This text deals with the methods of obtaining numerical solutions to engineering problems. The topics discussed are those that are normally covered in undergraduate engineering programmes. This includes an introduction to digital computers, function representation using Taylor's series, error considerations in iterative type computations, searching for roots of equations in a single variable, solution of simultaneous equations, function approximation and interpolation, numerical integration and differentiation, matrix eigenvalue problems, solution of nonlinear system of equations, and solution of ordinary and partial differential equations. Advanced topics such as the generation of boundary characteristic orthogonal polynomials, boundary value problems have been dealt with. Key features include: solved and unsolved examples given to illustrate the concepts and algorithms; numerous exercises; case studies; and provides insights into and appreciation of the working of commercially available numerical softwares.