Editing Mathematical analysis (section)

=== Numerical analysis ===
{{Main|Numerical analysis}}
Numerical analysis is the study of [[algorithm]]s that use numerical [[approximation]] (as opposed to general [[symbolic computation|symbolic manipulations]]) for the problems of mathematical analysis (as distinguished from [[discrete mathematics]]).<ref>{{cite book |last=Hildebrand |first=Francis B. | author-link=Francis B. Hildebrand | title=Introduction to Numerical Analysis | edition=2nd |date=1974 |publisher=McGraw-Hill |isbn= 978-0070287617}}</ref>

Modern numerical analysis does not seek exact answers, because exact answers are often impossible to obtain in practice. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors.

Numerical analysis naturally finds applications in all fields of engineering and the physical sciences, but in the 21st&nbsp;century, the life sciences and even the arts have adopted elements of scientific computations. [[Ordinary differential equation]]s appear in [[celestial mechanics]] (planets, stars and galaxies); [[numerical linear algebra]] is important for data analysis; [[stochastic differential equation]]s and [[Markov chain]]s are essential in simulating living cells for medicine and biology.