Neither of those are correct.
It would actually be phrased:
Are ECN470 and FIN470 the same course?
I.e. You need to use "are" for the plurality of the two course names, and then the singular "course".
It may seem counter-intuitive, but let's expand out the essential meaning to see what is singular and what is plural:
Are ECN470 and FIN470 two ...
This is something of a "magic words" question. This means that you are asking for the words that people say in some situation. The fact is that (with a few exceptions) there are no magic words. Any communication is a dialogue. So it is vitally important that you consider not only what you say, but what the other person is saying, and respond to that ...
You don't need to write a verb.
When you mark a letter "For the attention of Mr Jones", you are in effect saying:
This letter is for the attention of Mr Jones.
So, the verb is "is" (the present tense third-person singular of "to be"). But you don't need to write it.
English grammar rules are not always observed in instructions, or commands. You can ...
All of those are acceptable. There are subtleties about when you would use each though.
These are not comprehensive or absolute, but below are examples of how each might be used.
I will give you some water. If you have some water in your possession.
I will get you some water. If you need to leave the person to retrieve some water.
I will ...
Differentiate and distinguish share one synonymous meaning, but each word has other meanings that aren't synonymous.
For example, it's possible to use differentiate intransitively (example from Google) without a between structure:
the receptors are developed and differentiated into sense organs
but you can't substitute distinguish here.
Also, using ...
The verb 'damage' needs a direct object to be a part of a Predicative Verb in such a sentence. That is why 'damaging' is a predicative adjective here. A tense of the Predicative Verb is the Past Simple in the grammar construction with the linking verb 'be' here.
Inversion of subject and verb (auxiliary) in a subordinate clause is a literary construction equivalent to "if".
were it to be followed
is a literary way of saying
if it were to be followed
There is no difference in meaning between them.
I also cannot find any difference in meaning between those and
if it were followed
In other contexts ...
I expected "where the devil doesn't go" but there's "don't"
This isn't so much breaking grammatical rules, as using a non-standard dialect. That's why you didn't learn it; you are learning the dialect that newspapers and professional papers are written in, that is less regional.
If you mean 'microwave' as the wave in the radiation spectre, I'd recommend you such phrase as 'microwave radiation.' A listener could disambiguate the meaning of the whole sentence after such slight change. This change makes it necessary to transform the sentence into a kind as follows: Microwave radiation produces rapid and homogeneous heating in the oven ...
'Have' cannot be used in the continuous form when it means 'own' or 'possess'. So, you must say 'How long have you had (owned) your car?' 'Do you have a pet?' 'I have a lot of friends'. This is because 'have' with this meaning is a stative verb - it describes a state or condition.
'Have' can be simple or continuous when it is an active verb - it describes ...