       Re: solution of equation

• To: mathgroup at smc.vnet.net
• Subject: [mg116400] Re: solution of equation
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Sun, 13 Feb 2011 03:07:28 -0500 (EST)

```On 2/12/11 at 5:21 AM, pi.munik at gmail.com (Piotr Munik) wrote:

>I want to solve equation like this:

>L := 100; h := 1;

While the above is valid Mathematica syntax, it isn't the best
choice. First, there are a variety of built-in symbols in
Mathematica that are named with a single uppercase letter. So,
even though there currently is no built-in symbol L, it is a
good idea to not use single upper case letters as variables.

Second, SetDelayed (:=) delays assignment until the symbol is
used. What this means in algorithms such as FindRoot that supply
numeric values to the variables, is that every time FindRoot
samples your function it re-evaluates L and h. Now for simple
assignments such as what you are using, the evaluation time
isn't going to be significant. But, it would be better to use
Set so that the assignment is done once rather than repeatedly.

>n Tan[n L] == h

>I need roots of this equation in a list form

You are aware there are infinitely many roots for this equation
and FindRoot will only find one right?

>but I have a problem. I try findfoot

>FindRoot[n Tan[n L] == h, {n, 0.01}]

>but it's not good

What is not good? If I copy and past from your post I get

In:= L := 100; h := 1;

In:= FindRoot[n Tan[n L] == h, {n, 0.01}]

Out= {n->0.202208}

In:= n Tan[n L] /. %

Out= 1.

So, FindRoot is clearly doing what it is intended to do, find a

Did you need FindRoot to find the root nearest n = 0.01? If so, try

In:= FindRoot[n Tan[n L] == h, {n, 0.01, .0156}]

Out= {n->0.0155525}

```

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