Preface administration of Youngstown State University for providing us the opportunity, facilities and encouragement to complete this project. We would also like to thank some people who have made significant contributions to the history of numerical methods. Herman H. Goldstine has written an excellent book entitled A History of Numerical Analysis from the 16th Through the 19th Century [Golds] In addition, The words of mathematics [Schw], by Steven Schwartzman has been a help in compiling our historical material. Another source of excellent historical mathematical knowledge is the MacTutor History of Mathematics archive at the University of St Andrews in Scotland. It has been created by John J O'Connor and Edmund F. Robertson and has the http://www-gap.dcs.st-and.ac.uk/-history/ An incredible amount of work has gone into creating the material on this site, and we have found the information to be unfailingly accurate. Finally, thanks to all the contributors to wikipedia who have added their expertise to that site so that others can benefit from their In closing, thanks again to those who have spent the time and effort to contact us over the years. It has been wonderful to hear from so many students and faculty who used our book for their first exposure to the study of numerical methods. We hope this edition continues this exchange, and adds to the enjoyment of students studying numerical analysis If you have any suggestions for improving future editions of the book, we would, as always be grateful for your comments. We can be contacted most easily by electronic mail at the addresses listed below RichardBurden burden @math. ysu. edu J. Douglas faires faires @math. ysu. edu Copyright 2010 Cengage Learning. All Rights t materially affect the overall leaming eaperience Cengage Learning reserves the right to remo rty commen may be suppressed from the eBook andor eChaptert'sh. May no be copied, scanned, or duplicated, in whole or in part Due toxiv Preface administration of Youngstown State University for providing us the opportunity, facilities, and encouragement to complete this project. We would also like to thank some people who have made significant contributions to the history of numerical methods. Herman H. Goldstine has written an excellent book entitled A History of Numerical Analysis from the 16th Through the 19th Century [Golds]. In addition, The words of mathematics [Schw], by Steven Schwartzman has been a help in compiling our historical material. Another source of excellent historical mathematical knowledge is the MacTutor History of Mathematics archive at the University of St. Andrews in Scotland. It has been created by John J. O’Connor and Edmund F. Robertson and has the internet address http://www-gap.dcs.st-and.ac.uk/∼history/ . An incredible amount of work has gone into creating the material on this site, and we have found the information to be unfailingly accurate. Finally, thanks to all the contributors to Wikipedia who have added their expertise to that site so that others can benefit from their knowledge. In closing, thanks again to those who have spent the time and effort to contact us over the years. It has been wonderful to hear from so many students and faculty who used our book for their first exposure to the study of numerical methods. We hope this edition continues this exchange, and adds to the enjoyment of students studying numerical analysis. If you have any suggestions for improving future editions of the book, we would, as always, be grateful for your comments. We can be contacted most easily by electronic mail at the addresses listed below. Richard L. Burden burden@math.ysu.edu J. Douglas Faires faires@math.ysu.edu Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it