fresh 42, that example answers my question. Thanks. I had overlooked the fact that the zero function is linear.
All the directional derivatives of the function ## f ## at the origin exist and are equal to zero. To see this, let ## v = (v_1,v_2) ## be any direction. Then
D_vf(0) = \lim_{t...
Alright, so now that I think have some more "mathematical maturity", I have decided to go back and review/re-learn multivariable calculus. I've just started, and have gotten to differentiation.
From what I have seen, most books state the following sufficient condition for differentiability:
A...
I've been teaching myself a little bit of Complex Variables this semester, and I had a question concerning complex integrals.
If I understand correctly, then if a function f has an antiderivative F , then the line integral \int_C f(z) dz is path independent and always evaluates to F(z_1)...