Explores the dynamics of a simple pendulum and the intriguing Lorenz equations, highlighting sensitivity to initial conditions and the transition to chaos.
Explores the conservation of mechanical energy and stability of equilibrium points in dynamic systems, illustrated with examples like the mathematical pendulum and looping motion.
Explores curve integrals of vector fields, emphasizing energy considerations for motion against or with wind, and introduces unit tangent and unit normal vectors.
Introduces the state-space approach to modeling dynamical systems and its utility for high-speed solution of differential equations and computer algorithms.
Explores error estimation in numerical methods for solving ordinary differential equations, emphasizing the impact of errors on solution accuracy and stability.
