AAAHHH!!... (sorry), with that info i can take a look about sign changes of the function and analize the effects of minimum variations on the 3D function...

Even with this "regional analysis, can the tangent plane that contains the critical line give more information?... or cutting the f(x,y) with different planes?

(thanks for your time)

Yes sorry... it was a concept failure... I know that if the Hessian's Determinant >0 we have to analyze the second partial derivative Fxx in the hessian Matrix to classify the point as Min or Max. Then if the determinant < 0 the critical point is a saddle point... But when the determinant is equal to 0?...

In the example, critical points lie in the Y=X line so how can we analize the "critical line" with hessian's determinant = 0?

I'm too confused, because I plotted the contourplots of the function closing up the Neighborhood around the origin (0,0) and they have an hyperbolic form near the critical point 0,0 so origin (0,0) must be a saddle point, but what happens with the other points of the line?

It's really strange...

Literally, the problem of the lab is solve the Differential Equation:

L*diff(q(t),t,)+R*diff(q(t),t)+q(t)/C=E(t)

The first E(t) function is:

 "E(t) is the periodic function that it's value for the interval [0,2] is 2 and 0 for the interval ]2,4] (square waveform);"

We have defined only one oscilation using a piecewise function and maple solved it without problem but, really we need the periodical function... that is we don't knot... in addition we don't know if maple can solve it if it's defined periodically...

Thanks!

Thanks... Another Question... can Maple work ODEs with these functions?... as inputs?