Ebook: Numerical analysis

This well-respected text gives an introduction to the modern approximation techniques andexplains 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.  Read more... 1. Mathematical preliminaries and error analysis -- 2. Solutions of equations in one variable -- 3. Interpolation and polynomial approximation -- 4. Numerical differentiation and integration -- 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