E322 -- De usu functionum discontinuarum in analysi

(On the use of discontinuous functions in analysis)

Summary:

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.

According to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on December 9, 1762.

According to the records, it was presented to the Petersburg Academy on May 23, 1763.

Publication:

Originally published in Novi Commentarii academiae scientiarum Petropolitanae 11, 1767, pp. 67-102
Opera Omnia: Series 1, Volume 23, pp. 74 - 91

Documents Available:

Original publication: E322
The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E322 include:
- Dhombres J., “Some aspects of the history of functional-equations linked to the evolution of the function concept.” Archive for History of Exact Sciences, 36 (2), pp. 91-181 (1986).
- Ferraro G., “Differentials and differential coefficients in the Eulerian foundations of the calculus.” Historia Mathematica, 31 (1), pp. 34-61 (Feb 2004).

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