look to some comprehensive books including those mentioned above.