This completely revised Fourth Edition of the book, appropriate for all engineering under-graduate students, continues to provide a rigorous introduction to the fundamentals of numerical methods required in scientific and technological applications. The book focuses clearly on teaching students numerical methods and in helping them to develop problem-solving skills. A distinguishing feature of the present edition is that it provides references to MATLAB, IMSL and Numerical Recipes program libraries for implementing the numerical methods described in the book. Several exercises are included to illustrate the use of these libraries. Additional worked examples and exercises have been added for better appreciation and understanding of the material. Answers to some selected exercises have been provided. NEW TO THIS EDITION Expanded section on cubic splines with the inclusion of linear and quadratic splines. A new section on surface fitting by cubic splines. A new section on Fourier transforms including a discussion on fast Fourier transforms. Enlarged range of about 500 worked examples and exercises.