in the previous week

[color=red]1-In the previous week we had studied that problem.
[color=indigo]2-The previous week we had studied that problem.

In which case:
a-“week” is the period going from Sunday to Saturday and the problem was studied in the period before “this week” began?
b-“week” is just a period of seven days and the problem was studied in the seven-day period preceding the day about which we are talking.


There may be a tendency to interpret as 1b and 2a, but I wouldn’t want to rely on it.

You will also find disagreement about when the week starts. For me, it starts on Monday. The convention that the first day of the week should be Sunday has always seemed most strange to me. (Though when talking about “last week”, “next week”, and so on, people are often focusing on the working week of Monday to Friday, and the weekends are often perceived as “punctuation”.)

Thank you very much Dozy.

How about:
3-We had a lot of exercise last week.
4-We had a lot of exercise in the last week.

Is there a clear distinction between the two, 1 corresponding to the “calendar week” and 2 corresponding to “a period of seven days”?

When said on a weekday, #3 would normally be understood to refer to the previous calendar week. It could be more ambigous when said at a weekend, when it might refer to the previous Monday-to-Friday period, even though that is technically the same calendar week.

For me, #4 seems slightly mismatched. For your “period of seven days” meaning, I would more naturally say “We’ve had a lot of exercise in/over the last week.” (Though this refers more or less to a seven-day period, be aware that people can sometimes use “week” in a slightly fuzzy way to give a general idea of timescales rather than precise dates.)