MA619
Variational and Geometric Methods in Applied Mathematics
0.5 Credit

An introduction to the modern, coordinate-free, formulation of Lagrangian and Hamiltonian mechanics. This formulation provides a unifying framework for many seemingly disparate physical systems, such as N-particle systems, rigid bodies, fluids and other continua, and quantum systems. Topics comprise variational principles, Lagrangian and Hamiltonian dynamics, canonical transformations, Hamilton-Jacobi equations and control, symmetry, Noether's theorem and reduction, integrability, Poisson structures, Poisson brackets, and constrained systems. Applications may include N-particle problems, quantum models, shallow-water and wave dynamics, rigid bodies.

Additional Course Information
Prerequisites
One undergraduate course in differential equations, or by permission of the instructor.
Notes
It is recommended that students take MA660 - Dynamical Systems before MA619 - Variational and Geometric Methods in Applied Mathematics.