**1. Introduction and Prerequisites** basics of ODEs, including equilibria, periodic solutions, stability, simulation; maps and stability of fixed points; fundamental numerical methods
**2. Basic Nonlinear Phenomena** bifurcations

**3. Applications and Extensions** delay differential equations; nonsmooth dynamics; DAEs; nerve impulses; waves and pattern formation; deterministic risk

**4. Principles of Continuation** homotopy, predictor-corrector methods, step control

**5. Calculation of the Branching Behavior of Nonlinear Equations** calculating stability; bifurcation test functions; calculating bifurcation points; branch switching

**6. Calculating Branching Behavior of Boundary-Value Problems** numerical bifurcation for ODE boundary-value problems

**7. Stability of Periodic Solutions** monodromy matrix, Poincare map; period doubling; calculating bifurcation behavior

**8. Qualitative Instruments** normal forms; elementary catastrophes; center manifolds

**9. Chaos** attractors; routes to chaos; fractal dimension; control of chaos; Liapunov exponents; power spectra

**Appendices** basic background material