How do I solve a transcendental equation?

In summary, in order to find a solution to a transcendental equation, one needs to look at each case separately and google it according to the particular transcendental function(s) involved. There is no generic method for solving all transcendental equations, as the inverse of the transcendental function must be known in order to find the solution.
  • #1
shourie.j
2
0
Can anyone tell me how can i find a solution to a transcendental equation?
Any link, where i will get methods to solve them?

Thank you..
 
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  • #2
shourie.j said:
Can anyone tell me how can i find a solution to a transcendental equation?

$${}$$

In general, no. One needs to look at each case separately.


Any link, where i will get methods to solve them?

$${}$$

Google it according to your particular transcendental function(s).

DonAntonio



Thank you..
 
  • #3
[itex]e^x= 2[/itex] is a transcendental equation. Its solution is x= ln(2). There is no generic method of solving all transcendental equations- you have to know the inverse of the transcendental function.
 

What is a transcendental equation?

A transcendental equation is an equation that includes transcendental functions, such as logarithmic, exponential, or trigonometric functions. These equations cannot be solved algebraically and require numerical methods to find approximate solutions.

What is the difference between a transcendental equation and an algebraic equation?

The main difference between a transcendental equation and an algebraic equation is that algebraic equations only contain algebraic operations, such as addition, subtraction, multiplication, and division. Transcendental equations, on the other hand, involve transcendental functions in addition to algebraic operations.

Why are transcendental equations important?

Transcendental equations are important because they have many real-world applications, particularly in science and engineering. They are used to model and solve complex systems and phenomena, such as population growth, electrical circuits, and chemical reactions.

How are transcendental equations solved?

Transcendental equations cannot be solved algebraically, so numerical methods must be used. These methods involve using a computer or calculator to find approximate solutions through a process of iterative calculations.

What are some common examples of transcendental equations?

Some common examples of transcendental equations include the logistic equation, the Brachistochrone curve equation, and the Kepler equation. These are used to model population growth, the path of a particle moving under the influence of gravity, and the motion of planets in elliptical orbits, respectively.

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