Based on a lecture course in numerical methods in engineering given to second year undergraduates at the University of Manchester, this text is devoted to the solution of problems using numerical methods and, as such, is relevant to all engineering disciplines at undergraduate level. This text forms a bridge between classical mathematical and heavily computer code -based techniques such as the finite element and boundary element methods. The authors, both respected teachers in this field, have found that exisiting texts fall short of providing coverage of the range of material needed. For example, few books incorporate methods of weighted residuals in their treatment of the solution of ordinary differential equations, although these methods are central to the understanding of finite element techniques. Futhermore, although many existing texts do now incorporate computer code, this is not done in a systematic or didactic way. In contrast, the authors propose a philosophy of program-writing based on the use of sub-programs. The computer language employed is FORTRAN 77 (the chosen language of engineering), and so the subprograms are FORTRAN FUNCTIONS and SUBROUTINES. In this way, the book serves as an introduction to the use of powerful mathematical subroutine libraries. Every aspect of numerical analysis which is described in the book is illustrated by a compact program (there are over 40) which makes use of a simple library.