Engineering 281 - Columbia University

In Fall 1946, Columbia University began to offer regular, graduate, for-credit academic courses in computing taught by staff members of the Watson Scientific Computing Laboratory who also had faculty appointments. The first two courses were Wallace Eckert's Astronomy 111-112, Machine Methods, and Herb Grosch's Engineering 281, Numerical Methods. The Machine Method course listings are reproduced on the SSEC page. These are widely regarded as the first university computer science courses, anywhere, ever. Here's the Engineering 281 description from a 1951 bulletin:

Engineering 281—Numerican methods. 3 points Winter Session.
  Tu. Th.4:10-5:25. 232 Pupin.
  Use and construction of univariate and multivariate mathematical tables. Interpolation with uniform and non-uniform intervals. Reciprocal differences and other approximation methods. Simultaneous linear equations and determinants. Real and complex matrix calculations. Least squares solutions. Harmonic analysis. Accumulation of errors in extended calculations.
  This course is designed to acquaint research students in science with the theory and practice of computation; special reference will be made to methods useful with recently developed calculating equipment. Examples will be drawn from the fields of engineering and physical science.
  Prerequisite: A year's work in mathematics beyond calculus; permission of instructor required.

Engineering 281 was designed by Herb Grosch, who taught it from 1946 to 1950. After that it was given by Professor Eckert through 1956-57, and then by Ken King. Here is Herb's Engineering 281 reading list for 1950 (CLICK image to magnify and sharpen):

Engineering 281 Fall 1946 Syllabus - Click to enlarge

Students could find copies of these works in the 116th Street reference library.

References:

Grosch, Herbert R.J., Computer: Bit Slices from a Life, Third Edition, 2003 (in manuscript). First edition published by Third Millenium Books, Novato CA (1991), ISBN 0-88733-085, Pages 100-101.
Columbia University Bulletin, Announcement of the Watson Scientific Computing Laboratory and a Program of Study in Applied Methematics, various years, plus bulletins of the Graduate Faculties and School of Engineering.
Eckert, Wallace J., ENGINEERING 821 - Numerical Methods, Lecture notes, Spring 1951, Winter 1954 (approx. 100 pages, manuscript, partially handwritten). The notes show that as late as 1954, much of the lab work was done on the 602-A Calculating Punch, as well as sorters, collators, and gang punches. I expect that within a year or two, the IBM 650 was used.