Cauchy & Two-Dimensional Mean Value Theorems

by Molly Kruse
Mathematics
Faculty advisor: Dr. Nasser Dastrange

Augustin-Louis Cauchy’s contributions to math were great including his basis for modern complex variable theory and differential equations but were not possible without the beginning work of other mathematicians. We will look specifically at Cauchy’s contributions to the mean value theorem of differential calculus, and the mathematicians work in this area that preceded him. We begin with a brief introduction of Rolle’s Theorem and Lagrange’s Mean Value Theorem. Then, we will show the relationship between Cauchy’s Mean Value and the two theorems. Furthermore, we expand on Cauchy’s Mean Value Theorem for functions in two variables. Additionally, we will present some interesting examples and geometrical illustrations of the Mean Value Theorems to support the proofs.