Applications
These objects are first encountered in school algebra. In more advanced mathematics they play an important role in ring theory, especially in the construction of field extensions. They also provide an example of a nonarchimedean field (see Archimedean property).
Rational functions are used in numerical analysis for interpolation and approximation of functions, for example the Padé approximations introduced by Henri Padé. Approximations in terms of rational functions are well suited for computer algebra systems and other numerical software. Like polynomials, they can be evaluated straightforwardly, and at the same time they express more diverse behavior than polynomials.
Rational functions are used to approximate or model more complex equations in science and engineering including (i) fields and forces in physics, (ii) spectroscopy in analytical chemistry, (iii) enzyme kinetics in biochemistry, (iv) electronic circuitry, (v) aerodynamics, (vi) medicine concentrations in vivo, (vii) wave functions for atoms and molecules, (viii) optics and photography to improve image resolution, and (ix) acoustics and sound.
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