Numerical Analysis

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This well-respected text gives an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. The authors focus on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. With a wealth of examples and exercises, the text demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in real-life situations. In this edition, the presentation has been fine-tuned to make the book even more useful to the instructor and more interesting to the reader. Overall, students gain a theoretical understanding of, and a firm basis for future study of, numerical analysis and scientific computing. A more applied text with a different menu of topics is the authors' highly regarded NUMERICAL METHODS, Third Edition. Key Features 1.Updated technology coverage and programs to reflect current standards, incorporating more modern time-saving techniques. 2.Added exercises and applications per request from the market. 3.The authors have further curbed the use of theory and increased use of methods to keep up with Engineering-service trend while maintaining spread across audiences. 4.Limits course prerequisites to calculus with no overt Differential Equations or Linear Algebra dependencies. 5.Balances theory and methods to stake a wide middle ground between audiences who need to know the mathematics and audiences who only need to know the essential techniques. 6.Flexible coverage to suit one- or two-semester courses and differing student levels, with careful attention paid to marking optional material and alternate paths for instructors. 7.Theory coverage emphasizes mathematical thought and is especially accessible for students who've optionally taken undergrad math foundations courses like Real Analysis or Transition to Advanced Math. 8.Over 2,500 exercises from simple drill to advanced theoretical problems. 9.Numerous real-life applications to engineering, computer science, physical sciences, biological sciences, and social sciences. 10.Technology-neutral algorithms easily adapted to various software. Specific instructions given for Maple in limited cases where software-specific questions are absolutely required. 11.Language- and software-neutral programs in book supported on companion website by specific program code for Maple, Mathematica, MATLAB, C, FORTRAN, Java, and Pascal to cover all technologies the majority of the market will use. Author website includes mid-cycle updates and additions to this program code to keep up with new software releases. 12.Virtually every concept in the text is illustrated by example, and this edition contains more than 2000 class-tested exercises ranging from elementary applications of methods and algorithms to generalizations and extensions of the theory. 13.The exercise sets include many applied problems from diverse areas of engineering, as well as from the physical, computer, biological, and social sciences. 14.The design of the text gives instructors flexibility in choosing topics they wish to cover, selecting the level of theoretical rigor desired, and deciding which applications are most appropriate or interesting for their classes. Table of Contents 1.Mathematical Preliminaries And Error Analysis. 2. Solutions Of Equations In One Variable. 3. Interpolation And Polynomial Approximation.Interpolation And The Lagrange Polynomial. 4. Numerical Differentiation And Integration.Numerical Differentiation 5. Initial-Value Problems For Ordinary Differential Equations. 6. Direct Methods For Solving Linear Systems. 7. Iterative Techniques In Matrix Algebra. 8. Approximation Theory 9. Approximating Eigenvalues. 10. Numerical Solutions Of Nonlinear Systems Of Equations. 11. Boundary-Value Problems For Ordinary Differential Equations. 12. Numerical Solutions To Partial Differential Equations.