Extensions of the Mean Value Theorem on the Real Line and the Complex Plane
MetadataShow full item record
The goal of this SIP is to first analyze just a few of the many extensions to the Mean Value Theorem that have been proven in recent decades. This analysis follows a common structure that starts with stating each theorem and, with the help of the original documents, prove them in a detailed format. The proofs presented are in much greater detail than the original mathematicians' own work in order for the steps to be understandable to a wider audience including students who have only completed up to Calculus 2. The outline of most of these theorems is concluded with a real-world example of the given theorem. One of the extensions mentioned in the real domain is then applied in the complex domain where a similar guideline is followed. Once the complex domain is introduced throughly, the conclusion of this SIP will then begin to apply some critical thinking towards the complex world in the hopes of better understanding it as a whole.