This book is designed for the first-year engineering undergraduate students. This book aims to impart to students an in-depth knowledge of various aspects of mathematics as applied to engineering. This book contains 10 chapters covering all the disciplines of Engineering Mathematics and deals with Linear Algebra and Numerical Methods. This note covers the following topics: Matrices, Eigenvalues and Eigen vectors, Quadratic forms, Interpolation, Numerical Differentiation and Integration, Numerical solution of Ordinary Differential Equations.