The term differential-algebraic equation was coined to comprise
differential equations with constraints (differential equations on
manifolds) and singular implicit differential equations. Such problems
arise in a variety of applications, e.g. constrained mechanical systems,
fluid dynamics, chemical reaction kinetics, simulation of electrical
networks, and control engineering. From a more theoretical viewpoint,
the study of differential-algebraic problems gives insight into the
behaviour of numerical methods for stiff ordinary differential
equations. These lecture notes provide a self-contained and
comprehensive treatment of the numerical solution of
differential-algebraic systems using Runge-Kutta methods, and also
extrapolation methods. Readers are expected to have a background in the
numerical treatment of ordinary differential equations. The subject is
treated in its various aspects ranging from the theory through the
analysis to implementation and applications.