This highly successful and scholarly book introduces students
with diverse backgrounds to the various types of mathematical
analysis that are commonly needed in scientific computing.
The subject of numerical analysis is treated from a mathematical
point of view, offering a complete analysis of methods for
scientific computing with careful proofs and scientific background.
- Problems have been separated into Problems and
Computer Problems, and new problems have been added to each type.
- An extensive and updated bibliography of more than 400 items is included.
- A new appendix with pointers to mathematical software on the
Internet has been added.
- In an engaging and informal style, the authors demonstrate
that the many computational procedures and intriguing
questions of computer science arise from theorems and proofs.
- Algorithms are presented in pseudocode, so that students can
immediately write computer programs in standard languages or
use interactive mathematical software packages.
- The book occasionally broaches topics not usually a part of
standard textbooks at this level, including such topics as: the
Chebyshev theory of best approximation, homotopy (continuation)
methods for solving nonlinear equations, adaptive approximation,
adaptive quadrature, Sard's theory for best approximation of
functionals, delay differential equations, and the multigrid method.
- Advanced topics are marked with an asterisk in the
Table of Contents - so professors can easily include or
omit them at their discretion.