With beginnings in the formulation of calculus, Mathematical Analysis uses the concepts of limits and convergence to study numbers and functions in various metric spaces.

Research, Analysis

Partial Differential Equations

PDEs are used to investigate a wide variety of physical pheomena; for example minimal surfaces, as shown in the figure. Other important applications include temperature distributions inside an object, electrostatic potentials for electromagnetic fields, population distributions of species, capillary surfaces and much more.

(Acker, Jin, Lancaster)

Free Boundary Problems

Problems in differential equations in which a certain boundary is unknown and must be determined as part of the solution are known as free boundary problems. They arise in the study of physical phenomena such as waves, wakes, jets, bubbles, fluid flows in porous media, phase transition (melting and freezing) and capillary surfaces. Research work in free boundary problems at WSU varies from theoretical analysis to the development of computational algorithms for specific problems. An example of the latter is the determination of the shape of a drop of one fluid floating in equilibrium on top of another fluid as shown in the figure.

(Acker, Elcrat, Lancaster)

Several Complex Variables

Description

(Fridman, Ho, D.Ma)

Dynamical Systems

Description

(Wolf)