Numerical Analysis:
Mathematics of Scientific Computing, Third Edition
David Kincaid and Ward Cheney
Features
This highly successful and scholarly book
is now published by the
American Mathematical Society.
It 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.
The third edition contains the following features:
 A new chapter has been added on Optimization with sections such as
Methods of Descent, Quadratic Fitting Algorithms, NelderMeade Algorithm,
Simulated Annealing, Genetric Algorithms, Pareto Optimization, and Convex Programming.

The entire book has a new design and it has been reformatted for an improved appearance.

Some new problems have been added and a reordering of many problems.

Numereous improvements have been made throughout the book.

Most theorems are displayed with names or titles to help the reader remember them.

Many references to problems and to other parts of the book are now given with page
numbers to help the reader find them.

An extensive and updated bibliography of about 500 items is included.

The appendix on mathematics software has been updated with addition links to resources
available on the Internet.

Corrections have been made to all known errors in the previous edition.
 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, the multigrid method,
and optimization.

Software, errata, and teaching aids are available via the Internet.

The publisher has made available a
Solution Manual for instructors who adopt the books for their classes.