  The field of partial differential equations (PDEs) is vast in size and
diversity. The basic reason for this is that essentially all fundamental laws
of physics are formulated in terms of PDEs. In addition, approximations to
these fundamental laws, that form a patchwork of mathematical models covering
the range from the smallest to the largest observable space-time scales, are
also formulated in terms of PDEs. The diverse applications of PDEs in science
and technology testify to the flexibility and expressiveness of the language of
PDEs, but it also makes it a hard topic to teach right. Exactly because of the
diversity of applications, there are just so many different points of view when
it comes to PDEs. These lecture notes view the subject through the lens of
applied mathematics. From this point of view, the physical context for basic
equations like the heat equation, the wave equation and the Laplace equation
are introduced early on, and the focus of the lecture notes are on methods,
rather than precise mathematical definitions and proofs. With respect to
methods, both analytical and numerical approaches are discussed.
  These lecture notes has been succesfully used as the text for a master class
in partial differential equations for several years. The students attending
this class are assumed to have previously attended a standard beginners class
in ordinary differential equations and a standard beginners class in numerical
methods. It is also assumed that they are familiar with programming at the
level of a beginners class in informatics at the university level.
