Explorations in numerical analysis
- 2020 World Scientific Publishing, Singapore :
- xv, 658 p. ; ill., 25 cm
Includes bibliographical references and index.
This textbook introduces advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations. Topics covered include error analysis, computer arithmetic, solution of systems of linear equations, least squares problems, eigenvalue problems, polynomial interpolation and approximation, numerical differentiation and integration, nonlinear equations and ordinary differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the MATLAB programming language. This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra
9780000988638
Numerical analysis Mathematical problems Adam-Bashforth method Allen -Cahn equation Backward Euler's method Brayden's method Cartesian product rule Courant -Fischer minimax theorem Dahlquist's Barrier theorem Euler's method Fermat's theorem Galerkin method Ill-conditioned problem Jacobi method Least square problem Miller's method Power method Rolle's theorem Simpson's rule Taylor's theorem Well-condotioned problem