Harmonic oscillators. Conservative force fields. Central force fields. Linear systems with constant coefficients and real and complex eigenvalues. Exponentials of operators. Canonical forms of operators. Sinks and sources. Hyperbolic flows. The fundamental theorem. Existence and uniqueness. Continuity of solutions. Stability. Liapunov functions. Gradient systems. The Poincaré-Bendixson theorem. Periodic attractors. Classical mechanics.