This volume provides an introduction to the analytical and numerical aspects of partial
differential equations (PDEs). It unifies an analytical and computational approach for these
the qualitative behaviour of solutions being established using classical concepts: maximum
principles and energy methods. Notable inclusions are the treatment of irregularly shaped
boundaries polar coordinates and the use of flux-limiters when approximating hyperbolic
conservation laws. The numerical analysis of difference schemes is rigorously developed using
discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of
a chapter containing projects intended for either individual or group study that cover a
range of topics such as parabolic smoothing travelling waves isospectral matrices and the
approximation of multidimensional advection-diffusion problems.The underlying theory is
illustrated by numerous examples and there are around 300 exercises designed to promote and
test understanding. They are starred according to level of difficulty. Solutions to
odd-numbered exercises are available to all readers while even-numbered solutions are available
to authorised instructors.Written in an informal yet rigorous style Essential Partial
Differential Equations is designed for mathematics undergraduates in their final or penultimate
year of university study but will be equally useful for students following other scientific
and engineering disciplines in which PDEs are of practical importance. The only prerequisite is
a familiarity with the basic concepts of calculus and linear algebra.
