- #1
SamRoss
Gold Member
- 256
- 36
- TL;DR
- The author swaps one symbol for another in all places in an equation except one. Why?
In a certain derivation, the author begins with
$${g(-t)=}\frac 1 {2\pi}\int_{-\infty}^\infty {G(\omega)}e^{-i\omega t}d\omega$$
and then says he will replace ##t## with ##\omega## and ##\omega## with ##t##. He then writes
$${g(-\omega)=}\frac 1 {2\pi}\int_{-\infty}^\infty {G(t)}e^{-it\omega }d\omega$$
Why has ##d\omega## not been changed to ##dt##?
$${g(-t)=}\frac 1 {2\pi}\int_{-\infty}^\infty {G(\omega)}e^{-i\omega t}d\omega$$
and then says he will replace ##t## with ##\omega## and ##\omega## with ##t##. He then writes
$${g(-\omega)=}\frac 1 {2\pi}\int_{-\infty}^\infty {G(t)}e^{-it\omega }d\omega$$
Why has ##d\omega## not been changed to ##dt##?