FORMULAS APPROXIMATING DERIVATIVES OF A FUNCTION f(x)
Fisrt Forward-Differentiation Formulas:
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Fisrt Central-Differentiation Formulas:
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Fisrt Backward-Differentiation Formulas:
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Second Forward-Differentiation Formulas:
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Second Central-Differentiation Formulas:
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Second Backward-Differentiation Formulas:
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Euler's Method: xk+1 = xk+h
yk+1 = yk+hf(xk , yk) for k=0,1,2,3,……..
Heun's Method: xk+1 = xk+h
for k=0,1,2,3,……..
Backward Euler's Method: xk+1 = xk+h
yk+1 = yk+hf(xk+1 , yk+1) for k=0,1,2,3,……..
Fourth-Order Runge-Kutta Method:
, 
,
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Shooting Method:
Third guess =
first guess+(second guess-first guess) / (result of second guess-result of first guess)* (true value -result of first guess)
