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| {{expert|mathematics|date = October 2011}}
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| {{ref improve|date = October 2011}}
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| A '''transcendental equation''' is an [[equation]] containing a [[transcendental function]]. Such an equation cannot be solved for one factor in terms of another. Examples of such an equation are
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| :<math>x = e^{-x} </math>
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| :<math>x = \cos (x) </math>
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| ==Solution methods==
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| Some methods of finding solutions to a transcendental equation use graphical or [[numerical solution|numerical]] methods.
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| For a graphical solution, one method is to set each side of a single variable transcendental equation equal to a [[dependent variable]] and plot the two [[Graph of a function|graphs]], using their intersecting points to find solutions. | |
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| The numerical solution extends from finding the point at which the intersections occur using some kind of numerical calculation. The solution of transcendental equation obtained by numerical methods are approximate solutions.<ref name=Grewal>{{cite book|last=Grewal|first=B.|title=Higher Engineering Mathematics|publisher=Khanna Publishers|location=Delhi|isbn=81-7409-195-5}}</ref> Approximations can also be made by truncating the [[Taylor series]] if the variable is considered to be small. Additionally, the [[fixed point iteration method]], the [[bisection method]], the [[method of false position]], [[linear interpolation]], the [[method of chords]], the [[method of proportional parts]], the [[Newton-Raphson method]], [[secant method]] or [[method of tangents]] could be used to solve the equation.
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| Often [[special functions]] can be used to write the solutions to transcendental equations in [[closed form expression|closed form]]. In particular, the first example given above has a solution in terms of the [[Lambert W Function]].
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| ==References== | |
| {{reflist}}
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| == See also ==
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| *[[Transcendental number]]
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| *[[Lambert W Function]]
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| [[Category:Equations]]
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| {{mathanalysis-stub}}
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Revision as of 09:07, 12 February 2014
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