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We will introduce stochastic differential equations, which are ordinary differential equations with a random component. We could use this random component in many manners, one in particular is modeling an error term. So you could think of SDE (stochastic differential equations) as an ode (ordinary differential equation) with a built in error term. This lecture will develop what is called stochastic calculus which will be used to solve some SDEs. We will continue this discussion next spring to include numerical solutions to SDEs with many examples.
Biographical Note:Professor Isaac Klapper is an expert in fluid dynamics and the mathematical modeling of the various aspects of biofilm formation, evolution and its interactions with its environment. He is the author of numerous publications and the receiver of several grant awards. He received his A.B. in Mathematics from Harvard University in 1986 and his PhD in Applied Mathematics from the Courant Institute, New York University (NYU) in 1991. He was an NSF postdoctoral fellow at the University of Arizona and a visiting assistant professor at UCLA in the Departments of Applied Mathematics. He served as a tenure-track and tenured faculty and rose to the rank of Full Professor at Montana State University where he was also affiliated with the Center of Biofilm Engineering (CBE) at Montana State. In 2012 he moved to Temple University with the appointment of Full Professor, Department of Mathematics with secondary appointment in the Department of Biology.
Meredith Hegg is a Preceptor in Mathematics at Harvard University. She obtained her PhD in Applied Mathematics at Temple University in 2012; her thesis title was "Exact Relations for Elasticity Tensors of Fiber-Reinforced Composites" and her thesis advisor was Dr. Yury Grabovsky, Temple University. Her thesis research was on exact relations in composite materials. Exact relations describe material properties that are maintained during the construction of composites. The theory of exact relations utilizes a non-linear transformation that sends exact relations to subspaces with algebraic properties. Ideas from representation theory are then used to find all exact relations. Her work focuses on elasticity in fiber-reinforced composites. She also has an additional project modeling weather fronts using numerical simulation data. 2b1af7f3a8