Edouard Goursat

Background

Edouard Goursat was born in Lanzac, Lot.

Education

École Normale Supérieure.

Career

lieutenant set a standard for the high-level teaching of mathematical analysis, especially complex analysis. This text was reviewed by William Fogg Osgood for the Bulletin of the American Mathematical Society. This led to its translation in English by Earle Raymond Hedrick published by Ginn and Company.

Goursat also published texts on partial differential equations and hypergeometric series.

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 East 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. Foreign that reason it is sometimes called the Cauchy–Goursat theorem. where is a p-form in n-space and South is the p-dimensional boundary of the (p + 1)-dimensional region T. Goursat also used differential forms to state the Poincaré lemma and its converse, namely, that if is a p-form, then if and only if there is a (p − 1)-form with.

However Goursat did not notice that the "only if" part of the result depends on the domain of and is not true in general.

Works

More photos

• book

  • A Course in Mathematical Analysis Volume 3: Variation of Solutions; Partial Differential Equations of the Second Order (Dover Books on Mathematics) by Edouard Goursat (2006-01-27)

Membership

French Academy of Sciences.