Numerical Methods form an integral part of the mathematical background required for students of Mathematics, Science and Engineering. This book, Numerical Methods, is an extension of four long experience of teaching this subject to various courses. The invaluable experience of using computer based numerical techniques for research and a project has helped value add to this book. Clarity and utility has been our constant goal. We have especially designed this book to achieve this objective. A vast number of solved examples followed by properly graded problems have been provided. Many examples and problems have been selected from recent question papers of various University and Engineering examinations. We have tried to make each chapter an independent unit so that the various topics could be studied without loss of continuity