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Master in Applied Mathematics
with
concentration in Dynamical Systems
Major Code: 17031, SIMS Code: 776316
Program:
Students enrolled in the Dynamical Systems
program are required to complete a total of 31 credits
broken down as follows: A) 18 units of core
courses (inc. 6 units of research/thesis)
+ B) 12 units of electives
+ C) 1 unit of seminars
A.
Core courses -- 18 units:
(3 units each)
- MATH-538
Dynamical Systems & Chaos I
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 Modeling
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.)
- MATH-638
Dynamical Systems & Chaos II
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.
- MATH-693A Unconstraint Numerical Optimization
or
MATH-693B Numerical Solutions to Partial Differential Equations
M-693A: Prerequisites: M-524 and 541 with a grade of C (2.0) or better in each course.
Numerical optimization: Newton, Truncated-Newton, and QuasiNewton
methods for unconstrained optimization; with applications
to nonlinear least squares, orthogonal distance regression, and
nonlinear equations.
M-693B: Prerequisites: M-531 and 541 with a grade of C (2.0) or better in each course.
Methods for hyperbolic, parabolic, and elliptic partial differential
equations: consistency, stability, convergence.
- MATH-797 Research
Independent research supervised by one of our faculty.
This research will lead towards your thesis work (M-799A).
- MATH-799A Thesis or Project
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.
B. Electives
-- 12 units:
The 12 units of electives are
to be chosen with the approval of the graduate adviser.
Depending on demand and resources, Special topics
in Dynamical Systems might be offered periodically
(one per year).
Sample
of possible Special topics in Dynamical Systems:
(3 units each)
(offering of these courses depending on demand
and resources)
-
M-639 Nonlinear Waves:
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.
Prerequisites: Mathematics 531 or 537; or consent by instructor.
-
M-635 Pattern Formation:
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.
Prerequisites: Mathematics 337 or 531 and Mathematics 254 or 342A, 342B; or consent
by instructor.
Other
recommended electives for the remaining units:
(3 units each)
(other courses, even
in other departments, may be approved by adviser)
Introduction to Numerical Analysis and Computing
- MATH-542
Introduction to Numerical Solutions of Differential
Equations
- MATH-537/531 Ordinary/Partial Differential Equations
- MATH-543 Numerical Matrix Analysis
- MATH-668 Applied Fourier Analysis
- CS-553: Neural Networks
- PHYS-580 Computational Physics
- PHYS-585 Computer Simulations in the Physical Sciences
- PHYS-608 Classical Mechanics
C. Seminar in Communicating Mathematical Research
-- 1 unit:
Students must formally enroll in, at least, one unit
of Math-780 during their program.
However, we strongly encourage
students to attend seminars/talks all throughout the degree.
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
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