Example courses of study in 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 617 (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 570 (Intermediate Dynamics) be taken as soon as possible; otherwise it is not necessary. T&AM 578 (Nonlinear Dynamics and Chaos) is recommended as an introduction, regardless of which area the person chooses to emphasize. The three courses T&AM 671 (Advanced Dynamics), T&AM 675 (Nonlinear Vibrations), and Math 717 (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 671 and T&AM 675 are taken before Math 717. It is not required, bu much of Math 717 assumes familiarity with concepts covered in the other two courses. In addition, CS 621 (Matrix Computations) and especially CS 624 (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--TAM 578, Math 617, Math 611 (Analysis), Math 631 (Algebra)
- year 1, spring semester--(T&AM 671), Math 612 (Analysis)
- year 2, fall semester--T&AM 675, CS621, ORIE 651 (Probability)
- year 2, spring semester--T&AM 671, T&AM 613, CS 624
- year 3, fall semester--Math 717
- year 3, spring semester--(CS 624)
Applied emphasis:
- year 1, fall semester--T&AM 570, T&AM 578, Math 611 (Analysis), Math 631 (Algebra)
- year 1, spring semester--(T&AM 671)
- year 2, fall semester--Math 617, T&AM 675, Biometry 662 (Mathematical Ecology)
- year 2, spring semester--T&AM 671, T&AM 613, (CS 624)
- year 3, fall semester--Math 717, (T&AM 675), CS 621
- year 3, spring semester--CS 624
Dynamical Systems and Related Courses
- Math 617--Dynamical Systems
- Math 618--Ergodic Theory
- Math 717--Applied Dynamical Systems
- T&AM 570--Intermediate Dynamics
- T&AM 578--Nonlinear Dynamics and Chaos
- T&AM 610, 611, 612--Mathematical methods of Physics
- T&AM 613--Asymptotics and Perturbation Theory
- T&AM 671--Advanced Dynamics ***
- T&AM 675--Nonlinear Vibrations ***
- CS 621--Matrix Computations
- CS 624--Numerical Solutions of Differential Equations ***
Other related courses:
- Math 652--Differential Manifolds
- T&AM 672-673--Celestial Mechanics
- Cheme 753--Analysis of Nonlinear Systems: Stability, Bifurcation, and Continuation
- Btry 662--Mathematical Ecology
- Physics 680--Computational Physics
- Ele E 522--Nonlinear Systems: Analysis, Stability, Control, and Applications
*** offered alternate years