Providing a unified treatment of the subject, this text addresses modelling, qualitative analysis and simulation of real physical systems using ordinary differential equations. The scientific computational aspects are presented using the computer program, Mathematica.

Part 1 Mathematical methods for differential equations: models and differential equations; models and mathematical problems; stability and perturbation methods. Part 2 Mathematical methods of classical mechanics: Newtonian dynamics; rigid body dynamics; energy methods and Langragian mechanics. Part 3 Bifurcations chaotic dynamics, stochastic models, and discretization of continuous models: deterministic and stochastic models in applied sciences; stability bifurcations and chaotic dynamics; discrete models of continuous systems. Appendices: numerical methods for ordinary differential equations; kinematics, applied forces, momentum and mechanical energy; scientific programs.