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January 30th, 2018, 05:58 PM   #1
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Nonlinear Transcendental Equation

Hi,

I understand that transcendental equation is as equation that does not satisfy a polynomial or algebraic equation. Examples of transcendental equation are logarithm, exponential, trigonometric, and etc.... Correct me if I'm wrong.

However, I don't understand what does nonlinear transcendental equation mean.

Reference: https://en.wikipedia.org/wiki/Transc...ntal_functions
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January 31st, 2018, 03:59 AM   #2
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I searched the page you linked to and did not see the phrase "nonlinear transcendental equation" anywhere on it. Where did you see it?
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January 31st, 2018, 05:51 AM   #3
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The reference that I gave is the definition of transcendental function that I found. However, I couldn't find about the definition of nonlinear transcendental equation on any website.
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January 31st, 2018, 12:58 PM   #4
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Quote:
Originally Posted by wuiven64 View Post
The reference that I gave is the definition of transcendental function that I found. However, I couldn't find about the definition of nonlinear transcendental equation on any website.
Where did you see the expression?

Note your original note describes transcendental functions. I presume a transcendental equation is one involving a transcendental function.
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January 31st, 2018, 06:23 PM   #5
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The word nonlinear is redundant here since every linear map on $\mathbb{R}^n$ satisfies a polynomial equation. This is the Cayley-Hamilton theorem. Thus, every trancendental function is necessarily nonlinear.

That said, I've never seen the expression "nonlinear trancendental function" until your post so I'm also curious where you learned this from.
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