Preface About the text This book was written for a sequence of courses on the theory and application of numerical approximation techniques. It is designed primarily for junior-level mathematics, science, and engineering majors who have completed at least the standard college calculus sequence Familiarity with the fundamentals of linear algebra and differential equations is useful, but there is sufficient introductory material on these topics so that courses in these subjects are not needed as prerequisite Previous editions of Numerical Analysis have been used in a wide variety of situations some cases, the mathematical analysis underlying the development of approximation techniques was given more emphasis than the methods; in others, the emphasis was re- versed. The book has been used as a core reference for beginning graduate level courses in engineering and computer science programs and in first-year courses in introductory analysis offered at international universities. We have adapted the book to fit these diverse users without compromising our original purpose To introduce modern approximation techniques to explain how, why, and when they can be expected to work, and to provide a foundation for further study of numerical The book contains sufficient material for at least a full year of study, but we expect many people to use it for only a single-term course. In such a single-term course, students learn to identify the types of problems that require numerical techniques for their solution and see examples of the error propagation that can occur when numerical methods are applied They accurately approximate the solution of problems that cannot be solved exactly and arn typical techniques for estimating error bounds for the approximations. The remainder of the text then serves as a reference for methods not considered in the course. Either the full-year or single-course treatment is consistent with the philosophy of the text irtually every concept in the text is illustrated by example, and this edition contains more than 2600 class-tested exercises ranging from elementary applications of methods and algorithms to generalizations and extensions of the theory. In addition, the exercise sets include numerous applied problems from diverse areas of engineering as well as from the physical, computer, biological, economic, and social sciences. The chosen applications clearly and concisely demonstrate how numerical techniques can be, and often must be applied in real-life situations. A number of software packages, known as Computer Algebra Systems(CAS), been developed to produce symbolic mathematical computations. Maple Mathemat and MAtLAB are predominant among these in the academic environment, and versions of these software packages are available for most common computer systems. In addition, Sage, a free open source system, is now available. This system was developed primarily 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 LearningPreface About the Text This book was written for a sequence of courses on the theory and application of numerical approximation techniques. It is designed primarily for junior-level mathematics, science, and engineering majors who have completed at least the standard college calculus sequence. Familiarity with the fundamentals of linear algebra and differential equations is useful, but there is sufficient introductory material on these topics so that courses in these subjects are not needed as prerequisites. Previous editions of Numerical Analysis have been used in a wide variety of situations. In some cases, the mathematical analysis underlying the development of approximation techniques was given more emphasis than the methods; in others, the emphasis was re￾versed. The book has been used as a core reference for beginning graduate level courses in engineering and computer science programs and in first-year courses in introductory analysis offered at international universities. We have adapted the book to fit these diverse users without compromising our original purpose: To introduce modern approximation techniques; to explain how, why, and when they can be expected to work; and to provide a foundation for further study of numerical analysis and scientific computing. The book contains sufficient material for at least a full year of study, but we expect many people to use it for only a single-term course. In such a single-term course, students learn to identify the types of problems that require numerical techniques for their solution and see examples of the error propagation that can occur when numerical methods are applied. They accurately approximate the solution of problems that cannot be solved exactly and learn typical techniques for estimating error bounds for the approximations. The remainder of the text then serves as a reference for methods not considered in the course. Either the full-year or single-course treatment is consistent with the philosophy of the text. Virtually every concept in the text is illustrated by example, and this edition contains more than 2600 class-tested exercises ranging from elementary applications of methods and algorithms to generalizations and extensions of the theory. In addition, the exercise sets include numerous applied problems from diverse areas of engineering as well as from the physical, computer, biological, economic, and social sciences. The chosen applications clearly and concisely demonstrate how numerical techniques can be, and often must be, applied in real-life situations. A number of software packages, known as Computer Algebra Systems (CAS), have been developed to produce symbolic mathematical computations. Maple®, Mathematica®, and MATLAB® are predominant among these in the academic environment, and versions of these software packages are available for most common computer systems. In addition, Sage, a free open source system, is now available. This system was developed primarily ix 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