Laws of various types are discovered and have lead us to great understanding of the world. Many of these governing laws, especially the ones in physical sciences, are described by mathematical equations. Dr. Li's research is focused on the analysis of the solutions to these equations for better understanding and further applications in the related field. He is mainly focused on nonlinear Partial Differential Equations of elliptic, parabolic, or transport types with special emphasize on equations modeling incompressible fluid.
Analysis of solutions to nonlinear Partial Differential Equations of elliptic, parabolic, or transport types with special emphasize on equations form geometric analysis and from the study of incompressible fluid
APPM 2360 - Introduction to Differential Equations with Linear Algebra
Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Credit not granted for this course and both MATH 2130 and MATH 3430.
APPM 6470 - Advanced Partial Differential Equations
Continuation of APPM 5470. Advanced study of the properties and solutions of elliptic, parabolic, and hyperbolic partial differential equations. Topics include the study of Sobolev spaces and variational methods as they relate to PDEs, and other topics as time permits. Department enforced prerequisite: APPM 5470.