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NUMERICAL ANALYSIS is
the branch of mathematics concerned with the study of
computation and of its accuracy, stability, and often its
implementation on a computer. One central concern is the
determination of appropriate numerical models for applied
problems. Another is the construction and analysis of robust
and efficient algorithms for various mathematical problems
such as those of numerical integration and differentiation,
and combinatorial and constrained optimization problems.
One area of numerical analysis which finds use in many other
areas of science and engineering is the construction and
analysis of methods for the numerical solution of ordinary
and partial differential equations of all kinds.
The analysis of such
differential equations
as well as the analysis of the appropriate numerical algorithms
often requires tools from
functional analysis and
differential geometry.
(Adapted with much liberty from the Harper Collins Mathematics
Dictionary.)
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