Numerical methods. Design, analysis, and computer implementation of algorithms.
This is a textbook on numerical methods that offers a modern and rigorous presentation, at a medium level of training in Mathematics. It provides a well balanced amount of theory and illustrative examples, supported by an attractive exposition style. The reader can find proofs of the important results, technical details relevant for applications, as well as interesting information about the historical background. The presentation of various algorithms is accompanied by MATLAB codes. Exercises are carefully selected and an electronic version of a Solutions Manual is available.NEWLINENEWLINEThe material is structured in 14 chapters and two appendices, as follows: 1. Mathematical modeling, 2. Basic operations with MATLAB, 3. Monte Carlo methods, 4. Solution of a single nonlinear equation in one unknown, 5. Floating-point arithmetic, 6. Conditioning of problems; stability of algorithms, 7. Direct methods for solving linear systems and least squares problems, 8. Polynomial and piecewise polynomial interpolation, 9. Numerical differentiation and Richardson extrapolation, 10. Numerical integration, 11. Numerical solution of the initial value problem for ordinary differential equations, 12. More numerical linear algebra, eigenvalues and iterative methods for solving linear systems, 13. Numerical solution of two-point boundary value problems, 14. Numerical solution of partial differential equations, Appendix A. Review of linear algebra, Appendix B. Taylor's theorem in multidimensions.NEWLINENEWLINEThe book is equally recommended to students motivated for a deeper individual work and educators interested in the development of effective teaching instruments (lecture notes, computer exercises etc.).
scientific article; zbMATH DE number 6024385