Four Lectures on Differential-Algebraic Equations

Differential-algebraic equations (DAEs) arise in a variety of applications. Therefore their analysis and numerical treatment plays an important role in modern mathematics. This paper gives an introduction to the topic of DAEs. Examples of DAEs are considered showing their importance for practical problems. Several well known index concepts are introduced. In the context of the tractability index existence and uniqueness of solutions for low index linear DAEs is proved. Numerical methods applied to these equations are studied. Mathematics Subject Classification: 34A09, 65L80