Revolutionary advances in hardware and software technology have made computer aided design and analysis a standard tool in engineering practice. While this puts a lot of power at the hands of the end user, in order to use them wisely and interpret the results correctly, the users are expected to have a sound knowledge of the relationship between the physical world and the mathematical model and that between the mathematical model and the numerical approximation. The text examines the link between the mathematical and the numerical model in a succinct manner. Numerical algorithms relevant to engineers are developed and applied to solve industrial problems.The text is intended for senior level undergraduate and first year graduate students without rigorous training in numerical analysis. The following topics are covered both in theory and practical examples.-Roots of non-linear equations.-Systems of linear algebraic equations.-Interpolation and curve fitting.-Numerical differentiation and integration.-Ordinary differential equation - initial value problems.-Ordinary differential equations - boundary value problems.-Partial differential equations.