Sample program for the
Master in Applied Mathematics
concentration in Dynamical Systems
MS code: 776316
This sample program is intended to give
an idea on the timing of different courses.
Students enrolled in the Dynamical Systems program are
required to complete a total of 30 credits (15 units of
core courses + 12 units of electives + 3 units of Thesis/Project).
Fall - Year 1:
Ordinary Differential Equations1
Prerequisite: Mathematics 337.
Theory of ordinary differential equations: existence
and uniqueness, dependence on initial conditions and
parameters, linear systems, stability and asymptotic
behavior, plane autonomous systems, series solutions
at regular singular points.
Dynamical Systems & Chaos I1
Prerequisites: Mathematics 252 and 254.
Phase space analysis, equilibria and
stability in one and two dimensions, limit cycles, Floquet
theory, Poincaré maps, one and two dimensional
maps, chaos, period doubling, chaotic attractors. Applications
in biology, chemistry, physics, engineering and other
Prerequisites: Mathematics 254 and
337 or Mathematics 342A and 342B or Engineering
Advanced models from the physical, natural and social
sciences. Population dynamics, mechanical vibrations,
planetary motion, wave propagation, traffic flow.
Phase plane analysis, Inverse problems, fitting
a model to experimental data. (Formerly numbered
Spring - Year 1:
Partial Differential Equations1
Prerequisites: Mathematics 252 and
Boundary value problems for heat and wave equations:
eigenfunction expansions, Sturm-Liouville theory and
Fourier series. D'Alembert's solution to wave equation;
characteristics. Laplace's equation, maximum principles,
Prerequisites: Mathematics 337 or 531 and Mathematics 254 or 342A, 342B; or consent
Linear stability, marginal stability curves, classification.
One dimensional patterns, bifurcations. Two dimensional
patterns, square and hexagonal patterns, spirals, defects.
Diffusion driven instability, Turing patterns. Spatio-temporal
chaos. Applications in biology, chemistry, and physics.
Dynamical Systems & Chaos II1
Prerequisites: Mathematics 538 or 337;
or consent of instructor.
Nonlinear systems of differential equations,
Potential fields, periodic solutions, Lyapunov functions.
Chaos in differential equations, Lyapunov exponents,
chaotic attractors, Poincaré maps. Lorenz and
Rossler attractors, forced oscillators, Chua's circuit.
Stable manifolds, bifurcations. Applications in science
Fall - Year 2:
Prerequisites: Mathematics 531 or 537; or consent by instructor.
Linear waves, dissipation, dispersion. Conservation
laws. Water waves. KdV equation, solitary waves,
cnoidal waves. Scattering and inverse scattering.
Perturbation theory. Nonlinear Schroedinger equation,
dark and bright solitons, vortex solutions.
Variational techniques, modulational instability, stability.
Advanced Numerical Analysis
Prerequisites: Mathematics 524
and 542 or 543
Numerical optimization, Newton s methods for nonlinear
equations and unconstrained minimization. Global
methods, nonlinear least squares, integral equations.
Prerequisites: six units of graduate
Research in the area of Dynamical Systems. Maximum
six units applicable to a master's degree.
Spring - Year 2:
MATH-799A Thesis or Project3
Prerequisites: An officially appointed
thesis committee and advancement to candidacy.
Preparation of a project or thesis in the field
of Dynamical Systems for the master's degree.
topics in Dynamical Systems. These courses are offered depending
on demand and resources (typically one per year).
Students work on a research project under close supervision
of a member of the Dynamical Systems group.
Ricardo Carretero Gonzalez
Antonio Palacios Peter Blomgren Joe Mahaffy Diana Verzi Chris Curtis San Diego
San Diego State University SDSU California West coast MS master
masters PhD doctorate doctoral graduate undergraduate concentration
emphasis applied mathematics chaos chaotic fractal fractals dynamics
dynamical systems nonlinear nonlinear dynamical systems nonlinear
dynamics NLDS model modeling modelling publication publications
research preprints analysis adaptivity aggregation bifurcation
bifurcations bioloby blowup blow up blow-up bose bose-einstein
breather breathers CML CMLs condensates coupled map lattices delay
differential determinism deterministic differential einstein embedding
equation equations fluidization fluidized GPE heteroclinic homoclinic
ILM ILMs image restoration intrinsic localized modes lattices
manifold map maps math mathematical bioloby metastability moving
mesh NLS nonlinear waves numerics numerical ODE ODEs orbit orbits
pattern patterns PDE PDEs POD prediction proper orthogonal decomposition
reconstruction soliton solitons spatio temporal stable stochastic
studies study systems tangle temporal time series unstable