A complete walkthrough of the UNISA APM2614 syllabus — discrete and continuous dynamical systems, difference equations and cobweb analysis, linear systems solved with eigenvalues, singular (fixed) points and phase-plane analysis, stability and the trace–determinant plane, Lyapunov functions and limit cycles, and controllability & observability of linear control systems. Calculator-free, with AI quizzes, AI-marked written practice, and worked examples.