Derivative.txt

#NumericalAnalysis

calcDerivative - Calculates the derivative of a function at a point. Non-symbolic as of now. We could consider 
automatic differentiation or symbolic methods later on. One method which I am currently researching involves passing 
a method as a parameter to this class/function. As we know, we don't have access to pointers to functions here.
We could use something like a Callable interface, although I suggest a different approach. Please let me know what you
guys think about it. So the basic structure of the method that I am working on right now is this.

public double calcDerivative(String func, String op, double var, double val);

This is the prototype of the method. Instead of passing the function method as a parameter, we parse the original
expression and generate string inputs for the calcDerivative method.For e.g. to find out the derivative of say a trigonometric
function, we first need to classify it as a triginometric function and identify the variable on which the function will be
operating. <String func> will contain the class of function like trigonometric, polynomial etc. <String op> will contain the 
actual operation from among that class of function like sine, cosine etc. <double var> will have the variable with respect to
which we need to differentiate for e.g. x, y etc. Once we have the parameters we can further classify them and apply 
first principles to calculate the derivative of the function at the required point given by <double val>.

For e.g. f(x) = 4x^3 + 3x^2 + 6 at x = 6. Here <double val> will contain x = 6.

We will have a variable delta with a very small value that will help us in calculating the derivative.


                                       f(x + dx) - f(x)
The derivative:   Lim dx -> 0  f'(x) = ---------------- 
									         dx
Again, please let me know what you guys think and update or add a different file with your changes here.