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The aim of this book has throughout been to display numerical methods in a systematic manner supported by computer programs of standard methods in 'C' and 'C++' and 'MATLAB' languages. The text has been thoroughly revised and the number of illustrative examples has been increased. The problems form the latest university examination papers have been added and 'Objective Type of Questions' have been updated . 'Useful Information' has also been given in an Appendix. It is hoped that the book in its revised form will serve a more useful purpose. The author thanks the fellow professors for their suggestions and patronage of the book. In particular, he is grateful to Prof.B.Basu Malik, Institute of Engg. & Tech., Kolkata; Dr. B.R Chide, Baba Ramdev College of Engg., Nagpur; Porf. (Mrs.) Mankane Dass, Guwahati Engg. College Guwahati ; Porf. Shiv Kumar Sahu, N.I.T., Raipur ; Dr. B.K. Jain, B.I.T., Mesra ; Dr. SomNath, Siliguri Institute of Technology, Siliguri; Prof. M.Dhivya College of Engg. , Guindy, Chennai; Prof. Suresh Kumar Yadav, National Institute of Technology, Kurukshetra ; Prof. Ashok Chhobida Patel, Hasmukh Goswami College of Engg., & Management, Ahmedabad ; Prof. Amit Chauhan, LR Institute of Engg., & Technology, Solan (H.P) and Dr. Anindita Chakraborty, Bhillai Institute of Technology, Durg (CG). Suggestions for improvement of the text, and intimation of misprints will be thankfully acknowledged. B.S GREWAL