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January 30th, 2018, 06:58 PM  #1 
Newbie Joined: Jan 2018 From: Malaysia Posts: 2 Thanks: 0  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 
January 31st, 2018, 04:59 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 895 
I searched the page you linked to and did not see the phrase "nonlinear transcendental equation" anywhere on it. Where did you see it?

January 31st, 2018, 06:51 AM  #3 
Newbie Joined: Jan 2018 From: Malaysia Posts: 2 Thanks: 0 
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.

January 31st, 2018, 01:58 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,661 Thanks: 648  Quote:
Note your original note describes transcendental functions. I presume a transcendental equation is one involving a transcendental function.  
January 31st, 2018, 07:23 PM  #5 
Senior Member Joined: Sep 2016 From: USA Posts: 534 Thanks: 306 Math Focus: Dynamical systems, analytic function theory, numerics 
The word nonlinear is redundant here since every linear map on $\mathbb{R}^n$ satisfies a polynomial equation. This is the CayleyHamilton 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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