🚀 go-pugleaf

Stefano,
A good book on solving these types of equations iteratively is 
Burden and Faires, Numerical Analysis.  I have the 2nd and 3rd editions, 
but I think there may be a later edition.

They discuss several methods.  The method you are using might fit into 
something called the bisection method.  Nothing at all wrong with the 
method except it could take some time.  There is also a method called the 
Newton-Raphson method to find the solution of f(x)=0.

For Calculus students, this would be a great example to tie some of the 
concepts together.  Burden and Faires introduce the method using a Taylor 
series expansion so that f(x)+(x-x_bar)f'(x_bar) ~~ 0, assuming the 
function is twice differentiable on some closed set and ignoring the 
error term.

Guess at the solution then iterate until some convergence criteria is 
met.  The iterative relationship is

p_n = p_n-1 - f(p_n-1)/f'(p_n-1).



baro@pt.tizeta.it (Stefano Baraldi) wrote:
>Hi all!
>
>I'm going to give my Calculus exam next month, i still have real
>doubts about solving equations of this type (i don't knoe their exact
>name)
>
>exp(x)>x,    ln(x+a)<tan(x), ....
>
>and so on...
>I know the solution should be found graphically, please could you
>point me to books (available online) or tell me the method to do it?
>
>Up to now i made a simple comparing algorithm on my sci-calculator,
>but that's not so ortodox.. :))
>
>thank you and bye!
>
>See ya,
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