Math 函数

For people interest in Differential Equations, I've done a function that receive a string like: x^2+x^3 and put it in
2x+3x^2 witch is the differantial of the previous equation.
In the code there is one thing missing: the $string{$i} is often going outOfBound (Uninitialized string offset: 6 in...)
if your error setting is set a little too high... I just dont know how to fix this.
So there is the code for differential equation with (+ and -) only:
<?
function differentiel($equa)
{
 $equa = strtolower($equa);
 echo "Equation de depart: ".$equa."<br>";
 $final = ""; 
 
 for($i = 0; $i < strlen($equa); $i++)
 {
 //Make a new string from the receive $equa
 if($equa{$i} == "x" && $equa{$i+1} == "^")
 {
 $final .= $equa{$i+2};
 $final .= "x^";
 $final .= $equa{$i+2}-1;
 }
 elseif($equa{$i} == "+" || $equa{$i} == "-")
 {
 $final .= $equa{$i};
 }
 elseif(is_numeric($equa{$i}) && $i == 0)
 {
 //gerer parenthese et autre terme generaux + gerer ^apres: 2^2
 $final .= $equa{$i}."*";
 }
 elseif(is_numeric($equa{$i}) && $i > 0 && $equa{$i-1} != "^")
 {
 //gerer ^apres: 2^2
 $final .= $equa{$i}."*";
 }
 elseif($equa{$i} == "^")
 {
 continue;
 }
 elseif(is_numeric($equa{$i}) && $equa{$i-1} == "^")
 {
 continue;
 }
 else
 {
 if($equa{$i} == "x")
 {
 $final .= 1;
 }
 else
 {
 $final .= $equa{$i}; 
 }
 }
 }
 //
 //Manage multiplication add in the previous string $final
 //
 $finalMul = "";
 for($i = 0; $i < strlen($final); $i++)
 {
 if(is_numeric($final{$i}) && $final{$i+1} == "*" && is_numeric($final{$i+2}))
 {
 $finalMul .= $final{$i}*$final{$i+2};
 }
 elseif($final{$i} == "*")
 {
 continue;
 }
 elseif(is_numeric($final{$i}) && $final{$i+1} != "*" && $final{$i-1} == "*")
 {
 continue;
 }
 else
 {
 $finalMul .= $final{$i}; 
 }
 }
 echo "equa final: ".$finalMul;
}
?>
I know this is not optimal but i've done this quick :)
If you guys have any comment just email me.
I also want to do this fonction In C to add to phpCore maybe soon...
Patoff

If you're an aviator and needs to calculate windcorrection angles and groundspeed (e.g. during flightplanning) this can be very useful.
$windcorrection = rad2deg(asin((($windspeed * (sin(deg2rad($tt - ($winddirection-180))))/$tas))));
$groundspeed = $tas*cos(deg2rad($windcorrection)) + $windspeed*cos(deg2rad($tt-($winddirection-180)));
You can probably write these lines more beautiful, but they work!