TAYLOR FUNCTIONS RELATION TO ENGINEERING
§ Taylor
functions are used in areas such as power engineering, fluid mechanics and
bathymetry to simplify often complex functions into more understandable terms.
§ Manually
calculating Taylor functions is mind blowing - thankfully there is an array of
software tools to do this.
§ Where
some exact elements of an equation are not available, Taylor functions allow an
improvement on traditional approximation calculations.
The
Taylor Functions are series of sum terms that concern the values of the
derivatives of a given function at a given point, so they are a part of
Calculus. They are a clever practical way to expand and simplify complicated
and transcendental functions into computable polynomials. The number of the sum
terms that are used to represent the specific function is theoretically
infinite, so we are either following an “adequate approximation” approach or we
use software to calculate the series of the sum using a large number of terms.
What is their use in Engineering?
Most
real things and systems in nature, engineering practice and phenomena are
complex, at least to our mind. This means that their mathematical
representation is equally complex making things harder for us to calculate. Taylor
Functions are used exactly for the purpose of simplifying things to make them
easier to work with. Here are a couple of examples of where Taylor Functions
are used:
§
In power engineering, the flow
of electric power in an interconnected system involves many variables that are
initially unknown. To address this, engineers use the Newton-Raphson solution
method that is based on the use of Taylor Functions.
§
Fluid mechanics engineers
use the Taylor series in conjunction with the Navier-Stokes equation to achieve
an accurate calculation method when studying arbitrary shapes with the Galerkin
Computational method.
§
Similarly, bathymetry studies
involve Taylor Functions based on the Dirichlet-Neumann operator to represent
three-dimensional wave motion in two-dimensional mathematics (Hamiltonian).
§
Taylor functions are also used
in error propagation studies as an alternative to the Monte-Carlo method.
§
Harmonic oscillation systems can
be analysed more simply and essentially better understood through the use of
Taylor Functions.
§
Engineering and physics
simulation software such as ANSYS, MATLAB, and Abaqus use
Taylor functions to calculate heat and mass transfer, fluid dynamics, etc.
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