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Dynamical systems

These course sequence assume that the student will minor in Theoretical and Applied Mechanics (T&AM) since many dynamical systems courses are taught in that department. Other minors are possible, including several other engineering fields (such as Mechanical and Aerospace Engineering) and sciences (such as Biometrics).

One can either emphasize the mathematical theory or the applications of it. If one emphasizes the mathematical theory of dynamical systems, it is recommended that Math 6170 (Dynamical Systems) be taken as soon as possible; otherwise it is not necessary. Likewise, if one emphasizes the applications of dynamical systems, it is recommended that T &AM 5700 (Intermediate Dynamics) be taken as soon as possible; otherwise it is not necessary. T&AM 5780 (Nonlinear Dynamics and Chaos) is recommended as an introduction, regardless of which area the person chooses to emphasize. The three courses T&AM 6710 (Advanced Dynamics), T&AM 6750 (Nonlinear Vibrations), and Math 7170 (Applied Dynamical Systems) are all recommended regardless of one's area of emphasis. In addition, it is strongly recommended (though sometimes not possible) that both T&AM 6710 and T&AM 6750 are taken before Math 7170. It is not required, but much of Math 7170 assumes familiarity with concepts covered in the other two courses. In addition, CS 6210 (Matrix Computations) and especially CS 6240 (Num Solns of DE's) are also recommended regardless of one's area of emphasis.

Two possible sequences of course are given below. Courses given in parentheses are the alternative (and possibly less than ideal) semesters to take them; however, since they are only offered in alternate years, it may not be possible to take them in the particular order listed below.

Math emphasis:

  • year 1, fall semester--T&AM 5780, Math 6170, Math 6110 (Analysis), Math 6310 (Algebra)
  • year 1, spring semester--(T&AM 6710), Math 6120 (Analysis)
  • year 2, fall semester--T&AM 6750, CS6210, ORIE 6510 (Probability)
  • year 2, spring semester--T&AM 6710, T&AM 6130, CS 6240
  • year 3, fall semester--Math 7170
  • year 3, spring semester--(CS 6240)

Applied emphasis:

  • year 1, fall semester--T&AM 5700, T&AM 5780, Math 6110 (Analysis), Math 6310 (Algebra)
  • year 1, spring semester--(T&AM 6710)
  • year 2, fall semester--Math 6170, T&AM 6750, BIOEE 4600 (Theoretical Ecology)
  • year 2, spring semester--T&AM 6710, T&AM 6130, (CS 6240)
  • year 3, fall semester--Math 7170, (T&AM 6750), CS 6210
  • year 3, spring semester--CS 6240

Dynamical Systems and Related Courses

  • Math 6170--Dynamical Systems
  • Math 6180--Ergodic Theory
  • Math 7170--Applied Dynamical Systems
  • T&AM 5700--Intermediate Dynamics
  • T&AM 5780--Nonlinear Dynamics and Chaos
  • T&AM 6100, 6110, 6120--Mathematical methods of Physics
  • T&AM 6130--Asymptotics and Perturbation Theory
  • T&AM 6710--Advanced Dynamics ***
  • T&AM 6750--Nonlinear Vibrations ***
  • CS 6210--Matrix Computations
  • CS 6240--Numerical Solutions of Differential Equations ***

Other related courses:

  • Math 6520--Differential Manifolds
  • T&AM 6720-6730--Celestial Mechanics
  • Cheme 7530--Analysis of Nonlinear Systems: Stability, Bifurcation, and Continuation
  • Btry 6620--Mathematical Ecology
  • Physics 7680--Computational Physics
  • ECE 5220--Nonlinear Systems: Analysis, Stability, Control, and Applications

*** offered alternate years