What are $\Gamma(\Lambda^k(f^*(A))^*)$?

Question

Let $\pi:A\longrightarrow M$ be a vector bundle and $f:N\longrightarrow M$ be a smooth map.

Is there a charcterization of $\Gamma(\Lambda^k(f^*(A))^*)$?

Here $f^*(A)$ stands for the pullback of the bundle $A$ along $f$, $\Lambda^k((f^*(A))^*)$ stands for $k$-th exterior power of the dual bundle $(f^*(A))^*$ and $\Gamma(-)$ stands for the section functor.

Any book which does some computations with forms on the pullback will do.

Thanks