Numerical analysis is the study of algorithms written to solve problems in continuous mathematics. These algorithms do not seek exact answers, which are typically impossible to obtain in practice. Instead, much of numerical analysis is concerned with finding approximate solutions while ensuring reasonable bounds on error.
Some of the most basic uses of numerical analysis include approximating definite integrals, solving ordinary differential equations with specified initial conditions, minimizing or maximizing a given function, and solving nonlinear systems of equations. Natural applications of numerical analysis occur within all fields of engineering and physical sciences, but recently elements of scientific computation have proven useful in the life sciences and even the arts. Specific examples include the use of optimization in portfolio management, numerical linear algebra in quantitative psychology, and stochastic differential equations and Markov chains in computer simulation of living cells.