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APPLIED DYNAMICAL SYSTEMS, CHAOS AND MODELING

MATH 415
과목 설명

An introduction to nonlinear dynamical systems including stability, bifurcations and chaos. The course will give underlying mathematical ideas, but emphasize applications from many scientific fields.

선수과목

MATH 376 , (MATH 234 and MATH 319 ), (MATH 234 and MATH 320 ), (MATH 234 and MATH 340 ), (MATH 234 and MATH 341 ) or (MATH 234 and MATH 375 ) or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) program

충족 요건
학점

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미보고

평점
3.23

-1.22% 과거 데이터 대비

수료율
95%

-0.09% 과거 데이터 대비

A 비율
37.5%

-11.67% 과거 데이터 대비

학급 규모
40

33.33% 과거 데이터 대비

Cumulative Grade Distribution

강사 (2026 Summr)

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유사 과목

DYNAMICAL SYSTEMS

MATH 807

Treats the qualitative behavior of continuous and discrete dynamical systems, including Hamiltonian systems of differential equations. Typical topics include periodic and almost periodic solutions, the fixed point theorem of Poincare and Birkhoff, invariant curves and KAM theory, celestial mechanics, and chaotic behavior.

ORDINARY DIFFERENTIAL EQUATIONS

MATH 716

Existence, uniqueness, and continuous dependence theorems, linear systems, stability, singular points, and boundary value problems. Qualitative behavior of nonlinear equations, stability, Lyapunov functions, invariant manifolds, bifurcation theory, periodic orbits, and connecting orbits.

ORDINARY DIFFERENTIAL EQUATIONS

MATH 519

Provides a rigorous introduction to ordinary differential equations and dynamical systems. Intended for math majors and advanced (or graduate) students in other disciplines.

NONLINEAR SYSTEMS

ECE 817

Modelling nonlinear systems, linearization, equilibria, solution concepts, phase plane analysis, stability concepts, Lyapunov methods, oscillations, vector space methods, control system nonlinearities and design. Selected topics from the following: input-output methods, switching and variable structure systems, feedback linearization, and Lyapunov robustness. Knowledge of linear systems [such asE C E 717] strongly encouraged.

DATA-DRIVEN DYNAMICAL SYSTEMS, STOCHASTIC MODELING AND PREDICTION

MATH 616

An introduction to data-driven dynamical systems, including mathematical theory, methodology, numerical algorithms, applications and the use of a programming language to solve related coding problems. Topics include stochastic toolkits for dynamical systems and data science, linear Gaussian processes, nonlinear stochastic systems, elementary stochastic differential equations, data assimilation, parameter estimation, forecasting and prediction.