Numerical mathematics is the branch of mathematics that proposes, develops,
analyzes and applies methods from scientific computing to several fields including
analysis, linear algebra, geometry, approximation theory, functional
equations, optimization and differential equations. Other disciplines such as
physics, the natural and biological sciences, engineering, and economics and
the financial sciences frequently give rise to problems that need scientific computing
for their solutions.
As such, numerical mathematics is the crossroad of several disciplines of
great relevance in modern applied sciences, and can become a crucial tool for
their qualitative and quantitative analysis. This role is also emphasized by the
continual development of computers and algorithms, which make it possible
nowadays, using scientific computing, to tackle problems of such a large size
that real-life phenomena can be simulated providing accurate responses at
affordable computational cost.