Differential Equations as the Language of Change and Dynamical Systems
Artem introduces differential equations to students of neuroscience, physics, and applied math who need a conceptual bridge from everyday change to formal dynamical systems without getting buried in symbols.
Exponential Growth Model and Numerical Solution of Differential Equations
Students and researchers learning to transform continuous differential equations into discrete computational algorithms, particularly those working with biological or physical systems.
Parameter Estimation and Finite Precision in Dynamical Models
Artem cautions modelers who treat parameters in differential equations—like the growth rate (k)—as known constants rather than quantities that must be inferred from noisy data.
Phase Space, Vector Fields, and the Geometry of Trajectories
Artem introduces phase space to learners who have seen time-series plots but not yet the geometric “all-at-once” view of a system’s dynamics.
Predator–Prey Model and Coupled Differential Equations
Artem builds a classic predator–prey model for learners ready to move from single-variable ODEs to interacting dynamical variables.
Equilibria, Limit Cycles, and Stability in Predator–Prey Systems
Artem uses the predator–prey model to introduce equilibria and limit cycles to students who are beginning to think about stability and long-term behavior of dynamical systems.