As long as algebra and geometry proceeded along separate paths, their
advance was slow and their applications limited. But when these sciences
joined company they drew from each other fresh vitality and
thenceforward marched on at rapid pace towards perfection Joseph L.
Lagrange The theory of differential equations is one of the largest elds
within mathematics and probably most graduates in mathematics have
attended at least one course on differentialequations. But
differentialequationsare also offundamentalimportance in most applied
sciences; whenever a continuous process is modelled mathem- ically,
chances are high that differential equations appear. So it does not
surprise that many textbooks exist on both ordinary and partial
differential equations. But the huge majority of these books makes an
implicit assumption on the structure of the equations: either one deals
with scalar equations or with normal systems, i. e. with systems in
Cauchy-Kovalevskaya form. The main topic of this book is what happens,
if this popular assumption is dropped. This is not just an academic
exercise; non-normal systems are ubiquitous in - plications. Classical
examples include the incompressible Navier-Stokes equations of uid
dynamics, Maxwell's equations of electrodynamics, the Yang-Mills eq-
tions of the fundamental gauge theories in modern particle physics or
Einstein's equations of general relativity. But also the simulation and
control of multibody systems, electrical circuits or chemical reactions
lead to non-normal systems of - dinary differential equations, often
called differential algebraic equations. In fact, most of the
differentialequationsnowadaysencounteredby engineersand scientists are
probably not normal.
