"With" and "where" are being used here as clauses. This is common in English, but in several fields such as mathematics, engineering and computer programming these are sometimes used in a non-grammatical way too. The examples you quote seem to make grammatical sense, but you should consider whether they have further meaning specific to your field of study, especially as they contain the equals symbol which suggests that they are not intended to be wholly grammatical but representative of some logic.
"With" literally means "accompanied by". So using the example of UK traffic lights:
The red light with the amber light indicates that the lights are about to change to green.
This groups the first two conditions together using "with" to show the conditions for the second part of the statement to be true.
The same thing could be expressed this way...
Where the red light is still lit, the amber light indicates that the lights are about to change to green.
...however there is a difference. This is saying that the amber light can indicate the subsequent statement to be true, but only where another condition exists, namely the red light still being lit. It allows for the possibility that the amber light could mean something else too where the red light is not lit.