It all goes back to the ancient habit of defining what a Fourier transform is. By tradition long lost in the mist of history, physicists define a Fourier transform of a function $f(t)$ as $$F_p(\omega)=\int_{-\infty}^{+\infty}dt f(x) e^{\mathfrak i \omega t}$$$$F_p(\omega)=\int_{-\infty}^{+\infty}dt f(t) e^{\mathfrak i \omega t}$$ but engineers define it as $$F_e(\omega)=\int_{-\infty}^{+\infty}dt f(t) e^{-\mathfrak j \omega t}$$ so that we have $F_p(-\omega) = F_e(\omega)$. There is some reason in the engineers definition because we, at least I do, intuitively think in terms of positive frequencies and then since the Inverse transforms is $$f(t)=\frac{1}{2\pi}\int_{-\infty}^{+\infty}d\omega F_e(\omega) e^{\mathfrak j \omega t}$$ you can say that you assemble an arbitrary $f(t)$ from its frequency components represented at $\omega$ by the complex sinusoids $e^{\mathfrak j \omega t}$ with amplitudes $F_e(\omega)$. Of course a physicist would say his frequency contents are equally well represented at positive frequencies by the sinusoids $e^{-\mathfrak i \omega t}$. Don't worry, you get used to it, just mentally change every $\mathfrak j$ to $-\mathfrak i$ or $\mathfrak i$ to $-\mathfrak j$.
