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Sample program for the

Master in Applied Mathematics with
concentration in Dynamical Systems
Major Code: 17031, SIMS Code: 776316


Program:

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 31 credits (15 units of core courses + 12 units of electives + 3 units of Thesis/Project + 1 unit of seminar).

Year 1:

Fall - Year 1:

  • MATH-537 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.

  • MATH-538 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 sciences.


  • MATH-636 Mathematical Modeling1
    Prerequisites: Mathematics 254 and 337 or Mathematics 342A and 342B or Engineering 280.
    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 Mathematics 536.)

Spring - Year 1:
  • MATH-531 Partial Differential Equations1
     Prerequisites: Mathematics 252 and 337.
    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, Bessel functions.

  • MATH-635 Pattern Formation2
     Prerequisites: Mathematics 337 or 531 and Mathematics 254 or 342A, 342B; or consent by instructor.
    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.

  • MATH-638 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 and engineering.

Year 2:

Fall - Year 2:

  • MATH-639 Nonlinear Waves2
    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.

  • MATH-693A 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.

  • MATH-797 Research3
    Prerequisites: six units of graduate level mathematics.
    Research in the area of Dynamical Systems. Maximum six units applicable to a master's degree.

  • MATH-7804 Seminar in Communicating Mathematical Research (1 unit)
    Prerequisites: Consent of instructor.
    An intensive study in advanced mathematics.
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.


1 core courses
2 special topics in Dynamical Systems. These courses are offered depending on demand and resources (typically one per year).
3 research/thesis. Students work on a research project under close supervision of a member of the Dynamical Systems group.
4 the Math-780 seminar, 1 unit, can be taken during any semester. However, we strongly encourage students to attend seminars/talks all throughout the degree. Students work on a research project under close supervision of a member of the Dynamical Systems group.

 

Maintained by Ricardo Carretero
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