With Edouard Goursat, he names a theorem which states that the integral of a complex-valued function on a closed contour in a simply-connected domain 
With Edouard Goursat, he names a theorem which states that the integral of a complex-valued function on a closed contour in a simply-connected domain is zero. A generalization of his eponymous integral formula is used to define the coefficients of the terms in a Laurent series. With Bernhard Riemann, he is the namesake of two partial differential equations that are necessary and sufficient conditions to prove that a function is analytic. He developed a theory of elasticity that related stress to strain by a 6 by 6 tensor known as the stiffness matrix, effectively generalizing Hooke's law to three dimensions. FTP, name this French mathematician who, along with Hermann Schwarz, lends his name to a central inequality of linear algebra.
With Edouard Goursat, he names a theorem which states that the integral of a complex-valued function on a closed contour in a simply-connected domain is zero.
Augustin Louis {Cauchy}