High School Correctness of Equations in Electromagnetism Textbook

[DesertFox]

Hello buddies!
Please, check out these equations...
Tell me, please, are they mathematically correct or not?

I need a simple YES/NO answer.
I have not sufficient knowledge to understand them. I just need to know whether they are correct...

Thank you!

P.S. Am is amplitude; I guess it is a form of Fourier's inverse transform applied in electromagnetism...

 

[Dale]

What is the source of these equations?

 

[DesertFox]

What is the source of these equations?

A russian handbook for electricians..

 

[Dale]

Is it this same book that we have discussed here previously?

 

[DesertFox]

Is it this same book that we have discussed here previously?

No. This one is from Russian source! Is it correct?

 

[Dale]

After the third equal sign the expression loses its dependence on t, so that seems wrong. The infinity/-infinity is not terribly meaningful either.

 

[mathman]

You can simplify by taking Ame^{j\psi} outside the integral sign.
The resultant integrand looks like the Fourier transform of the delta function.

 

[Dragon27]

Are you sure you're copying it from the textbook correctly? Shouldn't amplitude $Am$ be with $m$ as a subscript (like in $A_m$ or something)? Can you just screenshot the page with equations (I doubt it is an actual screenshot from the textbook) or make a photo of it?
What is the name of the source and where in the source (page, equation number) one can find these equations?

After the third equal sign the expression loses its dependence on t, so that seems wrong.

Because it got buried in the notation like $\phi(f)=2\pi f_0 t + \psi$ (you can spot it somewhere at the end of this... mess). Not sure if it would help fully decipher it.