Edouard Jean-Baptiste Goursat (21 May 1858 – 25 November 1936) was a French mathematician, now remembered principally as an expositor for his Cours d'analyse mathématique, which appeared in the first decade of the twentieth century. It set a standard for the high-level teaching of mathematical analysis, especially complex analysis. He also published on partial differential equations.
He was born in Lanzac, Lot. He was a graduate of the École Normale Supérieure, where he later taught and developed his Cours. At that time the topological foundations of complex analysis were still not clarified, with the Jordan curve theorem considered a challenge to mathematical rigour (as it would remain until L. E. J. Brouwer took in hand the approach from combinatorial topology). Goursat’s work was considered by his contemporaries, including G. H. Hardy, to be exemplary in facing up to the difficulties inherent in stating the fundamental Cauchy integral theorem properly. For that reason it is sometimes called the Cauchy-Goursat theorem.