# Colloquium, Friday October 6: James Cook, Liberty University

Join us on Friday at 3 in 103A Walker Hall!

**On the application of abstract algebra to the solution of differential equations**

What happens to calculus when we replace real numbers with a commutative, real, associative unital algebra A?

Dr. Cook will discuss how differential and integral calculus naturally generalizes in this environment. He will then discuss the theory of differential equations over A: The usual theory of linear ODEs naturally transfers to the A-Calculus; however, the existence of zero-divisors produces novel solutions.

An algebra extension can be used to construct the solution set for any constant coefficient A-ODE of order n. Dr. Cook will conclude the talk by showing how the extension technique can be applied to solve every type of real constant coefficient n-th order ODE.

## CONTACT

**Mathematical Sciences**

342 Walker Hall

121 Bodenheimer Dr

Boone, NC 28608

828-262-3050

828-265-8617 fax

**Department Chairperson**

Dr. Eric Marland

marlandes@appstate.edu

**Assistant Chairperson**

Dr. Rick Klima

klimare@appstate.edu