It is my belief that a first course in differential and integral calculus in one real variable is one of
the most important basic learning experiences for science and engineering students. For most of them this
will be where they not only learn the basics, but understand the pillars around which their topics of choice
are built. It is also an opportunity for them to learn that the process by which things are achieved
is of fundamental importance.
To achieve this, I focus on the proofs of the main results and how these reflect in the different techniques
they will be applying. I also emphasise the historical perspective, in particular to pass on the idea that
there are pre-calculus (more empirical) and post-calculus (predictive, up to a point) eras.
I have supervised undergraduate and graduate students in analysis, with an emphasis on spectral theory of partial differential operators and their interactions with geometry and number theory. My current interests include spectral geometry, spectral determinants, etc.