A layer framework to investigate student understanding and application of the existence and uniqueness theorems of differential equations.

The focus of this paper is on student interpretation and usage of the existence and uniqueness theorems for first-order ordinary differential equations. The inherent structure of the theorems is made explicit by the introduction of a framework of layers concepts-conditions-connectives-conclusions, and we discuss the manners in which students' understanding of these layers construct their perception of the theorems as a whole. [ABSTRACT FROM AUTHOR]