## Definitions

- Equivalence relation
- Strong Equivalence of matrix pairs
- Regularity of a matrix pair
- Nilpotent matrix, Index of Nilpotency
- Index of a matrix pair
- (global) equivalence of pairs of matrix functions
- (local) equivalence of pairs of matrix functions
- strangeness index

## Introduction

- examples of DAEs
- application areas

## Basic Concepts

- what is a solution to a DAE?
- what are generally necessary conditions for the existence of a solution?

## Linear DAEs with constant coefficients

- Kronecker canonical form
- Kronecker form for regular matrix pairs
- Existence and representation of solutions

## Linear DAEs with time varying coefficients

- examples
- quantities
`a`

, `d`

, `s`

, (`u`

, `v`

)
- quantities
`r_i`

, `a_i`

, `s_i`

- derivative arrays

## Numerical Integration of DAEs

- RKM
- how to apply RKM for DAEs
- constant coefficients
- stiffly implicit methods
- nonlinear DAEs
- application examples
- BDF methods

## Index Reduction