by William Stein at the University of Washington, and was first released in February 2005 Information about sage can be found at the site http://www.sagemath.org Although there are differences among the packages, both in performance and price, all can perform standard algebra and calculus operations. The results in most of our examples and exercises have been generated using problems for which exact solutions are known, because this permits the performance of the approxi- mation method to be more easily monitored. For many numerical techniques the error analysis requires bounding a higher ordinary or partial derivative, which can be a tedious task and one that is not particularly instructive once the techniques of calculus have bee mastered. Having a symbolic computation package available can be very useful in the study of approximation techniques, because exact values for derivatives can easily be obtained. A little insight often permits a symbolic computation to aid in the bounding process as well We have chosen Maple as our standard package because of its wide academic distri- bution and because it now has a NumericalAnalysis package that contains programs that parallel the methods and algorithms in our text. However, other CAS can be substituted with only minor modifications mples and exercises have been added whenever we felt that a CAs would be of significant benefit, and we have discussed the approximation methods that CAS employ when they are unable to solve a problem exactl Algorithms and Programs In our first edition we introduced a feature that at the time was innovative and somewhat controversial. Instead of presenting our approximation techniques in a specific programmin language(FOrTRan was dominant at the time), we gave algorithms in a pseudo code that would lead to a well-structured program in a variety of languages. The programs are coded and available online in most common programming languages and CAS worksheet formats All of these are on the web site for the book. http://www.math.ysu.edu/-faires/numerical-analysis/ For each algorithm there is a program written in FORTRAN, Pascal, C, and Java. In addition, we have coded the programs using Maple, Mathematica, and MATLAB. This should ensure that a set of programs is available for most common computing systems Thie Every program is illustrated with a sample problem that is closely correlated to the text permits the program to be run initially in the language of your choice to see the form of the input and output. The programs can then be modified for other problems by making minor changes. The form of the input and output are, as nearly as possible, the same in each of the programming systems. This permits an instructor using the programs to discus them generically, without regard to the particular programming system an individual student chooses to use The programs are designed to run on a minimally configured computer and given in ASCII format for flexibility of use. This permits them to be altered using any editor or word essor that creates standard ASCll files(commonly called"Text Only "files). Extensive README files are included with the program files so that the peculiarities of the various programming systems can be individually addressed. The README files are presented both in ASCII format and as PDF files. As new software is developed, the programs will be updated and placed on the web site for the book or most of the programming systems the appropriate software is needed, such as a compiler for Pascal, FORTRAN, and C, or one of the computer algebra systems(Maple, Copyright 2010 Cengage Learning. All Rights May no be copied, scanned, or duplicated, in whole or in part Due to maternally aftec the overall leaning expenence. Cengage Learningx Preface by William Stein at the University of Washington, and was first released in February 2005. Information about Sage can be found at the site http://www.sagemath.org . Although there are differences among the packages, both in performance and price, all can perform standard algebra and calculus operations. The results in most of our examples and exercises have been generated using problems for which exact solutions are known, because this permits the performance of the approxi￾mation method to be more easily monitored. For many numerical techniques the error analysis requires bounding a higher ordinary or partial derivative, which can be a tedious task and one that is not particularly instructive once the techniques of calculus have been mastered. Having a symbolic computation package available can be very useful in the study of approximation techniques, because exact values for derivatives can easily be obtained. A little insight often permits a symbolic computation to aid in the bounding process as well. We have chosen Maple as our standard package because of its wide academic distri￾bution and because it now has a NumericalAnalysis package that contains programs that parallel the methods and algorithms in our text. However, other CAS can be substituted with only minor modifications. Examples and exercises have been added whenever we felt that a CAS would be of significant benefit, and we have discussed the approximation methods that CAS employ when they are unable to solve a problem exactly. Algorithms and Programs In our first edition we introduced a feature that at the time was innovative and somewhat controversial. Instead of presenting our approximation techniques in a specific programming language (FORTRAN was dominant at the time), we gave algorithms in a pseudo code that would lead to a well-structured program in a variety of languages. The programs are coded and available online in most common programming languages and CAS worksheet formats. All of these are on the web site for the book: http://www.math.ysu.edu/∼faires/Numerical-Analysis/ . For each algorithm there is a program written in FORTRAN, Pascal, C, and Java. In addition, we have coded the programs using Maple, Mathematica, and MATLAB. This should ensure that a set of programs is available for most common computing systems. Every program is illustrated with a sample problem that is closely correlated to the text. This permits the program to be run initially in the language of your choice to see the form of the input and output. The programs can then be modified for other problems by making minor changes. The form of the input and output are, as nearly as possible, the same in each of the programming systems. This permits an instructor using the programs to discuss them generically, without regard to the particular programming system an individual student chooses to use. The programs are designed to run on a minimally configured computer and given in ASCII format for flexibility of use. This permits them to be altered using any editor or word processor that creates standard ASCII files (commonly called “Text Only” files). Extensive README files are included with the program files so that the peculiarities of the various programming systems can be individually addressed. The README files are presented both in ASCII format and as PDF files. As new software is developed, the programs will be updated and placed on the web site for the book. For most of the programming systems the appropriate software is needed, such as a compiler for Pascal, FORTRAN, and C, or one of the computer algebra systems (Maple, 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