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 
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}