"extension course" is correct and usable in written English.
You can use it when referring to a course taken to gain additional knowledge or qualifications, for example, "I took an extension course in graphic design last summer."
An extension course to the current books and essays on bridge.
In December 1918, while enrolled in a playwriting extension course at Columbia University, Gertrude Edelstein met and married Lewis Berg.
Before Dec. 7th, there would be four or five graduates taking Japanese; now there are 20 regular students, and 21 in extension course.
The man is an entire extension course catalog: futurology, paleontology, gingrichology, history — did you know that Reagan's staff quit en masse, too?
After taking an extension course in screenwriting at U.C.L.A., Mr. Williamson penned his first script, "Teaching Mrs. Tingle," then wrote "Scream" in a three-day frenzy.
He studied television and journalism in an extension course at U.C.L.A., working part time as a waiter and at a movie house.
Simultaneously, he quit De Witt Clinton High School, without graduating; except for some extension courses in literature at Columbia later on, that was the end of his formal education.
"Harvard, for Less: Extension Courses' New Allure" suggests that Harvard University Extension School students are essentially getting a slightly diluted Harvard College experience for a fraction of the cost.
Since its inception, group instruction in the form of formal lectures, discussion groups, seminars, and workshops has remained the core of extension courses.
In "Harvard, for Less: Extension Courses' New Allure," a Harvard instructor is quoted as saying: "You could come and get a very similar experience and then have the Harvard name on your résumé.
Preoccupied with parish volunteer work and extension courses, Sylvia leaves the care of her children and her home to the new housekeeper, "a person of strange diction and eccentric ways of cleaning lavatories," whose arrival is welcomed as a stroke of luck.
