Most applications of Mathematics involve the use of a computer. Numerical analysis studies how formulas can be transformed into computations. The topics covered may include: numerical methods in Calculus, such as series expansions and rates of convergence, numerical integration and differentiation, finite interpolation methods, splines; and numerical methods for ordinary differential equations, such as root-finding methods, Fourier series and Fourier transform, least-squares approximation, regression, and principal component analysis.