The use of discontinuous functions in analysis
According to Jacobi, a treatise with this title was read to the Berlin Academy on December 9, 1762. According to St. Petersburg Academy records, it was presented to that Academy on May 23, 1763.
After various investigations into the basic concepts of infinitessimal calculation, Euler concludes that discontinuous functions can't be used if there is only one independent variable, but are unavoidable when dealing with functions of at least two independent variables.
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 11, pp. 2018-03-27.
Opera Omnia Citation
Series 1, Volume 23, pp.74-91.