James Meiss has published 124 refereed articles and four books. His research is on Hamiltonian, symplectic and volume preserving dynamics, the transition to chaos, the theory of transport, and computational topology. Problems studied include the break-up of invariant tori in conservative systems, the structure of tangles in stable and unstable manifolds, transport in a dynamical system through a complex mixture of regular and chaotic regions, quantifying and optimizing mixing in laminar, time-dependent fluids, and categorizing the topological properties of simplicial complexes approximating the invariant sets and motion of a dynamical system.
dynamical systems, Hamiltonian and Volume preserving dynamics, transition to chaos, transport and mixing, piecewise smooth dynamics and bifurcations, nonautonomous dynamics, computational topology
APPM 3010 - Chaos in Dynamical Systems
Introduces undergraduate students to chaotic dynamical systems. Topics include smooth and discrete dynamical systems, bifurcation theory, chaotic attractors, fractals, Lyapunov exponents, synchronization and networks of dynamical systems. Applications to engineering, biology and physics will be discussed.
APPM 3310 - Matrix Methods and Applications
Introduces linear algebra and matrices with an emphasis on applications, including methods to solve systems of linear algebraic and linear ordinary differential equations. Discusses vector space concepts, decomposition theorems, and eigenvalue problems. Degree credit not granted for this course and MATH 2130 and MATH 2135.
APPM 4440 - Undergraduate Applied Analysis 1
Provides a rigorous treatment of topics covered in Calculus 1 and 2. Topics include convergent sequences; continuous functions; differentiable functions; Darboux sums, Riemann sums, and integration; Taylor and power series and sequences of functions.
APPM 4450 - Undergraduate Applied Analysis 2
Spring 2018 / Spring 2019 / Spring 2021
Continuation of APPM 4440. Study of multidimensional analysis including n-dimensional Euclidean space, continuity and uniform continuity of functions of several variables, differentiation, linear and nonlinear approximation, inverse function and implicit function theorems, and a short introduction to metric spaces.
APPM 5460 - Methods in Applied Mathematics: Dynamical Systems and Differential Equations
Spring 2018 / Fall 2019 / Fall 2020
Introduces the theory and applications of dynamical systems through solutions to differential equations. Covers existence and uniqueness theory, local stability properties, qualitative analysis, global phase portraits, perturbation theory and bifurcation theory. Special topics may include Melnikov methods, averaging methods, bifurcations to chaos and Hamiltonian systems. Department enforced prerequisites: APPM 2360 and APPM 3310 and APPM 4440.