I was doing my Calculus 3 homework, which involved finding second and third order taylor approximations and their error bounds for a two variable function, and was getting tired of taking so many partial derivatives.
As an aid, I wrote up a Mathematica program which, when given a function of two variables, point on the function, and error bounds |x-x0| <= dx and |y-y0| <= dy, outputs the taylor approximations up to third order and the second and third order error bounds.
Mathematica File for Taylor Approximation and Bounded Errors
Edit: I recently added the graphs and the FindMaximum function to show at what points where the |f_xx| , |f_yy|, and |f_xy| achieve their maximums within the bounds of error.
Some screenshots from the program:
